TSTP Solution File: ITP215^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP215^1 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 03:20:24 EDT 2023
% Result : Timeout 299.61s 300.12s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 1.16/1.21 % Problem : ITP215^1 : TPTP v8.1.2. Released v8.1.0.
% 1.16/1.21 % Command : do_cvc5 %s %d
% 1.21/1.43 % Computer : n004.cluster.edu
% 1.21/1.43 % Model : x86_64 x86_64
% 1.21/1.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 1.21/1.43 % Memory : 8042.1875MB
% 1.21/1.43 % OS : Linux 3.10.0-693.el7.x86_64
% 1.21/1.43 % CPULimit : 300
% 1.21/1.43 % WCLimit : 300
% 1.21/1.43 % DateTime : Sun Aug 27 11:05:53 EDT 2023
% 1.21/1.43 % CPUTime :
% 2.39/2.69 %----Proving TH0
% 2.39/2.69 %------------------------------------------------------------------------------
% 2.39/2.69 % File : ITP215^1 : TPTP v8.1.2. Released v8.1.0.
% 2.39/2.69 % Domain : Interactive Theorem Proving
% 2.39/2.69 % Problem : Sledgehammer problem Automation 00192_006252
% 2.39/2.69 % Version : [Des22] axioms.
% 2.39/2.69 % English :
% 2.39/2.69
% 2.39/2.69 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 2.39/2.69 % : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 2.39/2.69 % Source : [Des22]
% 2.39/2.69 % Names : 0027_Automation_00192_006252 [Des22]
% 2.39/2.69
% 2.39/2.69 % Status : Theorem
% 2.39/2.69 % Rating : 1.00 v8.1.0
% 2.39/2.69 % Syntax : Number of formulae : 6335 (3386 unt; 887 typ; 0 def)
% 2.39/2.69 % Number of atoms : 12630 (6409 equ; 2 cnn)
% 2.39/2.69 % Maximal formula atoms : 11 ( 2 avg)
% 2.39/2.69 % Number of connectives : 47430 (1200 ~; 192 |; 645 &;41507 @)
% 2.39/2.69 % ( 0 <=>;3886 =>; 0 <=; 0 <~>)
% 2.39/2.69 % Maximal formula depth : 29 ( 5 avg)
% 2.39/2.69 % Number of types : 90 ( 89 usr)
% 2.39/2.69 % Number of type conns : 2792 (2792 >; 0 *; 0 +; 0 <<)
% 2.39/2.69 % Number of symbols : 802 ( 798 usr; 52 con; 0-6 aty)
% 2.39/2.69 % Number of variables : 12463 ( 619 ^;11736 !; 108 ?;12463 :)
% 2.39/2.69 % SPC : TH0_THM_EQU_NAR
% 2.39/2.69
% 2.39/2.69 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2.39/2.69 % from the van Emde Boas Trees session in the Archive of Formal
% 2.39/2.69 % proofs -
% 2.39/2.69 % www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 2.39/2.69 % 2022-02-17 15:59:58.079
% 2.39/2.69 %------------------------------------------------------------------------------
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% 2.39/2.70 semila4918476307565957903at_nat: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > set_Pr1261947904930325089at_nat > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > $o ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Set__Oset_It__Product____Type__Ounit_J,type,
% 2.39/2.70 semila4423693302617054363t_unit: ( set_Product_unit > set_Product_unit > set_Product_unit ) > set_Product_unit > ( set_Product_unit > set_Product_unit > $o ) > ( set_Product_unit > set_Product_unit > $o ) > $o ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
% 2.39/2.70 sup_su8463660629351352368_int_o: ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_Lattices_Osup__class_Osup_001t__Assertions__Oassn,type,
% 2.39/2.70 sup_sup_assn: assn > assn > assn ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_Lattices_Osup__class_Osup_001t__Int__Oint,type,
% 2.39/2.70 sup_sup_int: int > int > int ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_Lattices_Osup__class_Osup_001t__Nat__Onat,type,
% 2.39/2.70 sup_sup_nat: nat > nat > nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_Lattices_Osup__class_Osup_001t__Rat__Orat,type,
% 2.39/2.70 sup_sup_rat: rat > rat > rat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Int__Oint_J,type,
% 2.39/2.70 sup_sup_set_int: set_int > set_int > set_int ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Nat__Onat_J,type,
% 2.39/2.70 sup_sup_set_nat: set_nat > set_nat > set_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.39/2.70 sup_su6327502436637775413at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Ounit_J,type,
% 2.39/2.70 sup_su793286257634532545t_unit: set_Product_unit > set_Product_unit > set_Product_unit ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_Lattices__Big_Osemilattice__neutr__set_OF_001t__Nat__Onat,type,
% 2.39/2.70 lattic7826324295020591184_F_nat: ( nat > nat > nat ) > nat > set_nat > nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Oall__interval__int,type,
% 2.39/2.70 all_interval_int: ( int > $o ) > int > int > $o ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Oall__interval__nat,type,
% 2.39/2.70 all_interval_nat: ( nat > $o ) > nat > nat > $o ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Oappend_001t__Int__Oint,type,
% 2.39/2.70 append_int: list_int > list_int > list_int ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Oappend_001t__Nat__Onat,type,
% 2.39/2.70 append_nat: list_nat > list_nat > list_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Obind_001t__Int__Oint_001t__Int__Oint,type,
% 2.39/2.70 bind_int_int: list_int > ( int > list_int ) > list_int ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Obind_001t__Int__Oint_001t__Nat__Onat,type,
% 2.39/2.70 bind_int_nat: list_int > ( int > list_nat ) > list_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Obind_001t__Int__Oint_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 2.39/2.70 bind_i4941608653131063484n_assn: list_int > ( int > list_P8527749157015355191n_assn ) > list_P8527749157015355191n_assn ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Obind_001t__Nat__Onat_001t__Int__Oint,type,
% 2.39/2.70 bind_nat_int: list_nat > ( nat > list_int ) > list_int ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Obind_001t__Nat__Onat_001t__Nat__Onat,type,
% 2.39/2.70 bind_nat_nat: list_nat > ( nat > list_nat ) > list_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Obind_001t__Nat__Onat_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 2.39/2.70 bind_n3181571989377952280n_assn: list_nat > ( nat > list_P8527749157015355191n_assn ) > list_P8527749157015355191n_assn ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Obind_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J_001t__Int__Oint,type,
% 2.39/2.70 bind_P8081679045764635286sn_int: list_P8527749157015355191n_assn > ( produc6575502325842934193n_assn > list_int ) > list_int ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Obind_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J_001t__Nat__Onat,type,
% 2.39/2.70 bind_P8084169516273685562sn_nat: list_P8527749157015355191n_assn > ( produc6575502325842934193n_assn > list_nat ) > list_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Obind_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 2.39/2.70 bind_P5664457578022171847n_assn: list_P8527749157015355191n_assn > ( produc6575502325842934193n_assn > list_P8527749157015355191n_assn ) > list_P8527749157015355191n_assn ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Obutlast_001t__Nat__Onat,type,
% 2.39/2.70 butlast_nat: list_nat > list_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Ocoset_001t__Int__Oint,type,
% 2.39/2.70 coset_int: list_int > set_int ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Ocoset_001t__Nat__Onat,type,
% 2.39/2.70 coset_nat: list_nat > set_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Ocoset_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 2.39/2.70 coset_703488708621576356n_assn: list_P8527749157015355191n_assn > set_Pr5949110396991348497n_assn ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Ocoset_001t__Product____Type__Ounit,type,
% 2.39/2.70 coset_Product_unit: list_Product_unit > set_Product_unit ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Ocount__list_001t__Int__Oint,type,
% 2.39/2.70 count_list_int: list_int > int > nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Ocount__list_001t__Nat__Onat,type,
% 2.39/2.70 count_list_nat: list_nat > nat > nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Ocount__list_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 2.39/2.70 count_2530312006313534765n_assn: list_P8527749157015355191n_assn > produc6575502325842934193n_assn > nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Odistinct_001t__Int__Oint,type,
% 2.39/2.70 distinct_int: list_int > $o ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Odistinct_001t__Nat__Onat,type,
% 2.39/2.70 distinct_nat: list_nat > $o ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Odrop_001t__Nat__Onat,type,
% 2.39/2.70 drop_nat: nat > list_nat > list_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Oenumerate_001t__Int__Oint,type,
% 2.39/2.70 enumerate_int: nat > list_int > list_P3521021558325789923at_int ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Oenumerate_001t__Nat__Onat,type,
% 2.39/2.70 enumerate_nat: nat > list_nat > list_P6011104703257516679at_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Oenumerate_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 2.39/2.70 enumer9200277086812776726n_assn: nat > list_P8527749157015355191n_assn > list_P7711101519850957926n_assn ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Ofold_001t__Int__Oint_001t__Int__Oint,type,
% 2.39/2.70 fold_int_int: ( int > int > int ) > list_int > int > int ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Ofold_001t__Nat__Onat_001t__Nat__Onat,type,
% 2.39/2.70 fold_nat_nat: ( nat > nat > nat ) > list_nat > nat > nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Ofoldr_001t__Assertions__Oassn_001t__Assertions__Oassn,type,
% 2.39/2.70 foldr_assn_assn: ( assn > assn > assn ) > list_assn > assn > assn ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Ogen__length_001t__Int__Oint,type,
% 2.39/2.70 gen_length_int: nat > list_int > nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Ogen__length_001t__Nat__Onat,type,
% 2.39/2.70 gen_length_nat: nat > list_nat > nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Ogen__length_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 2.39/2.70 gen_le1182329135810803268n_assn: nat > list_P8527749157015355191n_assn > nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Oinsert_001t__Int__Oint,type,
% 2.39/2.70 insert_int: int > list_int > list_int ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Oinsert_001t__Nat__Onat,type,
% 2.39/2.70 insert_nat: nat > list_nat > list_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Oinsert_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 2.39/2.70 insert3246601298802261197n_assn: produc6575502325842934193n_assn > list_P8527749157015355191n_assn > list_P8527749157015355191n_assn ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Olast_001t__Nat__Onat,type,
% 2.39/2.70 last_nat: list_nat > nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Olinorder__class_Osort__key_001t__Int__Oint_001t__Int__Oint,type,
% 2.39/2.70 linord1735203802627413978nt_int: ( int > int ) > list_int > list_int ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Olinorder__class_Osort__key_001t__Nat__Onat_001t__Nat__Onat,type,
% 2.39/2.70 linord738340561235409698at_nat: ( nat > nat ) > list_nat > list_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Int__Oint,type,
% 2.39/2.70 linord2612477271533052124et_int: set_int > list_int ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Nat__Onat,type,
% 2.39/2.70 linord2614967742042102400et_nat: set_nat > list_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Olist_OCons_001_062_It__Int__Oint_Mt__Nat__Onat_J,type,
% 2.39/2.70 cons_int_nat: ( int > nat ) > list_int_nat > list_int_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Olist_OCons_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.39/2.70 cons_nat_nat: ( nat > nat ) > list_nat_nat > list_nat_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Olist_OCons_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
% 2.39/2.70 cons_P6219271836124797827_nat_o: ( produc3658429121746597890et_nat > $o ) > list_P7985473006766602707_nat_o > list_P7985473006766602707_nat_o ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Olist_OCons_001t__Assertions__Oassn,type,
% 2.39/2.70 cons_assn: assn > list_assn > list_assn ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Olist_OCons_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J,type,
% 2.39/2.70 cons_h4161061858534515843t_unit: heap_e7401611519738050253t_unit > list_h2745205591237434579t_unit > list_h2745205591237434579t_unit ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Olist_OCons_001t__Int__Oint,type,
% 2.39/2.70 cons_int: int > list_int > list_int ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Int__Oint_J,type,
% 2.39/2.70 cons_list_int: list_int > list_list_int > list_list_int ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Nat__Onat_J,type,
% 2.39/2.70 cons_list_nat: list_nat > list_list_nat > list_list_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J_J,type,
% 2.39/2.70 cons_l2423627976422276333n_assn: list_P8527749157015355191n_assn > list_l6351802567095793725n_assn > list_l6351802567095793725n_assn ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 2.39/2.70 cons_nat: nat > list_nat > list_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
% 2.39/2.70 cons_P6329468272379687876et_nat: produc2732055786443039994et_nat > list_P362550909693114634et_nat > list_P362550909693114634et_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
% 2.39/2.70 cons_P3419706843779801160et_nat: produc3925858234332021118et_nat > list_P2321686559999237006et_nat > list_P2321686559999237006et_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 2.39/2.70 cons_P2971678138204555879n_assn: produc6575502325842934193n_assn > list_P8527749157015355191n_assn > list_P8527749157015355191n_assn ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
% 2.39/2.70 cons_P2869003950965171916et_nat: produc3658429121746597890et_nat > list_P9062070895058802706et_nat > list_P9062070895058802706et_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 2.39/2.70 cons_P3334398858971670639nt_int: product_prod_int_int > list_P5707943133018811711nt_int > list_P5707943133018811711nt_int ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J,type,
% 2.39/2.70 cons_P7512249878480867347nt_nat: product_prod_int_nat > list_P8198026277950538467nt_nat > list_P8198026277950538467nt_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
% 2.39/2.70 cons_P2335045147070616083at_int: product_prod_nat_int > list_P3521021558325789923at_int > list_P3521021558325789923at_int ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.39/2.70 cons_P6512896166579812791at_nat: product_prod_nat_nat > list_P6011104703257516679at_nat > list_P6011104703257516679at_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Olist_OCons_001t__Set__Oset_It__Nat__Onat_J,type,
% 2.39/2.70 cons_set_nat: set_nat > list_set_nat > list_set_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Olist_ONil_001_062_It__Int__Oint_Mt__Nat__Onat_J,type,
% 2.39/2.70 nil_int_nat: list_int_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Olist_ONil_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.39/2.70 nil_nat_nat: list_nat_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Olist_ONil_001t__Assertions__Oassn,type,
% 2.39/2.70 nil_assn: list_assn ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Olist_ONil_001t__Int__Oint,type,
% 2.39/2.70 nil_int: list_int ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Olist_ONil_001t__List__Olist_It__Int__Oint_J,type,
% 2.39/2.70 nil_list_int: list_list_int ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Olist_ONil_001t__List__Olist_It__Nat__Onat_J,type,
% 2.39/2.70 nil_list_nat: list_list_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Olist_ONil_001t__List__Olist_It__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J_J,type,
% 2.39/2.70 nil_li5476096274760905021n_assn: list_l6351802567095793725n_assn ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 2.39/2.70 nil_nat: list_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Olist_ONil_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 2.39/2.70 nil_Pr5671120429643327159n_assn: list_P8527749157015355191n_assn ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Olist_ONil_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
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% 2.39/2.70 nth_he7452997726511547988t_unit: list_h2745205591237434579t_unit > nat > heap_e7401611519738050253t_unit ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Onth_001t__Int__Oint,type,
% 2.39/2.70 nth_int: list_int > nat > int ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 2.39/2.70 nth_nat: list_nat > nat > nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
% 2.39/2.70 nth_Pr7590663101126261939et_nat: list_P362550909693114634et_nat > nat > produc2732055786443039994et_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
% 2.39/2.70 nth_Pr3610913089060847927et_nat: list_P2321686559999237006et_nat > nat > produc3925858234332021118et_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 2.39/2.70 nth_Pr1769885009046257848n_assn: list_P8527749157015355191n_assn > nat > produc6575502325842934193n_assn ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
% 2.39/2.70 nth_Pr7683458668995092411et_nat: list_P9062070895058802706et_nat > nat > produc3658429121746597890et_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 2.39/2.70 nth_Pr4439495888332055232nt_int: list_P5707943133018811711nt_int > nat > product_prod_int_int ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J,type,
% 2.39/2.70 nth_Pr8617346907841251940nt_nat: list_P8198026277950538467nt_nat > nat > product_prod_int_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
% 2.39/2.70 nth_Pr3440142176431000676at_int: list_P3521021558325789923at_int > nat > product_prod_nat_int ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.39/2.70 nth_Pr7617993195940197384at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Onth_001t__Set__Oset_It__Nat__Onat_J,type,
% 2.39/2.70 nth_set_nat: list_set_nat > nat > set_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Onths_001t__Assertions__Oassn,type,
% 2.39/2.70 nths_assn: list_assn > set_nat > list_assn ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Onths_001t__Int__Oint,type,
% 2.39/2.70 nths_int: list_int > set_nat > list_int ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Onths_001t__Nat__Onat,type,
% 2.39/2.70 nths_nat: list_nat > set_nat > list_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Onths_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 2.39/2.70 nths_P5537322223065504949n_assn: list_P8527749157015355191n_assn > set_nat > list_P8527749157015355191n_assn ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Onull_001t__Int__Oint,type,
% 2.39/2.70 null_int: list_int > $o ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Onull_001t__Nat__Onat,type,
% 2.39/2.70 null_nat: list_nat > $o ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Onull_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 2.39/2.70 null_P7596217980778516671n_assn: list_P8527749157015355191n_assn > $o ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Oproduct_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
% 2.39/2.70 produc7119410244218060998et_nat: list_P7985473006766602707_nat_o > list_P2321686559999237006et_nat > list_P362550909693114634et_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Oproduct_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
% 2.39/2.70 produc2866688925348378442et_nat: list_P7985473006766602707_nat_o > list_P9062070895058802706et_nat > list_P2321686559999237006et_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Oproduct_001t__Assertions__Oassn_001t__Assertions__Oassn,type,
% 2.39/2.70 product_assn_assn: list_assn > list_assn > list_P8527749157015355191n_assn ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Oproduct_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Set__Oset_It__Nat__Onat_J,type,
% 2.39/2.70 produc7481864959766642638et_nat: list_h2745205591237434579t_unit > list_set_nat > list_P9062070895058802706et_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Oproduct_001t__Int__Oint_001t__Int__Oint,type,
% 2.39/2.70 product_int_int: list_int > list_int > list_P5707943133018811711nt_int ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Oproduct_001t__Int__Oint_001t__Nat__Onat,type,
% 2.39/2.70 product_int_nat: list_int > list_nat > list_P8198026277950538467nt_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__Int__Oint,type,
% 2.39/2.70 product_nat_int: list_nat > list_int > list_P3521021558325789923at_int ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__Nat__Onat,type,
% 2.39/2.70 product_nat_nat: list_nat > list_nat > list_P6011104703257516679at_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Oproduct__lists_001t__Int__Oint,type,
% 2.39/2.70 product_lists_int: list_list_int > list_list_int ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Oproduct__lists_001t__Nat__Onat,type,
% 2.39/2.70 product_lists_nat: list_list_nat > list_list_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Oproduct__lists_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 2.39/2.70 produc1566369527784499744n_assn: list_l6351802567095793725n_assn > list_l6351802567095793725n_assn ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Oremdups_001t__Nat__Onat,type,
% 2.39/2.70 remdups_nat: list_nat > list_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Orotate1_001t__Assertions__Oassn,type,
% 2.39/2.70 rotate1_assn: list_assn > list_assn ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Orotate1_001t__Int__Oint,type,
% 2.39/2.70 rotate1_int: list_int > list_int ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Orotate1_001t__Nat__Onat,type,
% 2.39/2.70 rotate1_nat: list_nat > list_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Orotate1_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 2.39/2.70 rotate328796349445179396n_assn: list_P8527749157015355191n_assn > list_P8527749157015355191n_assn ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Osorted__wrt_001t__Int__Oint,type,
% 2.39/2.70 sorted_wrt_int: ( int > int > $o ) > list_int > $o ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Osorted__wrt_001t__Nat__Onat,type,
% 2.39/2.70 sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Osplice_001t__Int__Oint,type,
% 2.39/2.70 splice_int: list_int > list_int > list_int ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Osplice_001t__Nat__Onat,type,
% 2.39/2.70 splice_nat: list_nat > list_nat > list_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Osplice_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 2.39/2.70 splice4588524007259616650n_assn: list_P8527749157015355191n_assn > list_P8527749157015355191n_assn > list_P8527749157015355191n_assn ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Osubseqs_001t__Int__Oint,type,
% 2.39/2.70 subseqs_int: list_int > list_list_int ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Osubseqs_001t__Nat__Onat,type,
% 2.39/2.70 subseqs_nat: list_nat > list_list_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Osubseqs_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 2.39/2.70 subseq184808802919281286n_assn: list_P8527749157015355191n_assn > list_l6351802567095793725n_assn ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Otake_001t__Nat__Onat,type,
% 2.39/2.70 take_nat: nat > list_nat > list_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Oupt,type,
% 2.39/2.70 upt: nat > nat > list_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Oupto,type,
% 2.39/2.70 upto: int > int > list_int ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Oupto__aux,type,
% 2.39/2.70 upto_aux: int > int > list_int > list_int ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Oupto__rel,type,
% 2.39/2.70 upto_rel: product_prod_int_int > product_prod_int_int > $o ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Ozip_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
% 2.39/2.70 zip_Pr8136144321567152340et_nat: list_P7985473006766602707_nat_o > list_P2321686559999237006et_nat > list_P362550909693114634et_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Ozip_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
% 2.39/2.70 zip_Pr7134870689397686104et_nat: list_P7985473006766602707_nat_o > list_P9062070895058802706et_nat > list_P2321686559999237006et_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Ozip_001t__Assertions__Oassn_001t__Assertions__Oassn,type,
% 2.39/2.70 zip_assn_assn: list_assn > list_assn > list_P8527749157015355191n_assn ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Ozip_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Set__Oset_It__Nat__Onat_J,type,
% 2.39/2.70 zip_he6711929980790699996et_nat: list_h2745205591237434579t_unit > list_set_nat > list_P9062070895058802706et_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Ozip_001t__Int__Oint_001t__Int__Oint,type,
% 2.39/2.70 zip_int_int: list_int > list_int > list_P5707943133018811711nt_int ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Ozip_001t__Int__Oint_001t__Nat__Onat,type,
% 2.39/2.70 zip_int_nat: list_int > list_nat > list_P8198026277950538467nt_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Ozip_001t__Int__Oint_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 2.39/2.70 zip_in7098856637274830732n_assn: list_int > list_P8527749157015355191n_assn > list_P1495281457390866698n_assn ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Ozip_001t__Nat__Onat_001t__Int__Oint,type,
% 2.39/2.70 zip_nat_int: list_nat > list_int > list_P3521021558325789923at_int ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Ozip_001t__Nat__Onat_001t__Nat__Onat,type,
% 2.39/2.70 zip_nat_nat: list_nat > list_nat > list_P6011104703257516679at_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Ozip_001t__Nat__Onat_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 2.39/2.70 zip_na5338819973521719528n_assn: list_nat > list_P8527749157015355191n_assn > list_P7711101519850957926n_assn ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Ozip_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J_001t__Int__Oint,type,
% 2.39/2.70 zip_Pr1015554993053626726sn_int: list_P8527749157015355191n_assn > list_int > list_P421884338359569308sn_int ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Ozip_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J_001t__Nat__Onat,type,
% 2.39/2.70 zip_Pr1018045463562677002sn_nat: list_P8527749157015355191n_assn > list_nat > list_P2911967483291296064sn_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_List_Ozip_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 2.39/2.70 zip_Pr8806919808394484215n_assn: list_P8527749157015355191n_assn > list_P8527749157015355191n_assn > list_P28140577958321773n_assn ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_Misc_Olist__collect__set_001t__Assertions__Oassn_001t__Int__Oint,type,
% 2.39/2.70 list_c1842222907148955684sn_int: ( assn > set_int ) > list_assn > set_int ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_Misc_Olist__collect__set_001t__Assertions__Oassn_001t__Nat__Onat,type,
% 2.39/2.70 list_c1844713377658005960sn_nat: ( assn > set_nat ) > list_assn > set_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_Misc_Olist__collect__set_001t__Int__Oint_001t__Int__Oint,type,
% 2.39/2.70 list_c3449203510989861672nt_int: ( int > set_int ) > list_int > set_int ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_Misc_Olist__collect__set_001t__Int__Oint_001t__Nat__Onat,type,
% 2.39/2.70 list_c3451693981498911948nt_nat: ( int > set_nat ) > list_int > set_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_Misc_Olist__collect__set_001t__Nat__Onat_001t__Int__Oint,type,
% 2.39/2.70 list_c2449849799088807116at_int: ( nat > set_int ) > list_nat > set_int ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_Misc_Olist__collect__set_001t__Nat__Onat_001t__Nat__Onat,type,
% 2.39/2.70 list_c2452340269597857392at_nat: ( nat > set_nat ) > list_nat > set_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_Misc_Olist__collect__set_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J_001t__Int__Oint,type,
% 2.39/2.70 list_c6059232572861898639sn_int: ( produc6575502325842934193n_assn > set_int ) > list_P8527749157015355191n_assn > set_int ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_Misc_Olist__collect__set_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J_001t__Nat__Onat,type,
% 2.39/2.70 list_c6061723043370948915sn_nat: ( produc6575502325842934193n_assn > set_nat ) > list_P8527749157015355191n_assn > set_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_Misc_Oslice_001t__Int__Oint,type,
% 2.39/2.70 slice_int: nat > nat > list_int > list_int ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_Misc_Oslice_001t__Nat__Onat,type,
% 2.39/2.70 slice_nat: nat > nat > list_nat > list_nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_Misc_Oslice_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 2.39/2.70 slice_7964966981652229398n_assn: nat > nat > list_P8527749157015355191n_assn > list_P8527749157015355191n_assn ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_Nat_OSuc,type,
% 2.39/2.70 suc: nat > nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 2.39/2.70 semiri1314217659103216013at_int: nat > int ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Rat__Orat,type,
% 2.39/2.70 semiri681578069525770553at_rat: nat > rat ).
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% 2.39/2.70
% 2.39/2.70 thf(sy_c_Product__Type_Oprod_Ofst_001t__Int__Oint_001t__Int__Oint,type,
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% 2.39/2.70
% 2.39/2.70 thf(sy_c_Product__Type_Oprod_Ofst_001t__Int__Oint_001t__Nat__Onat,type,
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% 2.39/2.70
% 2.39/2.70 thf(sy_c_Product__Type_Oprod_Ofst_001t__Nat__Onat_001t__Int__Oint,type,
% 2.39/2.70 product_fst_nat_int: product_prod_nat_int > nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_Product__Type_Oprod_Ofst_001t__Nat__Onat_001t__Nat__Onat,type,
% 2.39/2.70 product_fst_nat_nat: product_prod_nat_nat > nat ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_Product__Type_Oprod_Osnd_001t__Assertions__Oassn_001t__Assertions__Oassn,type,
% 2.39/2.70 produc2051961928117032727n_assn: produc6575502325842934193n_assn > assn ).
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% 2.39/2.70 produc6174133586879617921nteger: produc8923325533196201883nteger > code_integer ).
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% 2.39/2.70
% 2.39/2.70 thf(sy_c_Product__Type_Oprod_Osnd_001t__Int__Oint_001t__Int__Oint,type,
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% 2.39/2.70
% 2.39/2.70 thf(sy_c_Product__Type_Oprod_Osnd_001t__Int__Oint_001t__Nat__Onat,type,
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% 2.39/2.70
% 2.39/2.70 thf(sy_c_Product__Type_Oprod_Osnd_001t__Nat__Onat_001t__Int__Oint,type,
% 2.39/2.70 product_snd_nat_int: product_prod_nat_int > int ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_Product__Type_Oprod_Osnd_001t__Nat__Onat_001t__Nat__Onat,type,
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% 2.39/2.70
% 2.39/2.70 thf(sy_c_Product__Type_Oscomp_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Code____Numeral__Onatural_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
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% 2.39/2.70
% 2.39/2.70 thf(sy_c_Random_Oinc__shift,type,
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% 2.39/2.70
% 2.39/2.70 thf(sy_c_Random_Olog,type,
% 2.39/2.70 log: code_natural > code_natural > code_natural ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_Random_Olog__rel,type,
% 2.39/2.70 log_rel: produc7822875418678951345atural > produc7822875418678951345atural > $o ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_Random_Ominus__shift,type,
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% 2.39/2.70
% 2.39/2.70 thf(sy_c_Random_Onext,type,
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% 2.39/2.70
% 2.39/2.70 thf(sy_c_Random_Orange,type,
% 2.39/2.70 range: code_natural > produc7822875418678951345atural > produc5835291356934675326atural ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_Rat_OAbs__Rat,type,
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% 2.39/2.70
% 2.39/2.70 thf(sy_c_Rat_OFract,type,
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% 2.39/2.70
% 2.39/2.70 thf(sy_c_Rat_OFrct,type,
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% 2.39/2.70
% 2.39/2.70 thf(sy_c_Rat_ORep__Rat,type,
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% 2.39/2.70
% 2.39/2.70 thf(sy_c_Rat_Onormalize,type,
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% 2.39/2.70
% 2.39/2.70 thf(sy_c_Rat_Opcr__rat,type,
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% 2.39/2.70
% 2.39/2.70 thf(sy_c_Rat_Oquotient__of,type,
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% 2.39/2.70
% 2.39/2.70 thf(sy_c_Rat_Oratrel,type,
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% 2.39/2.70
% 2.39/2.70 thf(sy_c_Refine__Imp__Hol_Oassert_H,type,
% 2.39/2.70 refine_Imp_assert: $o > heap_T5738788834812785303t_unit ).
% 2.39/2.70
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% 2.39/2.70
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% 2.39/2.70
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% 2.39/2.70 thf(sy_c_Rings_Odivide__class_Odivide_001t__Rat__Orat,type,
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% 2.39/2.70 thf(sy_c_Rings_Odvd__class_Odvd_001t__Nat__Onat,type,
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% 2.39/2.70
% 2.39/2.70 thf(sy_c_Rings_Odvd__class_Odvd_001t__Rat__Orat,type,
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% 2.39/2.70 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Code____Numeral__Ointeger,type,
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% 2.39/2.70
% 2.39/2.70 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Int__Oint,type,
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% 2.39/2.70
% 2.39/2.70 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Nat__Onat,type,
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% 2.39/2.70
% 2.39/2.70 thf(sy_c_Rings_Ounit__factor__class_Ounit__factor_001t__Nat__Onat,type,
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% 2.39/2.70
% 2.39/2.70 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Code____Numeral__Ointeger,type,
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% 2.39/2.70
% 2.39/2.70 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Code____Numeral__Onatural,type,
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% 2.39/2.70
% 2.39/2.70 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Int__Oint,type,
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% 2.39/2.70
% 2.39/2.70 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Nat__Onat,type,
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% 2.39/2.70
% 2.39/2.70 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Rat__Orat,type,
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% 2.39/2.70
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% 2.39/2.70
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% 2.39/2.70 syntax3730441303064801268at_rat: rat > rat > $o ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_Typedef_Otype__definition_001t__Assertions__Oassn_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
% 2.39/2.70 type_d3909072315231072503_nat_o: ( assn > produc3658429121746597890et_nat > $o ) > ( ( produc3658429121746597890et_nat > $o ) > assn ) > set_Pr4532377907799695533_nat_o > $o ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
% 2.39/2.70 accp_P1862375125659990705et_nat: ( produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o ) > produc2732055786443039994et_nat > $o ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
% 2.39/2.70 accp_P8126237942716283194atural: ( produc7822875418678951345atural > produc7822875418678951345atural > $o ) > produc7822875418678951345atural > $o ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
% 2.39/2.70 accp_P5801069581201407417et_nat: ( produc3658429121746597890et_nat > produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 2.39/2.70 accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.39/2.70 accp_P4275260045618599050at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_member_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
% 2.39/2.70 member6576561426505652726_nat_o: ( produc3658429121746597890et_nat > $o ) > set_Pr4532377907799695533_nat_o > $o ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_member_001t__Int__Oint,type,
% 2.39/2.70 member_int2: int > set_int > $o ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_member_001t__List__Olist_It__Int__Oint_J,type,
% 2.39/2.70 member_list_int: list_int > set_list_int > $o ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
% 2.39/2.70 member_list_nat: list_nat > set_list_nat > $o ).
% 2.39/2.70
% 2.39/2.70 thf(sy_c_member_001t__Nat__Onat,type,
% 2.39/2.71 member_nat2: nat > set_nat > $o ).
% 2.39/2.71
% 2.39/2.71 thf(sy_c_member_001t__Product____Type__Oprod_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
% 2.39/2.71 member7957490590177025114n_assn: produc6575502325842934193n_assn > set_Pr5949110396991348497n_assn > $o ).
% 2.39/2.71
% 2.39/2.71 thf(sy_c_member_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 2.39/2.71 member5262025264175285858nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > $o ).
% 2.39/2.71
% 2.39/2.71 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.39/2.71 member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).
% 2.39/2.71
% 2.39/2.71 thf(sy_v_F,type,
% 2.39/2.71 f: assn ).
% 2.39/2.71
% 2.39/2.71 thf(sy_v_P,type,
% 2.39/2.71 p: assn ).
% 2.39/2.71
% 2.39/2.71 thf(sy_v_Q,type,
% 2.39/2.71 q: assn ).
% 2.39/2.71
% 2.39/2.71 % Relevant facts (5418)
% 2.39/2.71 thf(fact_0_assms,axiom,
% 2.39/2.71 fi @ nil_Pr5671120429643327159n_assn @ ( times_times_assn @ sln @ p ) @ ( times_times_assn @ sln @ q ) @ sln @ sln @ f ).
% 2.39/2.71
% 2.39/2.71 % assms
% 2.39/2.71 thf(fact_1_FI__QUERY__def,axiom,
% 2.39/2.71 ( fI_QUERY
% 2.39/2.71 = ( ^ [P: assn,Q: assn,F: assn] : ( entails @ P @ ( times_times_assn @ Q @ F ) ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % FI_QUERY_def
% 2.39/2.71 thf(fact_2_assn__aci_I10_J,axiom,
% 2.39/2.71 ! [A: assn,B: assn,C: assn] :
% 2.39/2.71 ( ( times_times_assn @ ( times_times_assn @ A @ B ) @ C )
% 2.39/2.71 = ( times_times_assn @ ( times_times_assn @ A @ C ) @ B ) ) ).
% 2.39/2.71
% 2.39/2.71 % assn_aci(10)
% 2.39/2.71 thf(fact_3_star__aci_I3_J,axiom,
% 2.39/2.71 ! [A: assn,B: assn,C: assn] :
% 2.39/2.71 ( ( times_times_assn @ A @ ( times_times_assn @ B @ C ) )
% 2.39/2.71 = ( times_times_assn @ B @ ( times_times_assn @ A @ C ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % star_aci(3)
% 2.39/2.71 thf(fact_4_star__aci_I2_J,axiom,
% 2.39/2.71 ( times_times_assn
% 2.39/2.71 = ( ^ [A2: assn,B2: assn] : ( times_times_assn @ B2 @ A2 ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % star_aci(2)
% 2.39/2.71 thf(fact_5_star__assoc,axiom,
% 2.39/2.71 ! [A: assn,B: assn,C: assn] :
% 2.39/2.71 ( ( times_times_assn @ ( times_times_assn @ A @ B ) @ C )
% 2.39/2.71 = ( times_times_assn @ A @ ( times_times_assn @ B @ C ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % star_assoc
% 2.39/2.71 thf(fact_6_SLN__left,axiom,
% 2.39/2.71 ! [P2: assn] :
% 2.39/2.71 ( ( times_times_assn @ sln @ P2 )
% 2.39/2.71 = P2 ) ).
% 2.39/2.71
% 2.39/2.71 % SLN_left
% 2.39/2.71 thf(fact_7_SLN__right,axiom,
% 2.39/2.71 ! [P2: assn] :
% 2.39/2.71 ( ( times_times_assn @ P2 @ sln )
% 2.39/2.71 = P2 ) ).
% 2.39/2.71
% 2.39/2.71 % SLN_right
% 2.39/2.71 thf(fact_8_is__entails,axiom,
% 2.39/2.71 ! [P2: assn,Q2: assn] :
% 2.39/2.71 ( ( entails @ P2 @ Q2 )
% 2.39/2.71 => ( entails @ P2 @ Q2 ) ) ).
% 2.39/2.71
% 2.39/2.71 % is_entails
% 2.39/2.71 thf(fact_9_ent__star__mono,axiom,
% 2.39/2.71 ! [P2: assn,P3: assn,Q2: assn,Q3: assn] :
% 2.39/2.71 ( ( entails @ P2 @ P3 )
% 2.39/2.71 => ( ( entails @ Q2 @ Q3 )
% 2.39/2.71 => ( entails @ ( times_times_assn @ P2 @ Q2 ) @ ( times_times_assn @ P3 @ Q3 ) ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % ent_star_mono
% 2.39/2.71 thf(fact_10_ent__iffI,axiom,
% 2.39/2.71 ! [A3: assn,B3: assn] :
% 2.39/2.71 ( ( entails @ A3 @ B3 )
% 2.39/2.71 => ( ( entails @ B3 @ A3 )
% 2.39/2.71 => ( A3 = B3 ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % ent_iffI
% 2.39/2.71 thf(fact_11_ent__refl,axiom,
% 2.39/2.71 ! [P2: assn] : ( entails @ P2 @ P2 ) ).
% 2.39/2.71
% 2.39/2.71 % ent_refl
% 2.39/2.71 thf(fact_12_ent__trans,axiom,
% 2.39/2.71 ! [P2: assn,Q2: assn,R: assn] :
% 2.39/2.71 ( ( entails @ P2 @ Q2 )
% 2.39/2.71 => ( ( entails @ Q2 @ R )
% 2.39/2.71 => ( entails @ P2 @ R ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % ent_trans
% 2.39/2.71 thf(fact_13_assn__times__comm,axiom,
% 2.39/2.71 ( times_times_assn
% 2.39/2.71 = ( ^ [P: assn,Q: assn] : ( times_times_assn @ Q @ P ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % assn_times_comm
% 2.39/2.71 thf(fact_14_assn__times__assoc,axiom,
% 2.39/2.71 ! [P2: assn,Q2: assn,R: assn] :
% 2.39/2.71 ( ( times_times_assn @ ( times_times_assn @ P2 @ Q2 ) @ R )
% 2.39/2.71 = ( times_times_assn @ P2 @ ( times_times_assn @ Q2 @ R ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % assn_times_assoc
% 2.39/2.71 thf(fact_15_mult_Oright__assoc,axiom,
% 2.39/2.71 ! [A: assn,B: assn,C: assn] :
% 2.39/2.71 ( ( times_times_assn @ ( times_times_assn @ A @ B ) @ C )
% 2.39/2.71 = ( times_times_assn @ A @ ( times_times_assn @ B @ C ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % mult.right_assoc
% 2.39/2.71 thf(fact_16_mult_Oright__assoc,axiom,
% 2.39/2.71 ! [A: nat,B: nat,C: nat] :
% 2.39/2.71 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 2.39/2.71 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % mult.right_assoc
% 2.39/2.71 thf(fact_17_mult_Oright__assoc,axiom,
% 2.39/2.71 ! [A: int,B: int,C: int] :
% 2.39/2.71 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 2.39/2.71 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % mult.right_assoc
% 2.39/2.71 thf(fact_18_mult_Oright__assoc,axiom,
% 2.39/2.71 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.71 ( ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 2.39/2.71 = ( times_3573771949741848930nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % mult.right_assoc
% 2.39/2.71 thf(fact_19_mult_Oright__assoc,axiom,
% 2.39/2.71 ! [A: code_natural,B: code_natural,C: code_natural] :
% 2.39/2.71 ( ( times_2397367101498566445atural @ ( times_2397367101498566445atural @ A @ B ) @ C )
% 2.39/2.71 = ( times_2397367101498566445atural @ A @ ( times_2397367101498566445atural @ B @ C ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % mult.right_assoc
% 2.39/2.71 thf(fact_20_mult_Oright__commute,axiom,
% 2.39/2.71 ! [A: assn,B: assn,C: assn] :
% 2.39/2.71 ( ( times_times_assn @ ( times_times_assn @ A @ B ) @ C )
% 2.39/2.71 = ( times_times_assn @ ( times_times_assn @ A @ C ) @ B ) ) ).
% 2.39/2.71
% 2.39/2.71 % mult.right_commute
% 2.39/2.71 thf(fact_21_mult_Oright__commute,axiom,
% 2.39/2.71 ! [A: nat,B: nat,C: nat] :
% 2.39/2.71 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 2.39/2.71 = ( times_times_nat @ ( times_times_nat @ A @ C ) @ B ) ) ).
% 2.39/2.71
% 2.39/2.71 % mult.right_commute
% 2.39/2.71 thf(fact_22_mult_Oright__commute,axiom,
% 2.39/2.71 ! [A: int,B: int,C: int] :
% 2.39/2.71 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 2.39/2.71 = ( times_times_int @ ( times_times_int @ A @ C ) @ B ) ) ).
% 2.39/2.71
% 2.39/2.71 % mult.right_commute
% 2.39/2.71 thf(fact_23_mult_Oright__commute,axiom,
% 2.39/2.71 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.71 ( ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 2.39/2.71 = ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ).
% 2.39/2.71
% 2.39/2.71 % mult.right_commute
% 2.39/2.71 thf(fact_24_mult_Oright__commute,axiom,
% 2.39/2.71 ! [A: code_natural,B: code_natural,C: code_natural] :
% 2.39/2.71 ( ( times_2397367101498566445atural @ ( times_2397367101498566445atural @ A @ B ) @ C )
% 2.39/2.71 = ( times_2397367101498566445atural @ ( times_2397367101498566445atural @ A @ C ) @ B ) ) ).
% 2.39/2.71
% 2.39/2.71 % mult.right_commute
% 2.39/2.71 thf(fact_25_mult_Oassoc,axiom,
% 2.39/2.71 ! [A: assn,B: assn,C: assn] :
% 2.39/2.71 ( ( times_times_assn @ ( times_times_assn @ A @ B ) @ C )
% 2.39/2.71 = ( times_times_assn @ A @ ( times_times_assn @ B @ C ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % mult.assoc
% 2.39/2.71 thf(fact_26_mult_Oassoc,axiom,
% 2.39/2.71 ! [A: nat,B: nat,C: nat] :
% 2.39/2.71 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 2.39/2.71 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % mult.assoc
% 2.39/2.71 thf(fact_27_mult_Oassoc,axiom,
% 2.39/2.71 ! [A: int,B: int,C: int] :
% 2.39/2.71 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 2.39/2.71 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % mult.assoc
% 2.39/2.71 thf(fact_28_mult_Oassoc,axiom,
% 2.39/2.71 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.71 ( ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 2.39/2.71 = ( times_3573771949741848930nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % mult.assoc
% 2.39/2.71 thf(fact_29_mult_Oassoc,axiom,
% 2.39/2.71 ! [A: code_natural,B: code_natural,C: code_natural] :
% 2.39/2.71 ( ( times_2397367101498566445atural @ ( times_2397367101498566445atural @ A @ B ) @ C )
% 2.39/2.71 = ( times_2397367101498566445atural @ A @ ( times_2397367101498566445atural @ B @ C ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % mult.assoc
% 2.39/2.71 thf(fact_30_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 2.39/2.71 ( times_times_assn
% 2.39/2.71 = ( ^ [A2: assn,B2: assn] : ( times_times_assn @ B2 @ A2 ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % ab_semigroup_mult_class.mult.commute
% 2.39/2.71 thf(fact_31_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 2.39/2.71 ( times_times_nat
% 2.39/2.71 = ( ^ [A2: nat,B2: nat] : ( times_times_nat @ B2 @ A2 ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % ab_semigroup_mult_class.mult.commute
% 2.39/2.71 thf(fact_32_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 2.39/2.71 ( times_times_int
% 2.39/2.71 = ( ^ [A2: int,B2: int] : ( times_times_int @ B2 @ A2 ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % ab_semigroup_mult_class.mult.commute
% 2.39/2.71 thf(fact_33_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 2.39/2.71 ( times_3573771949741848930nteger
% 2.39/2.71 = ( ^ [A2: code_integer,B2: code_integer] : ( times_3573771949741848930nteger @ B2 @ A2 ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % ab_semigroup_mult_class.mult.commute
% 2.39/2.71 thf(fact_34_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 2.39/2.71 ( times_2397367101498566445atural
% 2.39/2.71 = ( ^ [A2: code_natural,B2: code_natural] : ( times_2397367101498566445atural @ B2 @ A2 ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % ab_semigroup_mult_class.mult.commute
% 2.39/2.71 thf(fact_35_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 2.39/2.71 ! [B: assn,A: assn,C: assn] :
% 2.39/2.71 ( ( times_times_assn @ B @ ( times_times_assn @ A @ C ) )
% 2.39/2.71 = ( times_times_assn @ A @ ( times_times_assn @ B @ C ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % ab_semigroup_mult_class.mult.left_commute
% 2.39/2.71 thf(fact_36_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 2.39/2.71 ! [B: nat,A: nat,C: nat] :
% 2.39/2.71 ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 2.39/2.71 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % ab_semigroup_mult_class.mult.left_commute
% 2.39/2.71 thf(fact_37_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 2.39/2.71 ! [B: int,A: int,C: int] :
% 2.39/2.71 ( ( times_times_int @ B @ ( times_times_int @ A @ C ) )
% 2.39/2.71 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % ab_semigroup_mult_class.mult.left_commute
% 2.39/2.71 thf(fact_38_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 2.39/2.71 ! [B: code_integer,A: code_integer,C: code_integer] :
% 2.39/2.71 ( ( times_3573771949741848930nteger @ B @ ( times_3573771949741848930nteger @ A @ C ) )
% 2.39/2.71 = ( times_3573771949741848930nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % ab_semigroup_mult_class.mult.left_commute
% 2.39/2.71 thf(fact_39_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 2.39/2.71 ! [B: code_natural,A: code_natural,C: code_natural] :
% 2.39/2.71 ( ( times_2397367101498566445atural @ B @ ( times_2397367101498566445atural @ A @ C ) )
% 2.39/2.71 = ( times_2397367101498566445atural @ A @ ( times_2397367101498566445atural @ B @ C ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % ab_semigroup_mult_class.mult.left_commute
% 2.39/2.71 thf(fact_40_ent__wandI,axiom,
% 2.39/2.71 ! [Q2: assn,P2: assn,R: assn] :
% 2.39/2.71 ( ( entails @ ( times_times_assn @ Q2 @ P2 ) @ R )
% 2.39/2.71 => ( entails @ P2 @ ( wand_assn @ Q2 @ R ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % ent_wandI
% 2.39/2.71 thf(fact_41_ent__mp,axiom,
% 2.39/2.71 ! [P2: assn,Q2: assn] : ( entails @ ( times_times_assn @ P2 @ ( wand_assn @ P2 @ Q2 ) ) @ Q2 ) ).
% 2.39/2.71
% 2.39/2.71 % ent_mp
% 2.39/2.71 thf(fact_42_list__ex1__simps_I1_J,axiom,
% 2.39/2.71 ! [P2: produc6575502325842934193n_assn > $o] :
% 2.39/2.71 ~ ( list_e7761433933450087034n_assn @ P2 @ nil_Pr5671120429643327159n_assn ) ).
% 2.39/2.71
% 2.39/2.71 % list_ex1_simps(1)
% 2.39/2.71 thf(fact_43_list__ex1__simps_I1_J,axiom,
% 2.39/2.71 ! [P2: int > $o] :
% 2.39/2.71 ~ ( list_ex1_int @ P2 @ nil_int ) ).
% 2.39/2.71
% 2.39/2.71 % list_ex1_simps(1)
% 2.39/2.71 thf(fact_44_list__ex1__simps_I1_J,axiom,
% 2.39/2.71 ! [P2: nat > $o] :
% 2.39/2.71 ~ ( list_ex1_nat @ P2 @ nil_nat ) ).
% 2.39/2.71
% 2.39/2.71 % list_ex1_simps(1)
% 2.39/2.71 thf(fact_45_product_Osimps_I1_J,axiom,
% 2.39/2.71 ! [Uu: list_assn] :
% 2.39/2.71 ( ( product_assn_assn @ nil_assn @ Uu )
% 2.39/2.71 = nil_Pr5671120429643327159n_assn ) ).
% 2.39/2.71
% 2.39/2.71 % product.simps(1)
% 2.39/2.71 thf(fact_46_is__pure__assn__starI,axiom,
% 2.39/2.71 ! [A: assn,B: assn] :
% 2.39/2.71 ( ( is_pure_assn @ A )
% 2.39/2.71 => ( ( is_pure_assn @ B )
% 2.39/2.71 => ( is_pure_assn @ ( times_times_assn @ A @ B ) ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % is_pure_assn_starI
% 2.39/2.71 thf(fact_47_bind__simps_I1_J,axiom,
% 2.39/2.71 ! [F2: produc6575502325842934193n_assn > list_P8527749157015355191n_assn] :
% 2.39/2.71 ( ( bind_P5664457578022171847n_assn @ nil_Pr5671120429643327159n_assn @ F2 )
% 2.39/2.71 = nil_Pr5671120429643327159n_assn ) ).
% 2.39/2.71
% 2.39/2.71 % bind_simps(1)
% 2.39/2.71 thf(fact_48_bind__simps_I1_J,axiom,
% 2.39/2.71 ! [F2: produc6575502325842934193n_assn > list_int] :
% 2.39/2.71 ( ( bind_P8081679045764635286sn_int @ nil_Pr5671120429643327159n_assn @ F2 )
% 2.39/2.71 = nil_int ) ).
% 2.39/2.71
% 2.39/2.71 % bind_simps(1)
% 2.39/2.71 thf(fact_49_bind__simps_I1_J,axiom,
% 2.39/2.71 ! [F2: produc6575502325842934193n_assn > list_nat] :
% 2.39/2.71 ( ( bind_P8084169516273685562sn_nat @ nil_Pr5671120429643327159n_assn @ F2 )
% 2.39/2.71 = nil_nat ) ).
% 2.39/2.71
% 2.39/2.71 % bind_simps(1)
% 2.39/2.71 thf(fact_50_bind__simps_I1_J,axiom,
% 2.39/2.71 ! [F2: int > list_P8527749157015355191n_assn] :
% 2.39/2.71 ( ( bind_i4941608653131063484n_assn @ nil_int @ F2 )
% 2.39/2.71 = nil_Pr5671120429643327159n_assn ) ).
% 2.39/2.71
% 2.39/2.71 % bind_simps(1)
% 2.39/2.71 thf(fact_51_bind__simps_I1_J,axiom,
% 2.39/2.71 ! [F2: int > list_int] :
% 2.39/2.71 ( ( bind_int_int @ nil_int @ F2 )
% 2.39/2.71 = nil_int ) ).
% 2.39/2.71
% 2.39/2.71 % bind_simps(1)
% 2.39/2.71 thf(fact_52_bind__simps_I1_J,axiom,
% 2.39/2.71 ! [F2: int > list_nat] :
% 2.39/2.71 ( ( bind_int_nat @ nil_int @ F2 )
% 2.39/2.71 = nil_nat ) ).
% 2.39/2.71
% 2.39/2.71 % bind_simps(1)
% 2.39/2.71 thf(fact_53_bind__simps_I1_J,axiom,
% 2.39/2.71 ! [F2: nat > list_P8527749157015355191n_assn] :
% 2.39/2.71 ( ( bind_n3181571989377952280n_assn @ nil_nat @ F2 )
% 2.39/2.71 = nil_Pr5671120429643327159n_assn ) ).
% 2.39/2.71
% 2.39/2.71 % bind_simps(1)
% 2.39/2.71 thf(fact_54_bind__simps_I1_J,axiom,
% 2.39/2.71 ! [F2: nat > list_int] :
% 2.39/2.71 ( ( bind_nat_int @ nil_nat @ F2 )
% 2.39/2.71 = nil_int ) ).
% 2.39/2.71
% 2.39/2.71 % bind_simps(1)
% 2.39/2.71 thf(fact_55_bind__simps_I1_J,axiom,
% 2.39/2.71 ! [F2: nat > list_nat] :
% 2.39/2.71 ( ( bind_nat_nat @ nil_nat @ F2 )
% 2.39/2.71 = nil_nat ) ).
% 2.39/2.71
% 2.39/2.71 % bind_simps(1)
% 2.39/2.71 thf(fact_56_member__rec_I2_J,axiom,
% 2.39/2.71 ! [Y: produc6575502325842934193n_assn] :
% 2.39/2.71 ~ ( member743271071679453132n_assn @ nil_Pr5671120429643327159n_assn @ Y ) ).
% 2.39/2.71
% 2.39/2.71 % member_rec(2)
% 2.39/2.71 thf(fact_57_member__rec_I2_J,axiom,
% 2.39/2.71 ! [Y: int] :
% 2.39/2.71 ~ ( member_int @ nil_int @ Y ) ).
% 2.39/2.71
% 2.39/2.71 % member_rec(2)
% 2.39/2.71 thf(fact_58_member__rec_I2_J,axiom,
% 2.39/2.71 ! [Y: nat] :
% 2.39/2.71 ~ ( member_nat @ nil_nat @ Y ) ).
% 2.39/2.71
% 2.39/2.71 % member_rec(2)
% 2.39/2.71 thf(fact_59_mult_Osafe__commute,axiom,
% 2.39/2.71 ! [X: nat,Y: nat,A: nat,B: nat] :
% 2.39/2.71 ( ( syntax4682126007086162916at_nat @ ( times_times_nat @ X @ Y ) @ A )
% 2.39/2.71 => ( ( times_times_nat @ A @ B )
% 2.39/2.71 = ( times_times_nat @ B @ A ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % mult.safe_commute
% 2.39/2.71 thf(fact_60_mult_Osafe__commute,axiom,
% 2.39/2.71 ! [X: int,Y: int,A: int,B: int] :
% 2.39/2.71 ( ( syntax5678989248478167196nt_int @ ( times_times_int @ X @ Y ) @ A )
% 2.39/2.71 => ( ( times_times_int @ A @ B )
% 2.39/2.71 = ( times_times_int @ B @ A ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % mult.safe_commute
% 2.39/2.71 thf(fact_61_mult_Osafe__commute,axiom,
% 2.39/2.71 ! [X: code_integer,Y: code_integer,A: code_integer,B: code_integer] :
% 2.39/2.71 ( ( syntax380677951125133566nteger @ ( times_3573771949741848930nteger @ X @ Y ) @ A )
% 2.39/2.71 => ( ( times_3573771949741848930nteger @ A @ B )
% 2.39/2.71 = ( times_3573771949741848930nteger @ B @ A ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % mult.safe_commute
% 2.39/2.71 thf(fact_62_mult_Osafe__commute,axiom,
% 2.39/2.71 ! [X: code_natural,Y: code_natural,A: code_natural,B: code_natural] :
% 2.39/2.71 ( ( syntax2868745204708187284atural @ ( times_2397367101498566445atural @ X @ Y ) @ A )
% 2.39/2.71 => ( ( times_2397367101498566445atural @ A @ B )
% 2.39/2.71 = ( times_2397367101498566445atural @ B @ A ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % mult.safe_commute
% 2.39/2.71 thf(fact_63_mult_Osafe__commute,axiom,
% 2.39/2.71 ! [X: assn,Y: assn,A: assn,B: assn] :
% 2.39/2.71 ( ( syntax7398250324933576852n_assn @ ( times_times_assn @ X @ Y ) @ A )
% 2.39/2.71 => ( ( times_times_assn @ A @ B )
% 2.39/2.71 = ( times_times_assn @ B @ A ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % mult.safe_commute
% 2.39/2.71 thf(fact_64_assn__aci_I11_J,axiom,
% 2.39/2.71 ! [X: assn,Y: assn,A: assn,B: assn] :
% 2.39/2.71 ( ( syntax7398250324933576852n_assn @ ( times_times_assn @ X @ Y ) @ A )
% 2.39/2.71 => ( ( times_times_assn @ A @ B )
% 2.39/2.71 = ( times_times_assn @ B @ A ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % assn_aci(11)
% 2.39/2.71 thf(fact_65_ent__pure__pre__iff,axiom,
% 2.39/2.71 ! [P2: assn,B: $o,Q2: assn] :
% 2.39/2.71 ( ( entails @ ( times_times_assn @ P2 @ ( pure_assn @ B ) ) @ Q2 )
% 2.39/2.71 = ( B
% 2.39/2.71 => ( entails @ P2 @ Q2 ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % ent_pure_pre_iff
% 2.39/2.71 thf(fact_66_gen__length__code_I1_J,axiom,
% 2.39/2.71 ! [N: nat] :
% 2.39/2.71 ( ( gen_le1182329135810803268n_assn @ N @ nil_Pr5671120429643327159n_assn )
% 2.39/2.71 = N ) ).
% 2.39/2.71
% 2.39/2.71 % gen_length_code(1)
% 2.39/2.71 thf(fact_67_gen__length__code_I1_J,axiom,
% 2.39/2.71 ! [N: nat] :
% 2.39/2.71 ( ( gen_length_int @ N @ nil_int )
% 2.39/2.71 = N ) ).
% 2.39/2.71
% 2.39/2.71 % gen_length_code(1)
% 2.39/2.71 thf(fact_68_gen__length__code_I1_J,axiom,
% 2.39/2.71 ! [N: nat] :
% 2.39/2.71 ( ( gen_length_nat @ N @ nil_nat )
% 2.39/2.71 = N ) ).
% 2.39/2.71
% 2.39/2.71 % gen_length_code(1)
% 2.39/2.71 thf(fact_69_maps__simps_I2_J,axiom,
% 2.39/2.71 ! [F2: produc6575502325842934193n_assn > list_P8527749157015355191n_assn] :
% 2.39/2.71 ( ( maps_P4274076103917212289n_assn @ F2 @ nil_Pr5671120429643327159n_assn )
% 2.39/2.71 = nil_Pr5671120429643327159n_assn ) ).
% 2.39/2.71
% 2.39/2.71 % maps_simps(2)
% 2.39/2.71 thf(fact_70_maps__simps_I2_J,axiom,
% 2.39/2.71 ! [F2: produc6575502325842934193n_assn > list_int] :
% 2.39/2.71 ( ( maps_P5983552678929597788sn_int @ F2 @ nil_Pr5671120429643327159n_assn )
% 2.39/2.71 = nil_int ) ).
% 2.39/2.71
% 2.39/2.71 % maps_simps(2)
% 2.39/2.71 thf(fact_71_maps__simps_I2_J,axiom,
% 2.39/2.71 ! [F2: produc6575502325842934193n_assn > list_nat] :
% 2.39/2.71 ( ( maps_P5986043149438648064sn_nat @ F2 @ nil_Pr5671120429643327159n_assn )
% 2.39/2.71 = nil_nat ) ).
% 2.39/2.71
% 2.39/2.71 % maps_simps(2)
% 2.39/2.71 thf(fact_72_maps__simps_I2_J,axiom,
% 2.39/2.71 ! [F2: int > list_P8527749157015355191n_assn] :
% 2.39/2.71 ( ( maps_i2843482286296025986n_assn @ F2 @ nil_int )
% 2.39/2.71 = nil_Pr5671120429643327159n_assn ) ).
% 2.39/2.71
% 2.39/2.71 % maps_simps(2)
% 2.39/2.71 thf(fact_73_maps__simps_I2_J,axiom,
% 2.39/2.71 ! [F2: int > list_int] :
% 2.39/2.71 ( ( maps_int_int @ F2 @ nil_int )
% 2.39/2.71 = nil_int ) ).
% 2.39/2.71
% 2.39/2.71 % maps_simps(2)
% 2.39/2.71 thf(fact_74_maps__simps_I2_J,axiom,
% 2.39/2.71 ! [F2: int > list_nat] :
% 2.39/2.71 ( ( maps_int_nat @ F2 @ nil_int )
% 2.39/2.71 = nil_nat ) ).
% 2.39/2.71
% 2.39/2.71 % maps_simps(2)
% 2.39/2.71 thf(fact_75_maps__simps_I2_J,axiom,
% 2.39/2.71 ! [F2: nat > list_P8527749157015355191n_assn] :
% 2.39/2.71 ( ( maps_n1083445622542914782n_assn @ F2 @ nil_nat )
% 2.39/2.71 = nil_Pr5671120429643327159n_assn ) ).
% 2.39/2.71
% 2.39/2.71 % maps_simps(2)
% 2.39/2.71 thf(fact_76_maps__simps_I2_J,axiom,
% 2.39/2.71 ! [F2: nat > list_int] :
% 2.39/2.71 ( ( maps_nat_int @ F2 @ nil_nat )
% 2.39/2.71 = nil_int ) ).
% 2.39/2.71
% 2.39/2.71 % maps_simps(2)
% 2.39/2.71 thf(fact_77_maps__simps_I2_J,axiom,
% 2.39/2.71 ! [F2: nat > list_nat] :
% 2.39/2.71 ( ( maps_nat_nat @ F2 @ nil_nat )
% 2.39/2.71 = nil_nat ) ).
% 2.39/2.71
% 2.39/2.71 % maps_simps(2)
% 2.39/2.71 thf(fact_78_pure__assn__eq__conv,axiom,
% 2.39/2.71 ! [P2: $o,Q2: $o] :
% 2.39/2.71 ( ( ( pure_assn @ P2 )
% 2.39/2.71 = ( pure_assn @ Q2 ) )
% 2.39/2.71 = ( P2 = Q2 ) ) ).
% 2.39/2.71
% 2.39/2.71 % pure_assn_eq_conv
% 2.39/2.71 thf(fact_79_merge__pure__star,axiom,
% 2.39/2.71 ! [A: $o,B: $o] :
% 2.39/2.71 ( ( times_times_assn @ ( pure_assn @ A ) @ ( pure_assn @ B ) )
% 2.39/2.71 = ( pure_assn
% 2.39/2.71 @ ( A
% 2.39/2.71 & B ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % merge_pure_star
% 2.39/2.71 thf(fact_80_is__pure__assn__pure,axiom,
% 2.39/2.71 ! [P2: $o] : ( is_pure_assn @ ( pure_assn @ P2 ) ) ).
% 2.39/2.71
% 2.39/2.71 % is_pure_assn_pure
% 2.39/2.71 thf(fact_81_is__pure__assn__def,axiom,
% 2.39/2.71 ( is_pure_assn
% 2.39/2.71 = ( ^ [A2: assn] :
% 2.39/2.71 ? [P: $o] :
% 2.39/2.71 ( A2
% 2.39/2.71 = ( pure_assn @ P ) ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % is_pure_assn_def
% 2.39/2.71 thf(fact_82_is__pure__assnE,axiom,
% 2.39/2.71 ! [A: assn] :
% 2.39/2.71 ( ( is_pure_assn @ A )
% 2.39/2.71 => ~ ! [P4: $o] :
% 2.39/2.71 ( A
% 2.39/2.71 != ( pure_assn @ P4 ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % is_pure_assnE
% 2.39/2.71 thf(fact_83_syntax__fo__nomatch__def,axiom,
% 2.39/2.71 ( syntax7398250324933576852n_assn
% 2.39/2.71 = ( ^ [Pat: assn,Obj: assn] : $true ) ) ).
% 2.39/2.71
% 2.39/2.71 % syntax_fo_nomatch_def
% 2.39/2.71 thf(fact_84_ent__pure__post__iff,axiom,
% 2.39/2.71 ! [P2: assn,Q2: assn,B: $o] :
% 2.39/2.71 ( ( entails @ P2 @ ( times_times_assn @ Q2 @ ( pure_assn @ B ) ) )
% 2.39/2.71 = ( ! [H: produc3658429121746597890et_nat] :
% 2.39/2.71 ( ( rep_assn @ P2 @ H )
% 2.39/2.71 => B )
% 2.39/2.71 & ( entails @ P2 @ Q2 ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % ent_pure_post_iff
% 2.39/2.71 thf(fact_85_ent__pure__pre__iff__sng,axiom,
% 2.39/2.71 ! [B: $o,Q2: assn] :
% 2.39/2.71 ( ( entails @ ( pure_assn @ B ) @ Q2 )
% 2.39/2.71 = ( B
% 2.39/2.71 => ( entails @ one_one_assn @ Q2 ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % ent_pure_pre_iff_sng
% 2.39/2.71 thf(fact_86_ac__operator_Osafe__commute,axiom,
% 2.39/2.71 ! [F2: assn > assn > assn,X: assn,Y: assn,A: assn,B: assn] :
% 2.39/2.71 ( ( syntax3673046151410588037r_assn @ F2 )
% 2.39/2.71 => ( ( syntax7398250324933576852n_assn @ ( F2 @ X @ Y ) @ A )
% 2.39/2.71 => ( ( F2 @ A @ B )
% 2.39/2.71 = ( F2 @ B @ A ) ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % ac_operator.safe_commute
% 2.39/2.71 thf(fact_87_and__extract__pure__left__ctx__iff,axiom,
% 2.39/2.71 ! [P2: assn,B: $o,Q2: assn] :
% 2.39/2.71 ( ( inf_inf_assn @ ( times_times_assn @ P2 @ ( pure_assn @ B ) ) @ Q2 )
% 2.39/2.71 = ( times_times_assn @ ( inf_inf_assn @ P2 @ Q2 ) @ ( pure_assn @ B ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % and_extract_pure_left_ctx_iff
% 2.39/2.71 thf(fact_88_and__extract__pure__right__ctx__iff,axiom,
% 2.39/2.71 ! [P2: assn,Q2: assn,B: $o] :
% 2.39/2.71 ( ( inf_inf_assn @ P2 @ ( times_times_assn @ Q2 @ ( pure_assn @ B ) ) )
% 2.39/2.71 = ( times_times_assn @ ( inf_inf_assn @ P2 @ Q2 ) @ ( pure_assn @ B ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % and_extract_pure_right_ctx_iff
% 2.39/2.71 thf(fact_89_null__rec_I2_J,axiom,
% 2.39/2.71 null_P7596217980778516671n_assn @ nil_Pr5671120429643327159n_assn ).
% 2.39/2.71
% 2.39/2.71 % null_rec(2)
% 2.39/2.71 thf(fact_90_null__rec_I2_J,axiom,
% 2.39/2.71 null_int @ nil_int ).
% 2.39/2.71
% 2.39/2.71 % null_rec(2)
% 2.39/2.71 thf(fact_91_null__rec_I2_J,axiom,
% 2.39/2.71 null_nat @ nil_nat ).
% 2.39/2.71
% 2.39/2.71 % null_rec(2)
% 2.39/2.71 thf(fact_92_mem__Collect__eq,axiom,
% 2.39/2.71 ! [A: int,P2: int > $o] :
% 2.39/2.71 ( ( member_int2 @ A @ ( collect_int @ P2 ) )
% 2.39/2.71 = ( P2 @ A ) ) ).
% 2.39/2.71
% 2.39/2.71 % mem_Collect_eq
% 2.39/2.71 thf(fact_93_mem__Collect__eq,axiom,
% 2.39/2.71 ! [A: produc3658429121746597890et_nat > $o,P2: ( produc3658429121746597890et_nat > $o ) > $o] :
% 2.39/2.71 ( ( member6576561426505652726_nat_o @ A @ ( collec939566748876313656_nat_o @ P2 ) )
% 2.39/2.71 = ( P2 @ A ) ) ).
% 2.39/2.71
% 2.39/2.71 % mem_Collect_eq
% 2.39/2.71 thf(fact_94_mem__Collect__eq,axiom,
% 2.39/2.71 ! [A: list_nat,P2: list_nat > $o] :
% 2.39/2.71 ( ( member_list_nat @ A @ ( collect_list_nat @ P2 ) )
% 2.39/2.71 = ( P2 @ A ) ) ).
% 2.39/2.71
% 2.39/2.71 % mem_Collect_eq
% 2.39/2.71 thf(fact_95_mem__Collect__eq,axiom,
% 2.39/2.71 ! [A: nat,P2: nat > $o] :
% 2.39/2.71 ( ( member_nat2 @ A @ ( collect_nat @ P2 ) )
% 2.39/2.71 = ( P2 @ A ) ) ).
% 2.39/2.71
% 2.39/2.71 % mem_Collect_eq
% 2.39/2.71 thf(fact_96_mem__Collect__eq,axiom,
% 2.39/2.71 ! [A: product_prod_nat_nat,P2: product_prod_nat_nat > $o] :
% 2.39/2.71 ( ( member8440522571783428010at_nat @ A @ ( collec3392354462482085612at_nat @ P2 ) )
% 2.39/2.71 = ( P2 @ A ) ) ).
% 2.39/2.71
% 2.39/2.71 % mem_Collect_eq
% 2.39/2.71 thf(fact_97_Collect__mem__eq,axiom,
% 2.39/2.71 ! [A3: set_int] :
% 2.39/2.71 ( ( collect_int
% 2.39/2.71 @ ^ [X2: int] : ( member_int2 @ X2 @ A3 ) )
% 2.39/2.71 = A3 ) ).
% 2.39/2.71
% 2.39/2.71 % Collect_mem_eq
% 2.39/2.71 thf(fact_98_Collect__mem__eq,axiom,
% 2.39/2.71 ! [A3: set_Pr4532377907799695533_nat_o] :
% 2.39/2.71 ( ( collec939566748876313656_nat_o
% 2.39/2.71 @ ^ [X2: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X2 @ A3 ) )
% 2.39/2.71 = A3 ) ).
% 2.39/2.71
% 2.39/2.71 % Collect_mem_eq
% 2.39/2.71 thf(fact_99_Collect__mem__eq,axiom,
% 2.39/2.71 ! [A3: set_list_nat] :
% 2.39/2.71 ( ( collect_list_nat
% 2.39/2.71 @ ^ [X2: list_nat] : ( member_list_nat @ X2 @ A3 ) )
% 2.39/2.71 = A3 ) ).
% 2.39/2.71
% 2.39/2.71 % Collect_mem_eq
% 2.39/2.71 thf(fact_100_Collect__mem__eq,axiom,
% 2.39/2.71 ! [A3: set_nat] :
% 2.39/2.71 ( ( collect_nat
% 2.39/2.71 @ ^ [X2: nat] : ( member_nat2 @ X2 @ A3 ) )
% 2.39/2.71 = A3 ) ).
% 2.39/2.71
% 2.39/2.71 % Collect_mem_eq
% 2.39/2.71 thf(fact_101_Collect__mem__eq,axiom,
% 2.39/2.71 ! [A3: set_Pr1261947904930325089at_nat] :
% 2.39/2.71 ( ( collec3392354462482085612at_nat
% 2.39/2.71 @ ^ [X2: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X2 @ A3 ) )
% 2.39/2.71 = A3 ) ).
% 2.39/2.71
% 2.39/2.71 % Collect_mem_eq
% 2.39/2.71 thf(fact_102_Collect__cong,axiom,
% 2.39/2.71 ! [P2: ( produc3658429121746597890et_nat > $o ) > $o,Q2: ( produc3658429121746597890et_nat > $o ) > $o] :
% 2.39/2.71 ( ! [X3: produc3658429121746597890et_nat > $o] :
% 2.39/2.71 ( ( P2 @ X3 )
% 2.39/2.71 = ( Q2 @ X3 ) )
% 2.39/2.71 => ( ( collec939566748876313656_nat_o @ P2 )
% 2.39/2.71 = ( collec939566748876313656_nat_o @ Q2 ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % Collect_cong
% 2.39/2.71 thf(fact_103_Collect__cong,axiom,
% 2.39/2.71 ! [P2: list_nat > $o,Q2: list_nat > $o] :
% 2.39/2.71 ( ! [X3: list_nat] :
% 2.39/2.71 ( ( P2 @ X3 )
% 2.39/2.71 = ( Q2 @ X3 ) )
% 2.39/2.71 => ( ( collect_list_nat @ P2 )
% 2.39/2.71 = ( collect_list_nat @ Q2 ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % Collect_cong
% 2.39/2.71 thf(fact_104_Collect__cong,axiom,
% 2.39/2.71 ! [P2: nat > $o,Q2: nat > $o] :
% 2.39/2.71 ( ! [X3: nat] :
% 2.39/2.71 ( ( P2 @ X3 )
% 2.39/2.71 = ( Q2 @ X3 ) )
% 2.39/2.71 => ( ( collect_nat @ P2 )
% 2.39/2.71 = ( collect_nat @ Q2 ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % Collect_cong
% 2.39/2.71 thf(fact_105_Collect__cong,axiom,
% 2.39/2.71 ! [P2: product_prod_nat_nat > $o,Q2: product_prod_nat_nat > $o] :
% 2.39/2.71 ( ! [X3: product_prod_nat_nat] :
% 2.39/2.71 ( ( P2 @ X3 )
% 2.39/2.71 = ( Q2 @ X3 ) )
% 2.39/2.71 => ( ( collec3392354462482085612at_nat @ P2 )
% 2.39/2.71 = ( collec3392354462482085612at_nat @ Q2 ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % Collect_cong
% 2.39/2.71 thf(fact_106_eq__Nil__null,axiom,
% 2.39/2.71 ! [Xs: list_P8527749157015355191n_assn] :
% 2.39/2.71 ( ( Xs = nil_Pr5671120429643327159n_assn )
% 2.39/2.71 = ( null_P7596217980778516671n_assn @ Xs ) ) ).
% 2.39/2.71
% 2.39/2.71 % eq_Nil_null
% 2.39/2.71 thf(fact_107_eq__Nil__null,axiom,
% 2.39/2.71 ! [Xs: list_int] :
% 2.39/2.71 ( ( Xs = nil_int )
% 2.39/2.71 = ( null_int @ Xs ) ) ).
% 2.39/2.71
% 2.39/2.71 % eq_Nil_null
% 2.39/2.71 thf(fact_108_eq__Nil__null,axiom,
% 2.39/2.71 ! [Xs: list_nat] :
% 2.39/2.71 ( ( Xs = nil_nat )
% 2.39/2.71 = ( null_nat @ Xs ) ) ).
% 2.39/2.71
% 2.39/2.71 % eq_Nil_null
% 2.39/2.71 thf(fact_109_zip__Nil,axiom,
% 2.39/2.71 ! [Ys: list_assn] :
% 2.39/2.71 ( ( zip_assn_assn @ nil_assn @ Ys )
% 2.39/2.71 = nil_Pr5671120429643327159n_assn ) ).
% 2.39/2.71
% 2.39/2.71 % zip_Nil
% 2.39/2.71 thf(fact_110_Nil__eq__zip__iff,axiom,
% 2.39/2.71 ! [Xs: list_P8527749157015355191n_assn,Ys: list_P8527749157015355191n_assn] :
% 2.39/2.71 ( ( nil_Pr4327835960982145133n_assn
% 2.39/2.71 = ( zip_Pr8806919808394484215n_assn @ Xs @ Ys ) )
% 2.39/2.71 = ( ( Xs = nil_Pr5671120429643327159n_assn )
% 2.39/2.71 | ( Ys = nil_Pr5671120429643327159n_assn ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % Nil_eq_zip_iff
% 2.39/2.71 thf(fact_111_Nil__eq__zip__iff,axiom,
% 2.39/2.71 ! [Xs: list_P8527749157015355191n_assn,Ys: list_int] :
% 2.39/2.71 ( ( nil_Pr7991254345159696774sn_int
% 2.39/2.71 = ( zip_Pr1015554993053626726sn_int @ Xs @ Ys ) )
% 2.39/2.71 = ( ( Xs = nil_Pr5671120429643327159n_assn )
% 2.39/2.71 | ( Ys = nil_int ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % Nil_eq_zip_iff
% 2.39/2.71 thf(fact_112_Nil__eq__zip__iff,axiom,
% 2.39/2.71 ! [Xs: list_P8527749157015355191n_assn,Ys: list_nat] :
% 2.39/2.71 ( ( nil_Pr2945733327814117674sn_nat
% 2.39/2.71 = ( zip_Pr1018045463562677002sn_nat @ Xs @ Ys ) )
% 2.39/2.71 = ( ( Xs = nil_Pr5671120429643327159n_assn )
% 2.39/2.71 | ( Ys = nil_nat ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % Nil_eq_zip_iff
% 2.39/2.71 thf(fact_113_Nil__eq__zip__iff,axiom,
% 2.39/2.71 ! [Xs: list_int,Ys: list_P8527749157015355191n_assn] :
% 2.39/2.71 ( ( nil_Pr2440414457004260852n_assn
% 2.39/2.71 = ( zip_in7098856637274830732n_assn @ Xs @ Ys ) )
% 2.39/2.71 = ( ( Xs = nil_int )
% 2.39/2.71 | ( Ys = nil_Pr5671120429643327159n_assn ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % Nil_eq_zip_iff
% 2.39/2.71 thf(fact_114_Nil__eq__zip__iff,axiom,
% 2.39/2.71 ! [Xs: list_int,Ys: list_int] :
% 2.39/2.71 ( ( nil_Pr2300489316682597567nt_int
% 2.39/2.71 = ( zip_int_int @ Xs @ Ys ) )
% 2.39/2.71 = ( ( Xs = nil_int )
% 2.39/2.71 | ( Ys = nil_int ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % Nil_eq_zip_iff
% 2.39/2.71 thf(fact_115_Nil__eq__zip__iff,axiom,
% 2.39/2.71 ! [Xs: list_int,Ys: list_nat] :
% 2.39/2.71 ( ( nil_Pr6478340336191794275nt_nat
% 2.39/2.71 = ( zip_int_nat @ Xs @ Ys ) )
% 2.39/2.71 = ( ( Xs = nil_int )
% 2.39/2.71 | ( Ys = nil_nat ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % Nil_eq_zip_iff
% 2.39/2.71 thf(fact_116_Nil__eq__zip__iff,axiom,
% 2.39/2.71 ! [Xs: list_nat,Ys: list_P8527749157015355191n_assn] :
% 2.39/2.71 ( ( nil_Pr680377793251149648n_assn
% 2.39/2.71 = ( zip_na5338819973521719528n_assn @ Xs @ Ys ) )
% 2.39/2.71 = ( ( Xs = nil_nat )
% 2.39/2.71 | ( Ys = nil_Pr5671120429643327159n_assn ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % Nil_eq_zip_iff
% 2.39/2.71 thf(fact_117_Nil__eq__zip__iff,axiom,
% 2.39/2.71 ! [Xs: list_nat,Ys: list_int] :
% 2.39/2.71 ( ( nil_Pr1301135604781543011at_int
% 2.39/2.71 = ( zip_nat_int @ Xs @ Ys ) )
% 2.39/2.71 = ( ( Xs = nil_nat )
% 2.39/2.71 | ( Ys = nil_int ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % Nil_eq_zip_iff
% 2.39/2.71 thf(fact_118_Nil__eq__zip__iff,axiom,
% 2.39/2.71 ! [Xs: list_nat,Ys: list_nat] :
% 2.39/2.71 ( ( nil_Pr5478986624290739719at_nat
% 2.39/2.71 = ( zip_nat_nat @ Xs @ Ys ) )
% 2.39/2.71 = ( ( Xs = nil_nat )
% 2.39/2.71 | ( Ys = nil_nat ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % Nil_eq_zip_iff
% 2.39/2.71 thf(fact_119_Nil__eq__zip__iff,axiom,
% 2.39/2.71 ! [Xs: list_assn,Ys: list_assn] :
% 2.39/2.71 ( ( nil_Pr5671120429643327159n_assn
% 2.39/2.71 = ( zip_assn_assn @ Xs @ Ys ) )
% 2.39/2.71 = ( ( Xs = nil_assn )
% 2.39/2.71 | ( Ys = nil_assn ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % Nil_eq_zip_iff
% 2.39/2.71 thf(fact_120_zip__eq__Nil__iff,axiom,
% 2.39/2.71 ! [Xs: list_P8527749157015355191n_assn,Ys: list_P8527749157015355191n_assn] :
% 2.39/2.71 ( ( ( zip_Pr8806919808394484215n_assn @ Xs @ Ys )
% 2.39/2.71 = nil_Pr4327835960982145133n_assn )
% 2.39/2.71 = ( ( Xs = nil_Pr5671120429643327159n_assn )
% 2.39/2.71 | ( Ys = nil_Pr5671120429643327159n_assn ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % zip_eq_Nil_iff
% 2.39/2.71 thf(fact_121_zip__eq__Nil__iff,axiom,
% 2.39/2.71 ! [Xs: list_P8527749157015355191n_assn,Ys: list_int] :
% 2.39/2.71 ( ( ( zip_Pr1015554993053626726sn_int @ Xs @ Ys )
% 2.39/2.71 = nil_Pr7991254345159696774sn_int )
% 2.39/2.71 = ( ( Xs = nil_Pr5671120429643327159n_assn )
% 2.39/2.71 | ( Ys = nil_int ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % zip_eq_Nil_iff
% 2.39/2.71 thf(fact_122_zip__eq__Nil__iff,axiom,
% 2.39/2.71 ! [Xs: list_P8527749157015355191n_assn,Ys: list_nat] :
% 2.39/2.71 ( ( ( zip_Pr1018045463562677002sn_nat @ Xs @ Ys )
% 2.39/2.71 = nil_Pr2945733327814117674sn_nat )
% 2.39/2.71 = ( ( Xs = nil_Pr5671120429643327159n_assn )
% 2.39/2.71 | ( Ys = nil_nat ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % zip_eq_Nil_iff
% 2.39/2.71 thf(fact_123_zip__eq__Nil__iff,axiom,
% 2.39/2.71 ! [Xs: list_int,Ys: list_P8527749157015355191n_assn] :
% 2.39/2.71 ( ( ( zip_in7098856637274830732n_assn @ Xs @ Ys )
% 2.39/2.71 = nil_Pr2440414457004260852n_assn )
% 2.39/2.71 = ( ( Xs = nil_int )
% 2.39/2.71 | ( Ys = nil_Pr5671120429643327159n_assn ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % zip_eq_Nil_iff
% 2.39/2.71 thf(fact_124_zip__eq__Nil__iff,axiom,
% 2.39/2.71 ! [Xs: list_int,Ys: list_int] :
% 2.39/2.71 ( ( ( zip_int_int @ Xs @ Ys )
% 2.39/2.71 = nil_Pr2300489316682597567nt_int )
% 2.39/2.71 = ( ( Xs = nil_int )
% 2.39/2.71 | ( Ys = nil_int ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % zip_eq_Nil_iff
% 2.39/2.71 thf(fact_125_zip__eq__Nil__iff,axiom,
% 2.39/2.71 ! [Xs: list_int,Ys: list_nat] :
% 2.39/2.71 ( ( ( zip_int_nat @ Xs @ Ys )
% 2.39/2.71 = nil_Pr6478340336191794275nt_nat )
% 2.39/2.71 = ( ( Xs = nil_int )
% 2.39/2.71 | ( Ys = nil_nat ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % zip_eq_Nil_iff
% 2.39/2.71 thf(fact_126_zip__eq__Nil__iff,axiom,
% 2.39/2.71 ! [Xs: list_nat,Ys: list_P8527749157015355191n_assn] :
% 2.39/2.71 ( ( ( zip_na5338819973521719528n_assn @ Xs @ Ys )
% 2.39/2.71 = nil_Pr680377793251149648n_assn )
% 2.39/2.71 = ( ( Xs = nil_nat )
% 2.39/2.71 | ( Ys = nil_Pr5671120429643327159n_assn ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % zip_eq_Nil_iff
% 2.39/2.71 thf(fact_127_zip__eq__Nil__iff,axiom,
% 2.39/2.71 ! [Xs: list_nat,Ys: list_int] :
% 2.39/2.71 ( ( ( zip_nat_int @ Xs @ Ys )
% 2.39/2.71 = nil_Pr1301135604781543011at_int )
% 2.39/2.71 = ( ( Xs = nil_nat )
% 2.39/2.71 | ( Ys = nil_int ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % zip_eq_Nil_iff
% 2.39/2.71 thf(fact_128_zip__eq__Nil__iff,axiom,
% 2.39/2.71 ! [Xs: list_nat,Ys: list_nat] :
% 2.39/2.71 ( ( ( zip_nat_nat @ Xs @ Ys )
% 2.39/2.71 = nil_Pr5478986624290739719at_nat )
% 2.39/2.71 = ( ( Xs = nil_nat )
% 2.39/2.71 | ( Ys = nil_nat ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % zip_eq_Nil_iff
% 2.39/2.71 thf(fact_129_zip__eq__Nil__iff,axiom,
% 2.39/2.71 ! [Xs: list_assn,Ys: list_assn] :
% 2.39/2.71 ( ( ( zip_assn_assn @ Xs @ Ys )
% 2.39/2.71 = nil_Pr5671120429643327159n_assn )
% 2.39/2.71 = ( ( Xs = nil_assn )
% 2.39/2.71 | ( Ys = nil_assn ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % zip_eq_Nil_iff
% 2.39/2.71 thf(fact_130_mod__pure__star__dist,axiom,
% 2.39/2.71 ! [P2: assn,B: $o,H2: produc3658429121746597890et_nat] :
% 2.39/2.71 ( ( rep_assn @ ( times_times_assn @ P2 @ ( pure_assn @ B ) ) @ H2 )
% 2.39/2.71 = ( ( rep_assn @ P2 @ H2 )
% 2.39/2.71 & B ) ) ).
% 2.39/2.71
% 2.39/2.71 % mod_pure_star_dist
% 2.39/2.71 thf(fact_131_list__ex__simps_I2_J,axiom,
% 2.39/2.71 ! [P2: produc6575502325842934193n_assn > $o] :
% 2.39/2.71 ~ ( list_e1087220904399170805n_assn @ P2 @ nil_Pr5671120429643327159n_assn ) ).
% 2.39/2.71
% 2.39/2.71 % list_ex_simps(2)
% 2.39/2.71 thf(fact_132_list__ex__simps_I2_J,axiom,
% 2.39/2.71 ! [P2: int > $o] :
% 2.39/2.71 ~ ( list_ex_int @ P2 @ nil_int ) ).
% 2.39/2.71
% 2.39/2.71 % list_ex_simps(2)
% 2.39/2.71 thf(fact_133_list__ex__simps_I2_J,axiom,
% 2.39/2.71 ! [P2: nat > $o] :
% 2.39/2.71 ~ ( list_ex_nat @ P2 @ nil_nat ) ).
% 2.39/2.71
% 2.39/2.71 % list_ex_simps(2)
% 2.39/2.71 thf(fact_134_Rep__assn__inject,axiom,
% 2.39/2.71 ! [X: assn,Y: assn] :
% 2.39/2.71 ( ( ( rep_assn @ X )
% 2.39/2.71 = ( rep_assn @ Y ) )
% 2.39/2.71 = ( X = Y ) ) ).
% 2.39/2.71
% 2.39/2.71 % Rep_assn_inject
% 2.39/2.71 thf(fact_135_mult__1,axiom,
% 2.39/2.71 ! [A: rat] :
% 2.39/2.71 ( ( times_times_rat @ one_one_rat @ A )
% 2.39/2.71 = A ) ).
% 2.39/2.71
% 2.39/2.71 % mult_1
% 2.39/2.71 thf(fact_136_mult__1,axiom,
% 2.39/2.71 ! [A: assn] :
% 2.39/2.71 ( ( times_times_assn @ one_one_assn @ A )
% 2.39/2.71 = A ) ).
% 2.39/2.71
% 2.39/2.71 % mult_1
% 2.39/2.71 thf(fact_137_mult__1,axiom,
% 2.39/2.71 ! [A: nat] :
% 2.39/2.71 ( ( times_times_nat @ one_one_nat @ A )
% 2.39/2.71 = A ) ).
% 2.39/2.71
% 2.39/2.71 % mult_1
% 2.39/2.71 thf(fact_138_mult__1,axiom,
% 2.39/2.71 ! [A: int] :
% 2.39/2.71 ( ( times_times_int @ one_one_int @ A )
% 2.39/2.71 = A ) ).
% 2.39/2.71
% 2.39/2.71 % mult_1
% 2.39/2.71 thf(fact_139_mult__1,axiom,
% 2.39/2.71 ! [A: code_integer] :
% 2.39/2.71 ( ( times_3573771949741848930nteger @ one_one_Code_integer @ A )
% 2.39/2.71 = A ) ).
% 2.39/2.71
% 2.39/2.71 % mult_1
% 2.39/2.71 thf(fact_140_mult__1,axiom,
% 2.39/2.71 ! [A: code_natural] :
% 2.39/2.71 ( ( times_2397367101498566445atural @ one_one_Code_natural @ A )
% 2.39/2.71 = A ) ).
% 2.39/2.71
% 2.39/2.71 % mult_1
% 2.39/2.71 thf(fact_141_mult_Oright__neutral,axiom,
% 2.39/2.71 ! [A: rat] :
% 2.39/2.71 ( ( times_times_rat @ A @ one_one_rat )
% 2.39/2.71 = A ) ).
% 2.39/2.71
% 2.39/2.71 % mult.right_neutral
% 2.39/2.71 thf(fact_142_mult_Oright__neutral,axiom,
% 2.39/2.71 ! [A: assn] :
% 2.39/2.71 ( ( times_times_assn @ A @ one_one_assn )
% 2.39/2.71 = A ) ).
% 2.39/2.71
% 2.39/2.71 % mult.right_neutral
% 2.39/2.71 thf(fact_143_mult_Oright__neutral,axiom,
% 2.39/2.71 ! [A: nat] :
% 2.39/2.71 ( ( times_times_nat @ A @ one_one_nat )
% 2.39/2.71 = A ) ).
% 2.39/2.71
% 2.39/2.71 % mult.right_neutral
% 2.39/2.71 thf(fact_144_mult_Oright__neutral,axiom,
% 2.39/2.71 ! [A: int] :
% 2.39/2.71 ( ( times_times_int @ A @ one_one_int )
% 2.39/2.71 = A ) ).
% 2.39/2.71
% 2.39/2.71 % mult.right_neutral
% 2.39/2.71 thf(fact_145_mult_Oright__neutral,axiom,
% 2.39/2.71 ! [A: code_integer] :
% 2.39/2.71 ( ( times_3573771949741848930nteger @ A @ one_one_Code_integer )
% 2.39/2.71 = A ) ).
% 2.39/2.71
% 2.39/2.71 % mult.right_neutral
% 2.39/2.71 thf(fact_146_mult_Oright__neutral,axiom,
% 2.39/2.71 ! [A: code_natural] :
% 2.39/2.71 ( ( times_2397367101498566445atural @ A @ one_one_Code_natural )
% 2.39/2.71 = A ) ).
% 2.39/2.71
% 2.39/2.71 % mult.right_neutral
% 2.39/2.71 thf(fact_147_merge__pure__and,axiom,
% 2.39/2.71 ! [A: $o,B: $o] :
% 2.39/2.71 ( ( inf_inf_assn @ ( pure_assn @ A ) @ ( pure_assn @ B ) )
% 2.39/2.71 = ( pure_assn
% 2.39/2.71 @ ( A
% 2.39/2.71 & B ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % merge_pure_and
% 2.39/2.71 thf(fact_148_pure__true,axiom,
% 2.39/2.71 ( ( pure_assn @ $true )
% 2.39/2.71 = one_one_assn ) ).
% 2.39/2.71
% 2.39/2.71 % pure_true
% 2.39/2.71 thf(fact_149_pure__assn__eq__emp__iff,axiom,
% 2.39/2.71 ! [P2: $o] :
% 2.39/2.71 ( ( ( pure_assn @ P2 )
% 2.39/2.71 = one_one_assn )
% 2.39/2.71 = P2 ) ).
% 2.39/2.71
% 2.39/2.71 % pure_assn_eq_emp_iff
% 2.39/2.71 thf(fact_150_ent__pure__post__iff__sng,axiom,
% 2.39/2.71 ! [P2: assn,B: $o] :
% 2.39/2.71 ( ( entails @ P2 @ ( pure_assn @ B ) )
% 2.39/2.71 = ( ! [H: produc3658429121746597890et_nat] :
% 2.39/2.71 ( ( rep_assn @ P2 @ H )
% 2.39/2.71 => B )
% 2.39/2.71 & ( entails @ P2 @ one_one_assn ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % ent_pure_post_iff_sng
% 2.39/2.71 thf(fact_151_and__extract__pure__right__iff,axiom,
% 2.39/2.71 ! [P2: assn,B: $o] :
% 2.39/2.71 ( ( inf_inf_assn @ P2 @ ( pure_assn @ B ) )
% 2.39/2.71 = ( times_times_assn @ ( inf_inf_assn @ one_one_assn @ P2 ) @ ( pure_assn @ B ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % and_extract_pure_right_iff
% 2.39/2.71 thf(fact_152_and__extract__pure__left__iff,axiom,
% 2.39/2.71 ! [B: $o,Q2: assn] :
% 2.39/2.71 ( ( inf_inf_assn @ ( pure_assn @ B ) @ Q2 )
% 2.39/2.71 = ( times_times_assn @ ( inf_inf_assn @ one_one_assn @ Q2 ) @ ( pure_assn @ B ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % and_extract_pure_left_iff
% 2.39/2.71 thf(fact_153_norm__assertion__simps_I14_J,axiom,
% 2.39/2.71 ! [X: assn,Y: assn,Z: assn] :
% 2.39/2.71 ( ( inf_inf_assn @ ( inf_inf_assn @ X @ Y ) @ Z )
% 2.39/2.71 = ( inf_inf_assn @ X @ ( inf_inf_assn @ Y @ Z ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % norm_assertion_simps(14)
% 2.39/2.71 thf(fact_154_norm__assertion__simps_I31_J,axiom,
% 2.39/2.71 ! [X: assn] :
% 2.39/2.71 ( ( inf_inf_assn @ X @ X )
% 2.39/2.71 = X ) ).
% 2.39/2.71
% 2.39/2.71 % norm_assertion_simps(31)
% 2.39/2.71 thf(fact_155_assn__aci_I1_J,axiom,
% 2.39/2.71 ( inf_inf_assn
% 2.39/2.71 = ( ^ [X2: assn,Y2: assn] : ( inf_inf_assn @ Y2 @ X2 ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % assn_aci(1)
% 2.39/2.71 thf(fact_156_assn__aci_I3_J,axiom,
% 2.39/2.71 ! [X: assn,Y: assn,Z: assn] :
% 2.39/2.71 ( ( inf_inf_assn @ X @ ( inf_inf_assn @ Y @ Z ) )
% 2.39/2.71 = ( inf_inf_assn @ Y @ ( inf_inf_assn @ X @ Z ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % assn_aci(3)
% 2.39/2.71 thf(fact_157_assn__aci_I4_J,axiom,
% 2.39/2.71 ! [X: assn,Y: assn] :
% 2.39/2.71 ( ( inf_inf_assn @ X @ ( inf_inf_assn @ X @ Y ) )
% 2.39/2.71 = ( inf_inf_assn @ X @ Y ) ) ).
% 2.39/2.71
% 2.39/2.71 % assn_aci(4)
% 2.39/2.71 thf(fact_158_one__reorient,axiom,
% 2.39/2.71 ! [X: code_integer] :
% 2.39/2.71 ( ( one_one_Code_integer = X )
% 2.39/2.71 = ( X = one_one_Code_integer ) ) ).
% 2.39/2.71
% 2.39/2.71 % one_reorient
% 2.39/2.71 thf(fact_159_one__reorient,axiom,
% 2.39/2.71 ! [X: assn] :
% 2.39/2.71 ( ( one_one_assn = X )
% 2.39/2.71 = ( X = one_one_assn ) ) ).
% 2.39/2.71
% 2.39/2.71 % one_reorient
% 2.39/2.71 thf(fact_160_one__reorient,axiom,
% 2.39/2.71 ! [X: rat] :
% 2.39/2.71 ( ( one_one_rat = X )
% 2.39/2.71 = ( X = one_one_rat ) ) ).
% 2.39/2.71
% 2.39/2.71 % one_reorient
% 2.39/2.71 thf(fact_161_one__reorient,axiom,
% 2.39/2.71 ! [X: nat] :
% 2.39/2.71 ( ( one_one_nat = X )
% 2.39/2.71 = ( X = one_one_nat ) ) ).
% 2.39/2.71
% 2.39/2.71 % one_reorient
% 2.39/2.71 thf(fact_162_one__reorient,axiom,
% 2.39/2.71 ! [X: int] :
% 2.39/2.71 ( ( one_one_int = X )
% 2.39/2.71 = ( X = one_one_int ) ) ).
% 2.39/2.71
% 2.39/2.71 % one_reorient
% 2.39/2.71 thf(fact_163_mod__and__dist,axiom,
% 2.39/2.71 ! [P2: assn,Q2: assn,H2: produc3658429121746597890et_nat] :
% 2.39/2.71 ( ( rep_assn @ ( inf_inf_assn @ P2 @ Q2 ) @ H2 )
% 2.39/2.71 = ( ( rep_assn @ P2 @ H2 )
% 2.39/2.71 & ( rep_assn @ Q2 @ H2 ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % mod_and_dist
% 2.39/2.71 thf(fact_164_mod__starE,axiom,
% 2.39/2.71 ! [A: assn,B: assn,H2: produc3658429121746597890et_nat] :
% 2.39/2.71 ( ( rep_assn @ ( times_times_assn @ A @ B ) @ H2 )
% 2.39/2.71 => ~ ( ? [X_1: produc3658429121746597890et_nat] : ( rep_assn @ A @ X_1 )
% 2.39/2.71 => ! [H_2: produc3658429121746597890et_nat] :
% 2.39/2.71 ~ ( rep_assn @ B @ H_2 ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % mod_starE
% 2.39/2.71 thf(fact_165_mod__starD,axiom,
% 2.39/2.71 ! [A3: assn,B3: assn,H2: produc3658429121746597890et_nat] :
% 2.39/2.71 ( ( rep_assn @ ( times_times_assn @ A3 @ B3 ) @ H2 )
% 2.39/2.71 => ? [H1: produc3658429121746597890et_nat,H22: produc3658429121746597890et_nat] :
% 2.39/2.71 ( ( rep_assn @ A3 @ H1 )
% 2.39/2.71 & ( rep_assn @ B3 @ H22 ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % mod_starD
% 2.39/2.71 thf(fact_166_entails__def,axiom,
% 2.39/2.71 ( entails
% 2.39/2.71 = ( ^ [P: assn,Q: assn] :
% 2.39/2.71 ! [H: produc3658429121746597890et_nat] :
% 2.39/2.71 ( ( rep_assn @ P @ H )
% 2.39/2.71 => ( rep_assn @ Q @ H ) ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % entails_def
% 2.39/2.71 thf(fact_167_entailsI,axiom,
% 2.39/2.71 ! [P2: assn,Q2: assn] :
% 2.39/2.71 ( ! [H3: produc3658429121746597890et_nat] :
% 2.39/2.71 ( ( rep_assn @ P2 @ H3 )
% 2.39/2.71 => ( rep_assn @ Q2 @ H3 ) )
% 2.39/2.71 => ( entails @ P2 @ Q2 ) ) ).
% 2.39/2.71
% 2.39/2.71 % entailsI
% 2.39/2.71 thf(fact_168_entailsD,axiom,
% 2.39/2.71 ! [P2: assn,Q2: assn,H2: produc3658429121746597890et_nat] :
% 2.39/2.71 ( ( entails @ P2 @ Q2 )
% 2.39/2.71 => ( ( rep_assn @ P2 @ H2 )
% 2.39/2.71 => ( rep_assn @ Q2 @ H2 ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % entailsD
% 2.39/2.71 thf(fact_169_ent__fwd,axiom,
% 2.39/2.71 ! [P2: assn,H2: produc3658429121746597890et_nat,Q2: assn] :
% 2.39/2.71 ( ( rep_assn @ P2 @ H2 )
% 2.39/2.71 => ( ( entails @ P2 @ Q2 )
% 2.39/2.71 => ( rep_assn @ Q2 @ H2 ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % ent_fwd
% 2.39/2.71 thf(fact_170_mult_Ocomm__neutral,axiom,
% 2.39/2.71 ! [A: rat] :
% 2.39/2.71 ( ( times_times_rat @ A @ one_one_rat )
% 2.39/2.71 = A ) ).
% 2.39/2.71
% 2.39/2.71 % mult.comm_neutral
% 2.39/2.71 thf(fact_171_mult_Ocomm__neutral,axiom,
% 2.39/2.71 ! [A: assn] :
% 2.39/2.71 ( ( times_times_assn @ A @ one_one_assn )
% 2.39/2.71 = A ) ).
% 2.39/2.71
% 2.39/2.71 % mult.comm_neutral
% 2.39/2.71 thf(fact_172_mult_Ocomm__neutral,axiom,
% 2.39/2.71 ! [A: nat] :
% 2.39/2.71 ( ( times_times_nat @ A @ one_one_nat )
% 2.39/2.71 = A ) ).
% 2.39/2.71
% 2.39/2.71 % mult.comm_neutral
% 2.39/2.71 thf(fact_173_mult_Ocomm__neutral,axiom,
% 2.39/2.71 ! [A: int] :
% 2.39/2.71 ( ( times_times_int @ A @ one_one_int )
% 2.39/2.71 = A ) ).
% 2.39/2.71
% 2.39/2.71 % mult.comm_neutral
% 2.39/2.71 thf(fact_174_mult_Ocomm__neutral,axiom,
% 2.39/2.71 ! [A: code_integer] :
% 2.39/2.71 ( ( times_3573771949741848930nteger @ A @ one_one_Code_integer )
% 2.39/2.71 = A ) ).
% 2.39/2.71
% 2.39/2.71 % mult.comm_neutral
% 2.39/2.71 thf(fact_175_mult_Ocomm__neutral,axiom,
% 2.39/2.71 ! [A: code_natural] :
% 2.39/2.71 ( ( times_2397367101498566445atural @ A @ one_one_Code_natural )
% 2.39/2.71 = A ) ).
% 2.39/2.71
% 2.39/2.71 % mult.comm_neutral
% 2.39/2.71 thf(fact_176_comm__monoid__mult__class_Omult__1,axiom,
% 2.39/2.71 ! [A: rat] :
% 2.39/2.71 ( ( times_times_rat @ one_one_rat @ A )
% 2.39/2.71 = A ) ).
% 2.39/2.71
% 2.39/2.71 % comm_monoid_mult_class.mult_1
% 2.39/2.71 thf(fact_177_comm__monoid__mult__class_Omult__1,axiom,
% 2.39/2.71 ! [A: assn] :
% 2.39/2.71 ( ( times_times_assn @ one_one_assn @ A )
% 2.39/2.71 = A ) ).
% 2.39/2.71
% 2.39/2.71 % comm_monoid_mult_class.mult_1
% 2.39/2.71 thf(fact_178_comm__monoid__mult__class_Omult__1,axiom,
% 2.39/2.71 ! [A: nat] :
% 2.39/2.71 ( ( times_times_nat @ one_one_nat @ A )
% 2.39/2.71 = A ) ).
% 2.39/2.71
% 2.39/2.71 % comm_monoid_mult_class.mult_1
% 2.39/2.71 thf(fact_179_comm__monoid__mult__class_Omult__1,axiom,
% 2.39/2.71 ! [A: int] :
% 2.39/2.71 ( ( times_times_int @ one_one_int @ A )
% 2.39/2.71 = A ) ).
% 2.39/2.71
% 2.39/2.71 % comm_monoid_mult_class.mult_1
% 2.39/2.71 thf(fact_180_comm__monoid__mult__class_Omult__1,axiom,
% 2.39/2.71 ! [A: code_integer] :
% 2.39/2.71 ( ( times_3573771949741848930nteger @ one_one_Code_integer @ A )
% 2.39/2.71 = A ) ).
% 2.39/2.71
% 2.39/2.71 % comm_monoid_mult_class.mult_1
% 2.39/2.71 thf(fact_181_comm__monoid__mult__class_Omult__1,axiom,
% 2.39/2.71 ! [A: code_natural] :
% 2.39/2.71 ( ( times_2397367101498566445atural @ one_one_Code_natural @ A )
% 2.39/2.71 = A ) ).
% 2.39/2.71
% 2.39/2.71 % comm_monoid_mult_class.mult_1
% 2.39/2.71 thf(fact_182_ent__conjE2,axiom,
% 2.39/2.71 ! [B3: assn,C2: assn,A3: assn] :
% 2.39/2.71 ( ( entails @ B3 @ C2 )
% 2.39/2.71 => ( entails @ ( inf_inf_assn @ A3 @ B3 ) @ C2 ) ) ).
% 2.39/2.71
% 2.39/2.71 % ent_conjE2
% 2.39/2.71 thf(fact_183_ent__conjE1,axiom,
% 2.39/2.71 ! [A3: assn,C2: assn,B3: assn] :
% 2.39/2.71 ( ( entails @ A3 @ C2 )
% 2.39/2.71 => ( entails @ ( inf_inf_assn @ A3 @ B3 ) @ C2 ) ) ).
% 2.39/2.71
% 2.39/2.71 % ent_conjE1
% 2.39/2.71 thf(fact_184_ent__conjI,axiom,
% 2.39/2.71 ! [A3: assn,B3: assn,C2: assn] :
% 2.39/2.71 ( ( entails @ A3 @ B3 )
% 2.39/2.71 => ( ( entails @ A3 @ C2 )
% 2.39/2.71 => ( entails @ A3 @ ( inf_inf_assn @ B3 @ C2 ) ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % ent_conjI
% 2.39/2.71 thf(fact_185_assn__one__left,axiom,
% 2.39/2.71 ! [P2: assn] :
% 2.39/2.71 ( ( times_times_assn @ one_one_assn @ P2 )
% 2.39/2.71 = P2 ) ).
% 2.39/2.71
% 2.39/2.71 % assn_one_left
% 2.39/2.71 thf(fact_186_norm__assertion__simps_I1_J,axiom,
% 2.39/2.71 ! [A: assn] :
% 2.39/2.71 ( ( times_times_assn @ one_one_assn @ A )
% 2.39/2.71 = A ) ).
% 2.39/2.71
% 2.39/2.71 % norm_assertion_simps(1)
% 2.39/2.71 thf(fact_187_norm__assertion__simps_I2_J,axiom,
% 2.39/2.71 ! [A: assn] :
% 2.39/2.71 ( ( times_times_assn @ A @ one_one_assn )
% 2.39/2.71 = A ) ).
% 2.39/2.71
% 2.39/2.71 % norm_assertion_simps(2)
% 2.39/2.71 thf(fact_188_is__pure__assn__basic__simps_I2_J,axiom,
% 2.39/2.71 is_pure_assn @ one_one_assn ).
% 2.39/2.71
% 2.39/2.71 % is_pure_assn_basic_simps(2)
% 2.39/2.71 thf(fact_189_SLN__def,axiom,
% 2.39/2.71 sln = one_one_assn ).
% 2.39/2.71
% 2.39/2.71 % SLN_def
% 2.39/2.71 thf(fact_190_mult_Oac__operator__axioms,axiom,
% 2.39/2.71 syntax3673046151410588037r_assn @ times_times_assn ).
% 2.39/2.71
% 2.39/2.71 % mult.ac_operator_axioms
% 2.39/2.71 thf(fact_191_mult_Oac__operator__axioms,axiom,
% 2.39/2.71 syntax8800539067650720301or_nat @ times_times_nat ).
% 2.39/2.71
% 2.39/2.71 % mult.ac_operator_axioms
% 2.39/2.71 thf(fact_192_mult_Oac__operator__axioms,axiom,
% 2.39/2.71 syntax8798048597141670025or_int @ times_times_int ).
% 2.39/2.71
% 2.39/2.71 % mult.ac_operator_axioms
% 2.39/2.71 thf(fact_193_mult_Oac__operator__axioms,axiom,
% 2.39/2.71 syntax414191934074104506nteger @ times_3573771949741848930nteger ).
% 2.39/2.71
% 2.39/2.71 % mult.ac_operator_axioms
% 2.39/2.71 thf(fact_194_mult_Oac__operator__axioms,axiom,
% 2.39/2.71 syntax8461159122685597829atural @ times_2397367101498566445atural ).
% 2.39/2.71
% 2.39/2.71 % mult.ac_operator_axioms
% 2.39/2.71 thf(fact_195_zip_Osimps_I1_J,axiom,
% 2.39/2.71 ! [Xs: list_assn] :
% 2.39/2.71 ( ( zip_assn_assn @ Xs @ nil_assn )
% 2.39/2.71 = nil_Pr5671120429643327159n_assn ) ).
% 2.39/2.71
% 2.39/2.71 % zip.simps(1)
% 2.39/2.71 thf(fact_196_inf__apply,axiom,
% 2.39/2.71 ( inf_in3604695632404883862_int_o
% 2.39/2.71 = ( ^ [F3: product_prod_int_int > $o,G: product_prod_int_int > $o,X2: product_prod_int_int] : ( inf_inf_o @ ( F3 @ X2 ) @ ( G @ X2 ) ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_apply
% 2.39/2.71 thf(fact_197_inf__right__idem,axiom,
% 2.39/2.71 ! [X: assn,Y: assn] :
% 2.39/2.71 ( ( inf_inf_assn @ ( inf_inf_assn @ X @ Y ) @ Y )
% 2.39/2.71 = ( inf_inf_assn @ X @ Y ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_right_idem
% 2.39/2.71 thf(fact_198_inf__right__idem,axiom,
% 2.39/2.71 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 2.39/2.71 ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ Y )
% 2.39/2.71 = ( inf_in2572325071724192079at_nat @ X @ Y ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_right_idem
% 2.39/2.71 thf(fact_199_inf__right__idem,axiom,
% 2.39/2.71 ! [X: set_nat,Y: set_nat] :
% 2.39/2.71 ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ Y )
% 2.39/2.71 = ( inf_inf_set_nat @ X @ Y ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_right_idem
% 2.39/2.71 thf(fact_200_inf__right__idem,axiom,
% 2.39/2.71 ! [X: nat,Y: nat] :
% 2.39/2.71 ( ( inf_inf_nat @ ( inf_inf_nat @ X @ Y ) @ Y )
% 2.39/2.71 = ( inf_inf_nat @ X @ Y ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_right_idem
% 2.39/2.71 thf(fact_201_inf__right__idem,axiom,
% 2.39/2.71 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 2.39/2.71 ( ( inf_in3604695632404883862_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ Y )
% 2.39/2.71 = ( inf_in3604695632404883862_int_o @ X @ Y ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_right_idem
% 2.39/2.71 thf(fact_202_inf_Oright__idem,axiom,
% 2.39/2.71 ! [A: assn,B: assn] :
% 2.39/2.71 ( ( inf_inf_assn @ ( inf_inf_assn @ A @ B ) @ B )
% 2.39/2.71 = ( inf_inf_assn @ A @ B ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf.right_idem
% 2.39/2.71 thf(fact_203_inf_Oright__idem,axiom,
% 2.39/2.71 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.39/2.71 ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ B )
% 2.39/2.71 = ( inf_in2572325071724192079at_nat @ A @ B ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf.right_idem
% 2.39/2.71 thf(fact_204_inf_Oright__idem,axiom,
% 2.39/2.71 ! [A: set_nat,B: set_nat] :
% 2.39/2.71 ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ A @ B ) @ B )
% 2.39/2.71 = ( inf_inf_set_nat @ A @ B ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf.right_idem
% 2.39/2.71 thf(fact_205_inf_Oright__idem,axiom,
% 2.39/2.71 ! [A: nat,B: nat] :
% 2.39/2.71 ( ( inf_inf_nat @ ( inf_inf_nat @ A @ B ) @ B )
% 2.39/2.71 = ( inf_inf_nat @ A @ B ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf.right_idem
% 2.39/2.71 thf(fact_206_inf_Oright__idem,axiom,
% 2.39/2.71 ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 2.39/2.71 ( ( inf_in3604695632404883862_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ B )
% 2.39/2.71 = ( inf_in3604695632404883862_int_o @ A @ B ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf.right_idem
% 2.39/2.71 thf(fact_207_inf__left__idem,axiom,
% 2.39/2.71 ! [X: assn,Y: assn] :
% 2.39/2.71 ( ( inf_inf_assn @ X @ ( inf_inf_assn @ X @ Y ) )
% 2.39/2.71 = ( inf_inf_assn @ X @ Y ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_left_idem
% 2.39/2.71 thf(fact_208_inf__left__idem,axiom,
% 2.39/2.71 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 2.39/2.71 ( ( inf_in2572325071724192079at_nat @ X @ ( inf_in2572325071724192079at_nat @ X @ Y ) )
% 2.39/2.71 = ( inf_in2572325071724192079at_nat @ X @ Y ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_left_idem
% 2.39/2.71 thf(fact_209_inf__left__idem,axiom,
% 2.39/2.71 ! [X: set_nat,Y: set_nat] :
% 2.39/2.71 ( ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ X @ Y ) )
% 2.39/2.71 = ( inf_inf_set_nat @ X @ Y ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_left_idem
% 2.39/2.71 thf(fact_210_inf__left__idem,axiom,
% 2.39/2.71 ! [X: nat,Y: nat] :
% 2.39/2.71 ( ( inf_inf_nat @ X @ ( inf_inf_nat @ X @ Y ) )
% 2.39/2.71 = ( inf_inf_nat @ X @ Y ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_left_idem
% 2.39/2.71 thf(fact_211_inf__left__idem,axiom,
% 2.39/2.71 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 2.39/2.71 ( ( inf_in3604695632404883862_int_o @ X @ ( inf_in3604695632404883862_int_o @ X @ Y ) )
% 2.39/2.71 = ( inf_in3604695632404883862_int_o @ X @ Y ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_left_idem
% 2.39/2.71 thf(fact_212_inf_Oleft__idem,axiom,
% 2.39/2.71 ! [A: assn,B: assn] :
% 2.39/2.71 ( ( inf_inf_assn @ A @ ( inf_inf_assn @ A @ B ) )
% 2.39/2.71 = ( inf_inf_assn @ A @ B ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf.left_idem
% 2.39/2.71 thf(fact_213_inf_Oleft__idem,axiom,
% 2.39/2.71 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.39/2.71 ( ( inf_in2572325071724192079at_nat @ A @ ( inf_in2572325071724192079at_nat @ A @ B ) )
% 2.39/2.71 = ( inf_in2572325071724192079at_nat @ A @ B ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf.left_idem
% 2.39/2.71 thf(fact_214_inf_Oleft__idem,axiom,
% 2.39/2.71 ! [A: set_nat,B: set_nat] :
% 2.39/2.71 ( ( inf_inf_set_nat @ A @ ( inf_inf_set_nat @ A @ B ) )
% 2.39/2.71 = ( inf_inf_set_nat @ A @ B ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf.left_idem
% 2.39/2.71 thf(fact_215_inf_Oleft__idem,axiom,
% 2.39/2.71 ! [A: nat,B: nat] :
% 2.39/2.71 ( ( inf_inf_nat @ A @ ( inf_inf_nat @ A @ B ) )
% 2.39/2.71 = ( inf_inf_nat @ A @ B ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf.left_idem
% 2.39/2.71 thf(fact_216_inf_Oleft__idem,axiom,
% 2.39/2.71 ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 2.39/2.71 ( ( inf_in3604695632404883862_int_o @ A @ ( inf_in3604695632404883862_int_o @ A @ B ) )
% 2.39/2.71 = ( inf_in3604695632404883862_int_o @ A @ B ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf.left_idem
% 2.39/2.71 thf(fact_217_inf__idem,axiom,
% 2.39/2.71 ! [X: assn] :
% 2.39/2.71 ( ( inf_inf_assn @ X @ X )
% 2.39/2.71 = X ) ).
% 2.39/2.71
% 2.39/2.71 % inf_idem
% 2.39/2.71 thf(fact_218_inf__idem,axiom,
% 2.39/2.71 ! [X: set_Pr1261947904930325089at_nat] :
% 2.39/2.71 ( ( inf_in2572325071724192079at_nat @ X @ X )
% 2.39/2.71 = X ) ).
% 2.39/2.71
% 2.39/2.71 % inf_idem
% 2.39/2.71 thf(fact_219_inf__idem,axiom,
% 2.39/2.71 ! [X: set_nat] :
% 2.39/2.71 ( ( inf_inf_set_nat @ X @ X )
% 2.39/2.71 = X ) ).
% 2.39/2.71
% 2.39/2.71 % inf_idem
% 2.39/2.71 thf(fact_220_inf__idem,axiom,
% 2.39/2.71 ! [X: nat] :
% 2.39/2.71 ( ( inf_inf_nat @ X @ X )
% 2.39/2.71 = X ) ).
% 2.39/2.71
% 2.39/2.71 % inf_idem
% 2.39/2.71 thf(fact_221_inf__idem,axiom,
% 2.39/2.71 ! [X: product_prod_int_int > $o] :
% 2.39/2.71 ( ( inf_in3604695632404883862_int_o @ X @ X )
% 2.39/2.71 = X ) ).
% 2.39/2.71
% 2.39/2.71 % inf_idem
% 2.39/2.71 thf(fact_222_inf_Oidem,axiom,
% 2.39/2.71 ! [A: assn] :
% 2.39/2.71 ( ( inf_inf_assn @ A @ A )
% 2.39/2.71 = A ) ).
% 2.39/2.71
% 2.39/2.71 % inf.idem
% 2.39/2.71 thf(fact_223_inf_Oidem,axiom,
% 2.39/2.71 ! [A: set_Pr1261947904930325089at_nat] :
% 2.39/2.71 ( ( inf_in2572325071724192079at_nat @ A @ A )
% 2.39/2.71 = A ) ).
% 2.39/2.71
% 2.39/2.71 % inf.idem
% 2.39/2.71 thf(fact_224_inf_Oidem,axiom,
% 2.39/2.71 ! [A: set_nat] :
% 2.39/2.71 ( ( inf_inf_set_nat @ A @ A )
% 2.39/2.71 = A ) ).
% 2.39/2.71
% 2.39/2.71 % inf.idem
% 2.39/2.71 thf(fact_225_inf_Oidem,axiom,
% 2.39/2.71 ! [A: nat] :
% 2.39/2.71 ( ( inf_inf_nat @ A @ A )
% 2.39/2.71 = A ) ).
% 2.39/2.71
% 2.39/2.71 % inf.idem
% 2.39/2.71 thf(fact_226_inf_Oidem,axiom,
% 2.39/2.71 ! [A: product_prod_int_int > $o] :
% 2.39/2.71 ( ( inf_in3604695632404883862_int_o @ A @ A )
% 2.39/2.71 = A ) ).
% 2.39/2.71
% 2.39/2.71 % inf.idem
% 2.39/2.71 thf(fact_227_inf__fun__def,axiom,
% 2.39/2.71 ( inf_in3604695632404883862_int_o
% 2.39/2.71 = ( ^ [F3: product_prod_int_int > $o,G: product_prod_int_int > $o,X2: product_prod_int_int] : ( inf_inf_o @ ( F3 @ X2 ) @ ( G @ X2 ) ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_fun_def
% 2.39/2.71 thf(fact_228_inf__sup__aci_I4_J,axiom,
% 2.39/2.71 ! [X: assn,Y: assn] :
% 2.39/2.71 ( ( inf_inf_assn @ X @ ( inf_inf_assn @ X @ Y ) )
% 2.39/2.71 = ( inf_inf_assn @ X @ Y ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_sup_aci(4)
% 2.39/2.71 thf(fact_229_inf__sup__aci_I4_J,axiom,
% 2.39/2.71 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 2.39/2.71 ( ( inf_in2572325071724192079at_nat @ X @ ( inf_in2572325071724192079at_nat @ X @ Y ) )
% 2.39/2.71 = ( inf_in2572325071724192079at_nat @ X @ Y ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_sup_aci(4)
% 2.39/2.71 thf(fact_230_inf__sup__aci_I4_J,axiom,
% 2.39/2.71 ! [X: set_nat,Y: set_nat] :
% 2.39/2.71 ( ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ X @ Y ) )
% 2.39/2.71 = ( inf_inf_set_nat @ X @ Y ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_sup_aci(4)
% 2.39/2.71 thf(fact_231_inf__sup__aci_I4_J,axiom,
% 2.39/2.71 ! [X: nat,Y: nat] :
% 2.39/2.71 ( ( inf_inf_nat @ X @ ( inf_inf_nat @ X @ Y ) )
% 2.39/2.71 = ( inf_inf_nat @ X @ Y ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_sup_aci(4)
% 2.39/2.71 thf(fact_232_inf__sup__aci_I4_J,axiom,
% 2.39/2.71 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 2.39/2.71 ( ( inf_in3604695632404883862_int_o @ X @ ( inf_in3604695632404883862_int_o @ X @ Y ) )
% 2.39/2.71 = ( inf_in3604695632404883862_int_o @ X @ Y ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_sup_aci(4)
% 2.39/2.71 thf(fact_233_inf__sup__aci_I3_J,axiom,
% 2.39/2.71 ! [X: assn,Y: assn,Z: assn] :
% 2.39/2.71 ( ( inf_inf_assn @ X @ ( inf_inf_assn @ Y @ Z ) )
% 2.39/2.71 = ( inf_inf_assn @ Y @ ( inf_inf_assn @ X @ Z ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_sup_aci(3)
% 2.39/2.71 thf(fact_234_inf__sup__aci_I3_J,axiom,
% 2.39/2.71 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 2.39/2.71 ( ( inf_in2572325071724192079at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) )
% 2.39/2.71 = ( inf_in2572325071724192079at_nat @ Y @ ( inf_in2572325071724192079at_nat @ X @ Z ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_sup_aci(3)
% 2.39/2.71 thf(fact_235_inf__sup__aci_I3_J,axiom,
% 2.39/2.71 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 2.39/2.71 ( ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) )
% 2.39/2.71 = ( inf_inf_set_nat @ Y @ ( inf_inf_set_nat @ X @ Z ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_sup_aci(3)
% 2.39/2.71 thf(fact_236_inf__sup__aci_I3_J,axiom,
% 2.39/2.71 ! [X: nat,Y: nat,Z: nat] :
% 2.39/2.71 ( ( inf_inf_nat @ X @ ( inf_inf_nat @ Y @ Z ) )
% 2.39/2.71 = ( inf_inf_nat @ Y @ ( inf_inf_nat @ X @ Z ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_sup_aci(3)
% 2.39/2.71 thf(fact_237_inf__sup__aci_I3_J,axiom,
% 2.39/2.71 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 2.39/2.71 ( ( inf_in3604695632404883862_int_o @ X @ ( inf_in3604695632404883862_int_o @ Y @ Z ) )
% 2.39/2.71 = ( inf_in3604695632404883862_int_o @ Y @ ( inf_in3604695632404883862_int_o @ X @ Z ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_sup_aci(3)
% 2.39/2.71 thf(fact_238_inf__sup__aci_I2_J,axiom,
% 2.39/2.71 ! [X: assn,Y: assn,Z: assn] :
% 2.39/2.71 ( ( inf_inf_assn @ ( inf_inf_assn @ X @ Y ) @ Z )
% 2.39/2.71 = ( inf_inf_assn @ X @ ( inf_inf_assn @ Y @ Z ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_sup_aci(2)
% 2.39/2.71 thf(fact_239_inf__sup__aci_I2_J,axiom,
% 2.39/2.71 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 2.39/2.71 ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ Z )
% 2.39/2.71 = ( inf_in2572325071724192079at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_sup_aci(2)
% 2.39/2.71 thf(fact_240_inf__sup__aci_I2_J,axiom,
% 2.39/2.71 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 2.39/2.71 ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ Z )
% 2.39/2.71 = ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_sup_aci(2)
% 2.39/2.71 thf(fact_241_inf__sup__aci_I2_J,axiom,
% 2.39/2.71 ! [X: nat,Y: nat,Z: nat] :
% 2.39/2.71 ( ( inf_inf_nat @ ( inf_inf_nat @ X @ Y ) @ Z )
% 2.39/2.71 = ( inf_inf_nat @ X @ ( inf_inf_nat @ Y @ Z ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_sup_aci(2)
% 2.39/2.71 thf(fact_242_inf__sup__aci_I2_J,axiom,
% 2.39/2.71 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 2.39/2.71 ( ( inf_in3604695632404883862_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ Z )
% 2.39/2.71 = ( inf_in3604695632404883862_int_o @ X @ ( inf_in3604695632404883862_int_o @ Y @ Z ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_sup_aci(2)
% 2.39/2.71 thf(fact_243_inf__sup__aci_I1_J,axiom,
% 2.39/2.71 ( inf_inf_assn
% 2.39/2.71 = ( ^ [X2: assn,Y2: assn] : ( inf_inf_assn @ Y2 @ X2 ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_sup_aci(1)
% 2.39/2.71 thf(fact_244_inf__sup__aci_I1_J,axiom,
% 2.39/2.71 ( inf_in2572325071724192079at_nat
% 2.39/2.71 = ( ^ [X2: set_Pr1261947904930325089at_nat,Y2: set_Pr1261947904930325089at_nat] : ( inf_in2572325071724192079at_nat @ Y2 @ X2 ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_sup_aci(1)
% 2.39/2.71 thf(fact_245_inf__sup__aci_I1_J,axiom,
% 2.39/2.71 ( inf_inf_set_nat
% 2.39/2.71 = ( ^ [X2: set_nat,Y2: set_nat] : ( inf_inf_set_nat @ Y2 @ X2 ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_sup_aci(1)
% 2.39/2.71 thf(fact_246_inf__sup__aci_I1_J,axiom,
% 2.39/2.71 ( inf_inf_nat
% 2.39/2.71 = ( ^ [X2: nat,Y2: nat] : ( inf_inf_nat @ Y2 @ X2 ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_sup_aci(1)
% 2.39/2.71 thf(fact_247_inf__sup__aci_I1_J,axiom,
% 2.39/2.71 ( inf_in3604695632404883862_int_o
% 2.39/2.71 = ( ^ [X2: product_prod_int_int > $o,Y2: product_prod_int_int > $o] : ( inf_in3604695632404883862_int_o @ Y2 @ X2 ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_sup_aci(1)
% 2.39/2.71 thf(fact_248_inf_Oassoc,axiom,
% 2.39/2.71 ! [A: assn,B: assn,C: assn] :
% 2.39/2.71 ( ( inf_inf_assn @ ( inf_inf_assn @ A @ B ) @ C )
% 2.39/2.71 = ( inf_inf_assn @ A @ ( inf_inf_assn @ B @ C ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf.assoc
% 2.39/2.71 thf(fact_249_inf_Oassoc,axiom,
% 2.39/2.71 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat] :
% 2.39/2.71 ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ C )
% 2.39/2.71 = ( inf_in2572325071724192079at_nat @ A @ ( inf_in2572325071724192079at_nat @ B @ C ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf.assoc
% 2.39/2.71 thf(fact_250_inf_Oassoc,axiom,
% 2.39/2.71 ! [A: set_nat,B: set_nat,C: set_nat] :
% 2.39/2.71 ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ A @ B ) @ C )
% 2.39/2.71 = ( inf_inf_set_nat @ A @ ( inf_inf_set_nat @ B @ C ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf.assoc
% 2.39/2.71 thf(fact_251_inf_Oassoc,axiom,
% 2.39/2.71 ! [A: nat,B: nat,C: nat] :
% 2.39/2.71 ( ( inf_inf_nat @ ( inf_inf_nat @ A @ B ) @ C )
% 2.39/2.71 = ( inf_inf_nat @ A @ ( inf_inf_nat @ B @ C ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf.assoc
% 2.39/2.71 thf(fact_252_inf_Oassoc,axiom,
% 2.39/2.71 ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o,C: product_prod_int_int > $o] :
% 2.39/2.71 ( ( inf_in3604695632404883862_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ C )
% 2.39/2.71 = ( inf_in3604695632404883862_int_o @ A @ ( inf_in3604695632404883862_int_o @ B @ C ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf.assoc
% 2.39/2.71 thf(fact_253_inf__assoc,axiom,
% 2.39/2.71 ! [X: assn,Y: assn,Z: assn] :
% 2.39/2.71 ( ( inf_inf_assn @ ( inf_inf_assn @ X @ Y ) @ Z )
% 2.39/2.71 = ( inf_inf_assn @ X @ ( inf_inf_assn @ Y @ Z ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_assoc
% 2.39/2.71 thf(fact_254_inf__assoc,axiom,
% 2.39/2.71 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 2.39/2.71 ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ Z )
% 2.39/2.71 = ( inf_in2572325071724192079at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_assoc
% 2.39/2.71 thf(fact_255_inf__assoc,axiom,
% 2.39/2.71 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 2.39/2.71 ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ Z )
% 2.39/2.71 = ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_assoc
% 2.39/2.71 thf(fact_256_inf__assoc,axiom,
% 2.39/2.71 ! [X: nat,Y: nat,Z: nat] :
% 2.39/2.71 ( ( inf_inf_nat @ ( inf_inf_nat @ X @ Y ) @ Z )
% 2.39/2.71 = ( inf_inf_nat @ X @ ( inf_inf_nat @ Y @ Z ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_assoc
% 2.39/2.71 thf(fact_257_inf__assoc,axiom,
% 2.39/2.71 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 2.39/2.71 ( ( inf_in3604695632404883862_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ Z )
% 2.39/2.71 = ( inf_in3604695632404883862_int_o @ X @ ( inf_in3604695632404883862_int_o @ Y @ Z ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_assoc
% 2.39/2.71 thf(fact_258_inf_Ocommute,axiom,
% 2.39/2.71 ( inf_inf_assn
% 2.39/2.71 = ( ^ [A2: assn,B2: assn] : ( inf_inf_assn @ B2 @ A2 ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf.commute
% 2.39/2.71 thf(fact_259_inf_Ocommute,axiom,
% 2.39/2.71 ( inf_in2572325071724192079at_nat
% 2.39/2.71 = ( ^ [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] : ( inf_in2572325071724192079at_nat @ B2 @ A2 ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf.commute
% 2.39/2.71 thf(fact_260_inf_Ocommute,axiom,
% 2.39/2.71 ( inf_inf_set_nat
% 2.39/2.71 = ( ^ [A2: set_nat,B2: set_nat] : ( inf_inf_set_nat @ B2 @ A2 ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf.commute
% 2.39/2.71 thf(fact_261_inf_Ocommute,axiom,
% 2.39/2.71 ( inf_inf_nat
% 2.39/2.71 = ( ^ [A2: nat,B2: nat] : ( inf_inf_nat @ B2 @ A2 ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf.commute
% 2.39/2.71 thf(fact_262_inf_Ocommute,axiom,
% 2.39/2.71 ( inf_in3604695632404883862_int_o
% 2.39/2.71 = ( ^ [A2: product_prod_int_int > $o,B2: product_prod_int_int > $o] : ( inf_in3604695632404883862_int_o @ B2 @ A2 ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf.commute
% 2.39/2.71 thf(fact_263_inf__commute,axiom,
% 2.39/2.71 ( inf_inf_assn
% 2.39/2.71 = ( ^ [X2: assn,Y2: assn] : ( inf_inf_assn @ Y2 @ X2 ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_commute
% 2.39/2.71 thf(fact_264_inf__commute,axiom,
% 2.39/2.71 ( inf_in2572325071724192079at_nat
% 2.39/2.71 = ( ^ [X2: set_Pr1261947904930325089at_nat,Y2: set_Pr1261947904930325089at_nat] : ( inf_in2572325071724192079at_nat @ Y2 @ X2 ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_commute
% 2.39/2.71 thf(fact_265_inf__commute,axiom,
% 2.39/2.71 ( inf_inf_set_nat
% 2.39/2.71 = ( ^ [X2: set_nat,Y2: set_nat] : ( inf_inf_set_nat @ Y2 @ X2 ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_commute
% 2.39/2.71 thf(fact_266_inf__commute,axiom,
% 2.39/2.71 ( inf_inf_nat
% 2.39/2.71 = ( ^ [X2: nat,Y2: nat] : ( inf_inf_nat @ Y2 @ X2 ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_commute
% 2.39/2.71 thf(fact_267_inf__commute,axiom,
% 2.39/2.71 ( inf_in3604695632404883862_int_o
% 2.39/2.71 = ( ^ [X2: product_prod_int_int > $o,Y2: product_prod_int_int > $o] : ( inf_in3604695632404883862_int_o @ Y2 @ X2 ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_commute
% 2.39/2.71 thf(fact_268_inf_Oleft__commute,axiom,
% 2.39/2.71 ! [B: assn,A: assn,C: assn] :
% 2.39/2.71 ( ( inf_inf_assn @ B @ ( inf_inf_assn @ A @ C ) )
% 2.39/2.71 = ( inf_inf_assn @ A @ ( inf_inf_assn @ B @ C ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf.left_commute
% 2.39/2.71 thf(fact_269_inf_Oleft__commute,axiom,
% 2.39/2.71 ! [B: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat] :
% 2.39/2.71 ( ( inf_in2572325071724192079at_nat @ B @ ( inf_in2572325071724192079at_nat @ A @ C ) )
% 2.39/2.71 = ( inf_in2572325071724192079at_nat @ A @ ( inf_in2572325071724192079at_nat @ B @ C ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf.left_commute
% 2.39/2.71 thf(fact_270_inf_Oleft__commute,axiom,
% 2.39/2.71 ! [B: set_nat,A: set_nat,C: set_nat] :
% 2.39/2.71 ( ( inf_inf_set_nat @ B @ ( inf_inf_set_nat @ A @ C ) )
% 2.39/2.71 = ( inf_inf_set_nat @ A @ ( inf_inf_set_nat @ B @ C ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf.left_commute
% 2.39/2.71 thf(fact_271_inf_Oleft__commute,axiom,
% 2.39/2.71 ! [B: nat,A: nat,C: nat] :
% 2.39/2.71 ( ( inf_inf_nat @ B @ ( inf_inf_nat @ A @ C ) )
% 2.39/2.71 = ( inf_inf_nat @ A @ ( inf_inf_nat @ B @ C ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf.left_commute
% 2.39/2.71 thf(fact_272_inf_Oleft__commute,axiom,
% 2.39/2.71 ! [B: product_prod_int_int > $o,A: product_prod_int_int > $o,C: product_prod_int_int > $o] :
% 2.39/2.71 ( ( inf_in3604695632404883862_int_o @ B @ ( inf_in3604695632404883862_int_o @ A @ C ) )
% 2.39/2.71 = ( inf_in3604695632404883862_int_o @ A @ ( inf_in3604695632404883862_int_o @ B @ C ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf.left_commute
% 2.39/2.71 thf(fact_273_inf__left__commute,axiom,
% 2.39/2.71 ! [X: assn,Y: assn,Z: assn] :
% 2.39/2.71 ( ( inf_inf_assn @ X @ ( inf_inf_assn @ Y @ Z ) )
% 2.39/2.71 = ( inf_inf_assn @ Y @ ( inf_inf_assn @ X @ Z ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_left_commute
% 2.39/2.71 thf(fact_274_inf__left__commute,axiom,
% 2.39/2.71 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 2.39/2.71 ( ( inf_in2572325071724192079at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) )
% 2.39/2.71 = ( inf_in2572325071724192079at_nat @ Y @ ( inf_in2572325071724192079at_nat @ X @ Z ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_left_commute
% 2.39/2.71 thf(fact_275_inf__left__commute,axiom,
% 2.39/2.71 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 2.39/2.71 ( ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) )
% 2.39/2.71 = ( inf_inf_set_nat @ Y @ ( inf_inf_set_nat @ X @ Z ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_left_commute
% 2.39/2.71 thf(fact_276_inf__left__commute,axiom,
% 2.39/2.71 ! [X: nat,Y: nat,Z: nat] :
% 2.39/2.71 ( ( inf_inf_nat @ X @ ( inf_inf_nat @ Y @ Z ) )
% 2.39/2.71 = ( inf_inf_nat @ Y @ ( inf_inf_nat @ X @ Z ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_left_commute
% 2.39/2.71 thf(fact_277_inf__left__commute,axiom,
% 2.39/2.71 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 2.39/2.71 ( ( inf_in3604695632404883862_int_o @ X @ ( inf_in3604695632404883862_int_o @ Y @ Z ) )
% 2.39/2.71 = ( inf_in3604695632404883862_int_o @ Y @ ( inf_in3604695632404883862_int_o @ X @ Z ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_left_commute
% 2.39/2.71 thf(fact_278_boolean__algebra__cancel_Oinf1,axiom,
% 2.39/2.71 ! [A3: assn,K: assn,A: assn,B: assn] :
% 2.39/2.71 ( ( A3
% 2.39/2.71 = ( inf_inf_assn @ K @ A ) )
% 2.39/2.71 => ( ( inf_inf_assn @ A3 @ B )
% 2.39/2.71 = ( inf_inf_assn @ K @ ( inf_inf_assn @ A @ B ) ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % boolean_algebra_cancel.inf1
% 2.39/2.71 thf(fact_279_boolean__algebra__cancel_Oinf1,axiom,
% 2.39/2.71 ! [A3: set_Pr1261947904930325089at_nat,K: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.39/2.71 ( ( A3
% 2.39/2.71 = ( inf_in2572325071724192079at_nat @ K @ A ) )
% 2.39/2.71 => ( ( inf_in2572325071724192079at_nat @ A3 @ B )
% 2.39/2.71 = ( inf_in2572325071724192079at_nat @ K @ ( inf_in2572325071724192079at_nat @ A @ B ) ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % boolean_algebra_cancel.inf1
% 2.39/2.71 thf(fact_280_boolean__algebra__cancel_Oinf1,axiom,
% 2.39/2.71 ! [A3: set_nat,K: set_nat,A: set_nat,B: set_nat] :
% 2.39/2.71 ( ( A3
% 2.39/2.71 = ( inf_inf_set_nat @ K @ A ) )
% 2.39/2.71 => ( ( inf_inf_set_nat @ A3 @ B )
% 2.39/2.71 = ( inf_inf_set_nat @ K @ ( inf_inf_set_nat @ A @ B ) ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % boolean_algebra_cancel.inf1
% 2.39/2.71 thf(fact_281_boolean__algebra__cancel_Oinf1,axiom,
% 2.39/2.71 ! [A3: nat,K: nat,A: nat,B: nat] :
% 2.39/2.71 ( ( A3
% 2.39/2.71 = ( inf_inf_nat @ K @ A ) )
% 2.39/2.71 => ( ( inf_inf_nat @ A3 @ B )
% 2.39/2.71 = ( inf_inf_nat @ K @ ( inf_inf_nat @ A @ B ) ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % boolean_algebra_cancel.inf1
% 2.39/2.71 thf(fact_282_boolean__algebra__cancel_Oinf1,axiom,
% 2.39/2.71 ! [A3: product_prod_int_int > $o,K: product_prod_int_int > $o,A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 2.39/2.71 ( ( A3
% 2.39/2.71 = ( inf_in3604695632404883862_int_o @ K @ A ) )
% 2.39/2.71 => ( ( inf_in3604695632404883862_int_o @ A3 @ B )
% 2.39/2.71 = ( inf_in3604695632404883862_int_o @ K @ ( inf_in3604695632404883862_int_o @ A @ B ) ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % boolean_algebra_cancel.inf1
% 2.39/2.71 thf(fact_283_boolean__algebra__cancel_Oinf2,axiom,
% 2.39/2.71 ! [B3: assn,K: assn,B: assn,A: assn] :
% 2.39/2.71 ( ( B3
% 2.39/2.71 = ( inf_inf_assn @ K @ B ) )
% 2.39/2.71 => ( ( inf_inf_assn @ A @ B3 )
% 2.39/2.71 = ( inf_inf_assn @ K @ ( inf_inf_assn @ A @ B ) ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % boolean_algebra_cancel.inf2
% 2.39/2.71 thf(fact_284_boolean__algebra__cancel_Oinf2,axiom,
% 2.39/2.71 ! [B3: set_Pr1261947904930325089at_nat,K: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 2.39/2.71 ( ( B3
% 2.39/2.71 = ( inf_in2572325071724192079at_nat @ K @ B ) )
% 2.39/2.71 => ( ( inf_in2572325071724192079at_nat @ A @ B3 )
% 2.39/2.71 = ( inf_in2572325071724192079at_nat @ K @ ( inf_in2572325071724192079at_nat @ A @ B ) ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % boolean_algebra_cancel.inf2
% 2.39/2.71 thf(fact_285_boolean__algebra__cancel_Oinf2,axiom,
% 2.39/2.71 ! [B3: set_nat,K: set_nat,B: set_nat,A: set_nat] :
% 2.39/2.71 ( ( B3
% 2.39/2.71 = ( inf_inf_set_nat @ K @ B ) )
% 2.39/2.71 => ( ( inf_inf_set_nat @ A @ B3 )
% 2.39/2.71 = ( inf_inf_set_nat @ K @ ( inf_inf_set_nat @ A @ B ) ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % boolean_algebra_cancel.inf2
% 2.39/2.71 thf(fact_286_boolean__algebra__cancel_Oinf2,axiom,
% 2.39/2.71 ! [B3: nat,K: nat,B: nat,A: nat] :
% 2.39/2.71 ( ( B3
% 2.39/2.71 = ( inf_inf_nat @ K @ B ) )
% 2.39/2.71 => ( ( inf_inf_nat @ A @ B3 )
% 2.39/2.71 = ( inf_inf_nat @ K @ ( inf_inf_nat @ A @ B ) ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % boolean_algebra_cancel.inf2
% 2.39/2.71 thf(fact_287_boolean__algebra__cancel_Oinf2,axiom,
% 2.39/2.71 ! [B3: product_prod_int_int > $o,K: product_prod_int_int > $o,B: product_prod_int_int > $o,A: product_prod_int_int > $o] :
% 2.39/2.71 ( ( B3
% 2.39/2.71 = ( inf_in3604695632404883862_int_o @ K @ B ) )
% 2.39/2.71 => ( ( inf_in3604695632404883862_int_o @ A @ B3 )
% 2.39/2.71 = ( inf_in3604695632404883862_int_o @ K @ ( inf_in3604695632404883862_int_o @ A @ B ) ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % boolean_algebra_cancel.inf2
% 2.39/2.71 thf(fact_288_mult_Omonoid__axioms,axiom,
% 2.39/2.71 monoid_rat @ times_times_rat @ one_one_rat ).
% 2.39/2.71
% 2.39/2.71 % mult.monoid_axioms
% 2.39/2.71 thf(fact_289_mult_Omonoid__axioms,axiom,
% 2.39/2.71 monoid_assn @ times_times_assn @ one_one_assn ).
% 2.39/2.71
% 2.39/2.71 % mult.monoid_axioms
% 2.39/2.71 thf(fact_290_mult_Omonoid__axioms,axiom,
% 2.39/2.71 monoid_nat @ times_times_nat @ one_one_nat ).
% 2.39/2.71
% 2.39/2.71 % mult.monoid_axioms
% 2.39/2.71 thf(fact_291_mult_Omonoid__axioms,axiom,
% 2.39/2.71 monoid_int @ times_times_int @ one_one_int ).
% 2.39/2.71
% 2.39/2.71 % mult.monoid_axioms
% 2.39/2.71 thf(fact_292_mult_Omonoid__axioms,axiom,
% 2.39/2.71 monoid_Code_integer @ times_3573771949741848930nteger @ one_one_Code_integer ).
% 2.39/2.71
% 2.39/2.71 % mult.monoid_axioms
% 2.39/2.71 thf(fact_293_mult_Omonoid__axioms,axiom,
% 2.39/2.71 monoid_Code_natural @ times_2397367101498566445atural @ one_one_Code_natural ).
% 2.39/2.71
% 2.39/2.71 % mult.monoid_axioms
% 2.39/2.71 thf(fact_294_ent__false__iff,axiom,
% 2.39/2.71 ! [P2: assn] :
% 2.39/2.71 ( ( entails @ P2 @ bot_bot_assn )
% 2.39/2.71 = ( ! [H: produc3658429121746597890et_nat] :
% 2.39/2.71 ~ ( rep_assn @ P2 @ H ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % ent_false_iff
% 2.39/2.71 thf(fact_295_mult_Ocomm__monoid__axioms,axiom,
% 2.39/2.71 comm_monoid_rat @ times_times_rat @ one_one_rat ).
% 2.39/2.71
% 2.39/2.71 % mult.comm_monoid_axioms
% 2.39/2.71 thf(fact_296_mult_Ocomm__monoid__axioms,axiom,
% 2.39/2.71 comm_monoid_assn @ times_times_assn @ one_one_assn ).
% 2.39/2.71
% 2.39/2.71 % mult.comm_monoid_axioms
% 2.39/2.71 thf(fact_297_mult_Ocomm__monoid__axioms,axiom,
% 2.39/2.71 comm_monoid_nat @ times_times_nat @ one_one_nat ).
% 2.39/2.71
% 2.39/2.71 % mult.comm_monoid_axioms
% 2.39/2.71 thf(fact_298_mult_Ocomm__monoid__axioms,axiom,
% 2.39/2.71 comm_monoid_int @ times_times_int @ one_one_int ).
% 2.39/2.71
% 2.39/2.71 % mult.comm_monoid_axioms
% 2.39/2.71 thf(fact_299_mult_Ocomm__monoid__axioms,axiom,
% 2.39/2.71 comm_m1654649897431166824nteger @ times_3573771949741848930nteger @ one_one_Code_integer ).
% 2.39/2.71
% 2.39/2.71 % mult.comm_monoid_axioms
% 2.39/2.71 thf(fact_300_mult_Ocomm__monoid__axioms,axiom,
% 2.39/2.71 comm_m478245049187884339atural @ times_2397367101498566445atural @ one_one_Code_natural ).
% 2.39/2.71
% 2.39/2.71 % mult.comm_monoid_axioms
% 2.39/2.71 thf(fact_301_map__filter__simps_I2_J,axiom,
% 2.39/2.71 ! [F2: produc6575502325842934193n_assn > option7057359848497031415n_assn] :
% 2.39/2.71 ( ( map_fi2680429960852639882n_assn @ F2 @ nil_Pr5671120429643327159n_assn )
% 2.39/2.71 = nil_Pr5671120429643327159n_assn ) ).
% 2.39/2.71
% 2.39/2.71 % map_filter_simps(2)
% 2.39/2.71 thf(fact_302_map__filter__simps_I2_J,axiom,
% 2.39/2.71 ! [F2: produc6575502325842934193n_assn > option_int] :
% 2.39/2.71 ( ( map_fi8666144670822621843sn_int @ F2 @ nil_Pr5671120429643327159n_assn )
% 2.39/2.71 = nil_int ) ).
% 2.39/2.71
% 2.39/2.71 % map_filter_simps(2)
% 2.39/2.71 thf(fact_303_map__filter__simps_I2_J,axiom,
% 2.39/2.71 ! [F2: produc6575502325842934193n_assn > option_nat] :
% 2.39/2.71 ( ( map_fi8668635141331672119sn_nat @ F2 @ nil_Pr5671120429643327159n_assn )
% 2.39/2.71 = nil_nat ) ).
% 2.39/2.71
% 2.39/2.71 % map_filter_simps(2)
% 2.39/2.71 thf(fact_304_map__filter__simps_I2_J,axiom,
% 2.39/2.71 ! [F2: int > option7057359848497031415n_assn] :
% 2.39/2.71 ( ( map_fi5526074278189050041n_assn @ F2 @ nil_int )
% 2.39/2.71 = nil_Pr5671120429643327159n_assn ) ).
% 2.39/2.71
% 2.39/2.71 % map_filter_simps(2)
% 2.39/2.71 thf(fact_305_map__filter__simps_I2_J,axiom,
% 2.39/2.71 ! [F2: int > option_int] :
% 2.39/2.71 ( ( map_filter_int_int @ F2 @ nil_int )
% 2.39/2.71 = nil_int ) ).
% 2.39/2.71
% 2.39/2.71 % map_filter_simps(2)
% 2.39/2.71 thf(fact_306_map__filter__simps_I2_J,axiom,
% 2.39/2.71 ! [F2: int > option_nat] :
% 2.39/2.71 ( ( map_filter_int_nat @ F2 @ nil_int )
% 2.39/2.71 = nil_nat ) ).
% 2.39/2.71
% 2.39/2.71 % map_filter_simps(2)
% 2.39/2.71 thf(fact_307_map__filter__simps_I2_J,axiom,
% 2.39/2.71 ! [F2: nat > option7057359848497031415n_assn] :
% 2.39/2.71 ( ( map_fi3766037614435938837n_assn @ F2 @ nil_nat )
% 2.39/2.71 = nil_Pr5671120429643327159n_assn ) ).
% 2.39/2.71
% 2.39/2.71 % map_filter_simps(2)
% 2.39/2.71 thf(fact_308_map__filter__simps_I2_J,axiom,
% 2.39/2.71 ! [F2: nat > option_int] :
% 2.39/2.71 ( ( map_filter_nat_int @ F2 @ nil_nat )
% 2.39/2.71 = nil_int ) ).
% 2.39/2.71
% 2.39/2.71 % map_filter_simps(2)
% 2.39/2.71 thf(fact_309_map__filter__simps_I2_J,axiom,
% 2.39/2.71 ! [F2: nat > option_nat] :
% 2.39/2.71 ( ( map_filter_nat_nat @ F2 @ nil_nat )
% 2.39/2.71 = nil_nat ) ).
% 2.39/2.71
% 2.39/2.71 % map_filter_simps(2)
% 2.39/2.71 thf(fact_310_splice__Nil2,axiom,
% 2.39/2.71 ! [Xs: list_P8527749157015355191n_assn] :
% 2.39/2.71 ( ( splice4588524007259616650n_assn @ Xs @ nil_Pr5671120429643327159n_assn )
% 2.39/2.71 = Xs ) ).
% 2.39/2.71
% 2.39/2.71 % splice_Nil2
% 2.39/2.71 thf(fact_311_splice__Nil2,axiom,
% 2.39/2.71 ! [Xs: list_int] :
% 2.39/2.71 ( ( splice_int @ Xs @ nil_int )
% 2.39/2.71 = Xs ) ).
% 2.39/2.71
% 2.39/2.71 % splice_Nil2
% 2.39/2.71 thf(fact_312_splice__Nil2,axiom,
% 2.39/2.71 ! [Xs: list_nat] :
% 2.39/2.71 ( ( splice_nat @ Xs @ nil_nat )
% 2.39/2.71 = Xs ) ).
% 2.39/2.71
% 2.39/2.71 % splice_Nil2
% 2.39/2.71 thf(fact_313_split__Nil__iff,axiom,
% 2.39/2.71 ! [Xs: list_P8527749157015355191n_assn,Ys: list_P8527749157015355191n_assn] :
% 2.39/2.71 ( ( ( splice4588524007259616650n_assn @ Xs @ Ys )
% 2.39/2.71 = nil_Pr5671120429643327159n_assn )
% 2.39/2.71 = ( ( Xs = nil_Pr5671120429643327159n_assn )
% 2.39/2.71 & ( Ys = nil_Pr5671120429643327159n_assn ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % split_Nil_iff
% 2.39/2.71 thf(fact_314_split__Nil__iff,axiom,
% 2.39/2.71 ! [Xs: list_int,Ys: list_int] :
% 2.39/2.71 ( ( ( splice_int @ Xs @ Ys )
% 2.39/2.71 = nil_int )
% 2.39/2.71 = ( ( Xs = nil_int )
% 2.39/2.71 & ( Ys = nil_int ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % split_Nil_iff
% 2.39/2.71 thf(fact_315_split__Nil__iff,axiom,
% 2.39/2.71 ! [Xs: list_nat,Ys: list_nat] :
% 2.39/2.71 ( ( ( splice_nat @ Xs @ Ys )
% 2.39/2.71 = nil_nat )
% 2.39/2.71 = ( ( Xs = nil_nat )
% 2.39/2.71 & ( Ys = nil_nat ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % split_Nil_iff
% 2.39/2.71 thf(fact_316_rotate1__is__Nil__conv,axiom,
% 2.39/2.71 ! [Xs: list_P8527749157015355191n_assn] :
% 2.39/2.71 ( ( ( rotate328796349445179396n_assn @ Xs )
% 2.39/2.71 = nil_Pr5671120429643327159n_assn )
% 2.39/2.71 = ( Xs = nil_Pr5671120429643327159n_assn ) ) ).
% 2.39/2.71
% 2.39/2.71 % rotate1_is_Nil_conv
% 2.39/2.71 thf(fact_317_rotate1__is__Nil__conv,axiom,
% 2.39/2.71 ! [Xs: list_int] :
% 2.39/2.71 ( ( ( rotate1_int @ Xs )
% 2.39/2.71 = nil_int )
% 2.39/2.71 = ( Xs = nil_int ) ) ).
% 2.39/2.71
% 2.39/2.71 % rotate1_is_Nil_conv
% 2.39/2.71 thf(fact_318_rotate1__is__Nil__conv,axiom,
% 2.39/2.71 ! [Xs: list_nat] :
% 2.39/2.71 ( ( ( rotate1_nat @ Xs )
% 2.39/2.71 = nil_nat )
% 2.39/2.71 = ( Xs = nil_nat ) ) ).
% 2.39/2.71
% 2.39/2.71 % rotate1_is_Nil_conv
% 2.39/2.71 thf(fact_319_enumerate__simps_I1_J,axiom,
% 2.39/2.71 ! [N: nat] :
% 2.39/2.71 ( ( enumer9200277086812776726n_assn @ N @ nil_Pr5671120429643327159n_assn )
% 2.39/2.71 = nil_Pr680377793251149648n_assn ) ).
% 2.39/2.71
% 2.39/2.71 % enumerate_simps(1)
% 2.39/2.71 thf(fact_320_enumerate__simps_I1_J,axiom,
% 2.39/2.71 ! [N: nat] :
% 2.39/2.71 ( ( enumerate_int @ N @ nil_int )
% 2.39/2.71 = nil_Pr1301135604781543011at_int ) ).
% 2.39/2.71
% 2.39/2.71 % enumerate_simps(1)
% 2.39/2.71 thf(fact_321_enumerate__simps_I1_J,axiom,
% 2.39/2.71 ! [N: nat] :
% 2.39/2.71 ( ( enumerate_nat @ N @ nil_nat )
% 2.39/2.71 = nil_Pr5478986624290739719at_nat ) ).
% 2.39/2.71
% 2.39/2.71 % enumerate_simps(1)
% 2.39/2.71 thf(fact_322_mod__star__trueI,axiom,
% 2.39/2.71 ! [P2: assn,H2: produc3658429121746597890et_nat] :
% 2.39/2.71 ( ( rep_assn @ P2 @ H2 )
% 2.39/2.71 => ( rep_assn @ ( times_times_assn @ P2 @ top_top_assn ) @ H2 ) ) ).
% 2.39/2.71
% 2.39/2.71 % mod_star_trueI
% 2.39/2.71 thf(fact_323_mod__star__trueE,axiom,
% 2.39/2.71 ! [P2: assn,H2: produc3658429121746597890et_nat] :
% 2.39/2.71 ( ( rep_assn @ ( times_times_assn @ P2 @ top_top_assn ) @ H2 )
% 2.39/2.71 => ~ ! [H4: produc3658429121746597890et_nat] :
% 2.39/2.71 ~ ( rep_assn @ P2 @ H4 ) ) ).
% 2.39/2.71
% 2.39/2.71 % mod_star_trueE
% 2.39/2.71 thf(fact_324_boolean__algebra_Oconj__zero__right,axiom,
% 2.39/2.71 ! [X: set_Pr1261947904930325089at_nat] :
% 2.39/2.71 ( ( inf_in2572325071724192079at_nat @ X @ bot_bo2099793752762293965at_nat )
% 2.39/2.71 = bot_bo2099793752762293965at_nat ) ).
% 2.39/2.71
% 2.39/2.71 % boolean_algebra.conj_zero_right
% 2.39/2.71 thf(fact_325_boolean__algebra_Oconj__zero__right,axiom,
% 2.39/2.71 ! [X: product_prod_int_int > $o] :
% 2.39/2.71 ( ( inf_in3604695632404883862_int_o @ X @ bot_bo8147686125503663512_int_o )
% 2.39/2.71 = bot_bo8147686125503663512_int_o ) ).
% 2.39/2.71
% 2.39/2.71 % boolean_algebra.conj_zero_right
% 2.39/2.71 thf(fact_326_boolean__algebra_Oconj__zero__right,axiom,
% 2.39/2.71 ! [X: assn] :
% 2.39/2.71 ( ( inf_inf_assn @ X @ bot_bot_assn )
% 2.39/2.71 = bot_bot_assn ) ).
% 2.39/2.71
% 2.39/2.71 % boolean_algebra.conj_zero_right
% 2.39/2.71 thf(fact_327_boolean__algebra_Oconj__zero__right,axiom,
% 2.39/2.71 ! [X: set_nat] :
% 2.39/2.71 ( ( inf_inf_set_nat @ X @ bot_bot_set_nat )
% 2.39/2.71 = bot_bot_set_nat ) ).
% 2.39/2.71
% 2.39/2.71 % boolean_algebra.conj_zero_right
% 2.39/2.71 thf(fact_328_boolean__algebra_Oconj__zero__right,axiom,
% 2.39/2.71 ! [X: set_int] :
% 2.39/2.71 ( ( inf_inf_set_int @ X @ bot_bot_set_int )
% 2.39/2.71 = bot_bot_set_int ) ).
% 2.39/2.71
% 2.39/2.71 % boolean_algebra.conj_zero_right
% 2.39/2.71 thf(fact_329_boolean__algebra_Oconj__zero__left,axiom,
% 2.39/2.71 ! [X: set_Pr1261947904930325089at_nat] :
% 2.39/2.71 ( ( inf_in2572325071724192079at_nat @ bot_bo2099793752762293965at_nat @ X )
% 2.39/2.71 = bot_bo2099793752762293965at_nat ) ).
% 2.39/2.71
% 2.39/2.71 % boolean_algebra.conj_zero_left
% 2.39/2.71 thf(fact_330_boolean__algebra_Oconj__zero__left,axiom,
% 2.39/2.71 ! [X: product_prod_int_int > $o] :
% 2.39/2.71 ( ( inf_in3604695632404883862_int_o @ bot_bo8147686125503663512_int_o @ X )
% 2.39/2.71 = bot_bo8147686125503663512_int_o ) ).
% 2.39/2.71
% 2.39/2.71 % boolean_algebra.conj_zero_left
% 2.39/2.71 thf(fact_331_boolean__algebra_Oconj__zero__left,axiom,
% 2.39/2.71 ! [X: assn] :
% 2.39/2.71 ( ( inf_inf_assn @ bot_bot_assn @ X )
% 2.39/2.71 = bot_bot_assn ) ).
% 2.39/2.71
% 2.39/2.71 % boolean_algebra.conj_zero_left
% 2.39/2.71 thf(fact_332_boolean__algebra_Oconj__zero__left,axiom,
% 2.39/2.71 ! [X: set_nat] :
% 2.39/2.71 ( ( inf_inf_set_nat @ bot_bot_set_nat @ X )
% 2.39/2.71 = bot_bot_set_nat ) ).
% 2.39/2.71
% 2.39/2.71 % boolean_algebra.conj_zero_left
% 2.39/2.71 thf(fact_333_boolean__algebra_Oconj__zero__left,axiom,
% 2.39/2.71 ! [X: set_int] :
% 2.39/2.71 ( ( inf_inf_set_int @ bot_bot_set_int @ X )
% 2.39/2.71 = bot_bot_set_int ) ).
% 2.39/2.71
% 2.39/2.71 % boolean_algebra.conj_zero_left
% 2.39/2.71 thf(fact_334_inf__bot__right,axiom,
% 2.39/2.71 ! [X: set_Pr1261947904930325089at_nat] :
% 2.39/2.71 ( ( inf_in2572325071724192079at_nat @ X @ bot_bo2099793752762293965at_nat )
% 2.39/2.71 = bot_bo2099793752762293965at_nat ) ).
% 2.39/2.71
% 2.39/2.71 % inf_bot_right
% 2.39/2.71 thf(fact_335_inf__bot__right,axiom,
% 2.39/2.71 ! [X: product_prod_int_int > $o] :
% 2.39/2.71 ( ( inf_in3604695632404883862_int_o @ X @ bot_bo8147686125503663512_int_o )
% 2.39/2.71 = bot_bo8147686125503663512_int_o ) ).
% 2.39/2.71
% 2.39/2.71 % inf_bot_right
% 2.39/2.71 thf(fact_336_inf__bot__right,axiom,
% 2.39/2.71 ! [X: assn] :
% 2.39/2.71 ( ( inf_inf_assn @ X @ bot_bot_assn )
% 2.39/2.71 = bot_bot_assn ) ).
% 2.39/2.71
% 2.39/2.71 % inf_bot_right
% 2.39/2.71 thf(fact_337_inf__bot__right,axiom,
% 2.39/2.71 ! [X: set_nat] :
% 2.39/2.71 ( ( inf_inf_set_nat @ X @ bot_bot_set_nat )
% 2.39/2.71 = bot_bot_set_nat ) ).
% 2.39/2.71
% 2.39/2.71 % inf_bot_right
% 2.39/2.71 thf(fact_338_inf__bot__right,axiom,
% 2.39/2.71 ! [X: set_int] :
% 2.39/2.71 ( ( inf_inf_set_int @ X @ bot_bot_set_int )
% 2.39/2.71 = bot_bot_set_int ) ).
% 2.39/2.71
% 2.39/2.71 % inf_bot_right
% 2.39/2.71 thf(fact_339_inf__bot__left,axiom,
% 2.39/2.71 ! [X: set_Pr1261947904930325089at_nat] :
% 2.39/2.71 ( ( inf_in2572325071724192079at_nat @ bot_bo2099793752762293965at_nat @ X )
% 2.39/2.71 = bot_bo2099793752762293965at_nat ) ).
% 2.39/2.71
% 2.39/2.71 % inf_bot_left
% 2.39/2.71 thf(fact_340_inf__bot__left,axiom,
% 2.39/2.71 ! [X: product_prod_int_int > $o] :
% 2.39/2.71 ( ( inf_in3604695632404883862_int_o @ bot_bo8147686125503663512_int_o @ X )
% 2.39/2.71 = bot_bo8147686125503663512_int_o ) ).
% 2.39/2.71
% 2.39/2.71 % inf_bot_left
% 2.39/2.71 thf(fact_341_inf__bot__left,axiom,
% 2.39/2.71 ! [X: assn] :
% 2.39/2.71 ( ( inf_inf_assn @ bot_bot_assn @ X )
% 2.39/2.71 = bot_bot_assn ) ).
% 2.39/2.71
% 2.39/2.71 % inf_bot_left
% 2.39/2.71 thf(fact_342_inf__bot__left,axiom,
% 2.39/2.71 ! [X: set_nat] :
% 2.39/2.71 ( ( inf_inf_set_nat @ bot_bot_set_nat @ X )
% 2.39/2.71 = bot_bot_set_nat ) ).
% 2.39/2.71
% 2.39/2.71 % inf_bot_left
% 2.39/2.71 thf(fact_343_inf__bot__left,axiom,
% 2.39/2.71 ! [X: set_int] :
% 2.39/2.71 ( ( inf_inf_set_int @ bot_bot_set_int @ X )
% 2.39/2.71 = bot_bot_set_int ) ).
% 2.39/2.71
% 2.39/2.71 % inf_bot_left
% 2.39/2.71 thf(fact_344_inf__top_Oright__neutral,axiom,
% 2.39/2.71 ! [A: set_Pr1261947904930325089at_nat] :
% 2.39/2.71 ( ( inf_in2572325071724192079at_nat @ A @ top_to4669805908274784177at_nat )
% 2.39/2.71 = A ) ).
% 2.39/2.71
% 2.39/2.71 % inf_top.right_neutral
% 2.39/2.71 thf(fact_345_inf__top_Oright__neutral,axiom,
% 2.39/2.71 ! [A: set_nat] :
% 2.39/2.71 ( ( inf_inf_set_nat @ A @ top_top_set_nat )
% 2.39/2.71 = A ) ).
% 2.39/2.71
% 2.39/2.71 % inf_top.right_neutral
% 2.39/2.71 thf(fact_346_inf__top_Oright__neutral,axiom,
% 2.39/2.71 ! [A: product_prod_int_int > $o] :
% 2.39/2.71 ( ( inf_in3604695632404883862_int_o @ A @ top_to1578927101902068148_int_o )
% 2.39/2.71 = A ) ).
% 2.39/2.71
% 2.39/2.71 % inf_top.right_neutral
% 2.39/2.71 thf(fact_347_inf__top_Oright__neutral,axiom,
% 2.39/2.71 ! [A: assn] :
% 2.39/2.71 ( ( inf_inf_assn @ A @ top_top_assn )
% 2.39/2.71 = A ) ).
% 2.39/2.71
% 2.39/2.71 % inf_top.right_neutral
% 2.39/2.71 thf(fact_348_inf__top_Oright__neutral,axiom,
% 2.39/2.71 ! [A: set_Product_unit] :
% 2.39/2.71 ( ( inf_in4660618365625256667t_unit @ A @ top_to1996260823553986621t_unit )
% 2.39/2.71 = A ) ).
% 2.39/2.71
% 2.39/2.71 % inf_top.right_neutral
% 2.39/2.71 thf(fact_349_inf__top_Oneutr__eq__iff,axiom,
% 2.39/2.71 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.39/2.71 ( ( top_to4669805908274784177at_nat
% 2.39/2.71 = ( inf_in2572325071724192079at_nat @ A @ B ) )
% 2.39/2.71 = ( ( A = top_to4669805908274784177at_nat )
% 2.39/2.71 & ( B = top_to4669805908274784177at_nat ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_top.neutr_eq_iff
% 2.39/2.71 thf(fact_350_inf__top_Oneutr__eq__iff,axiom,
% 2.39/2.71 ! [A: set_nat,B: set_nat] :
% 2.39/2.71 ( ( top_top_set_nat
% 2.39/2.71 = ( inf_inf_set_nat @ A @ B ) )
% 2.39/2.71 = ( ( A = top_top_set_nat )
% 2.39/2.71 & ( B = top_top_set_nat ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_top.neutr_eq_iff
% 2.39/2.71 thf(fact_351_inf__top_Oneutr__eq__iff,axiom,
% 2.39/2.71 ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 2.39/2.71 ( ( top_to1578927101902068148_int_o
% 2.39/2.71 = ( inf_in3604695632404883862_int_o @ A @ B ) )
% 2.39/2.71 = ( ( A = top_to1578927101902068148_int_o )
% 2.39/2.71 & ( B = top_to1578927101902068148_int_o ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_top.neutr_eq_iff
% 2.39/2.71 thf(fact_352_inf__top_Oneutr__eq__iff,axiom,
% 2.39/2.71 ! [A: assn,B: assn] :
% 2.39/2.71 ( ( top_top_assn
% 2.39/2.71 = ( inf_inf_assn @ A @ B ) )
% 2.39/2.71 = ( ( A = top_top_assn )
% 2.39/2.71 & ( B = top_top_assn ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_top.neutr_eq_iff
% 2.39/2.71 thf(fact_353_inf__top_Oneutr__eq__iff,axiom,
% 2.39/2.71 ! [A: set_Product_unit,B: set_Product_unit] :
% 2.39/2.71 ( ( top_to1996260823553986621t_unit
% 2.39/2.71 = ( inf_in4660618365625256667t_unit @ A @ B ) )
% 2.39/2.71 = ( ( A = top_to1996260823553986621t_unit )
% 2.39/2.71 & ( B = top_to1996260823553986621t_unit ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_top.neutr_eq_iff
% 2.39/2.71 thf(fact_354_inf__top_Oleft__neutral,axiom,
% 2.39/2.71 ! [A: set_Pr1261947904930325089at_nat] :
% 2.39/2.71 ( ( inf_in2572325071724192079at_nat @ top_to4669805908274784177at_nat @ A )
% 2.39/2.71 = A ) ).
% 2.39/2.71
% 2.39/2.71 % inf_top.left_neutral
% 2.39/2.71 thf(fact_355_inf__top_Oleft__neutral,axiom,
% 2.39/2.71 ! [A: set_nat] :
% 2.39/2.71 ( ( inf_inf_set_nat @ top_top_set_nat @ A )
% 2.39/2.71 = A ) ).
% 2.39/2.71
% 2.39/2.71 % inf_top.left_neutral
% 2.39/2.71 thf(fact_356_inf__top_Oleft__neutral,axiom,
% 2.39/2.71 ! [A: product_prod_int_int > $o] :
% 2.39/2.71 ( ( inf_in3604695632404883862_int_o @ top_to1578927101902068148_int_o @ A )
% 2.39/2.71 = A ) ).
% 2.39/2.71
% 2.39/2.71 % inf_top.left_neutral
% 2.39/2.71 thf(fact_357_inf__top_Oleft__neutral,axiom,
% 2.39/2.71 ! [A: assn] :
% 2.39/2.71 ( ( inf_inf_assn @ top_top_assn @ A )
% 2.39/2.71 = A ) ).
% 2.39/2.71
% 2.39/2.71 % inf_top.left_neutral
% 2.39/2.71 thf(fact_358_inf__top_Oleft__neutral,axiom,
% 2.39/2.71 ! [A: set_Product_unit] :
% 2.39/2.71 ( ( inf_in4660618365625256667t_unit @ top_to1996260823553986621t_unit @ A )
% 2.39/2.71 = A ) ).
% 2.39/2.71
% 2.39/2.71 % inf_top.left_neutral
% 2.39/2.71 thf(fact_359_inf__top_Oeq__neutr__iff,axiom,
% 2.39/2.71 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.39/2.71 ( ( ( inf_in2572325071724192079at_nat @ A @ B )
% 2.39/2.71 = top_to4669805908274784177at_nat )
% 2.39/2.71 = ( ( A = top_to4669805908274784177at_nat )
% 2.39/2.71 & ( B = top_to4669805908274784177at_nat ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_top.eq_neutr_iff
% 2.39/2.71 thf(fact_360_inf__top_Oeq__neutr__iff,axiom,
% 2.39/2.71 ! [A: set_nat,B: set_nat] :
% 2.39/2.71 ( ( ( inf_inf_set_nat @ A @ B )
% 2.39/2.71 = top_top_set_nat )
% 2.39/2.71 = ( ( A = top_top_set_nat )
% 2.39/2.71 & ( B = top_top_set_nat ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_top.eq_neutr_iff
% 2.39/2.71 thf(fact_361_inf__top_Oeq__neutr__iff,axiom,
% 2.39/2.71 ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 2.39/2.71 ( ( ( inf_in3604695632404883862_int_o @ A @ B )
% 2.39/2.71 = top_to1578927101902068148_int_o )
% 2.39/2.71 = ( ( A = top_to1578927101902068148_int_o )
% 2.39/2.71 & ( B = top_to1578927101902068148_int_o ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_top.eq_neutr_iff
% 2.39/2.71 thf(fact_362_inf__top_Oeq__neutr__iff,axiom,
% 2.39/2.71 ! [A: assn,B: assn] :
% 2.39/2.71 ( ( ( inf_inf_assn @ A @ B )
% 2.39/2.71 = top_top_assn )
% 2.39/2.71 = ( ( A = top_top_assn )
% 2.39/2.71 & ( B = top_top_assn ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_top.eq_neutr_iff
% 2.39/2.71 thf(fact_363_inf__top_Oeq__neutr__iff,axiom,
% 2.39/2.71 ! [A: set_Product_unit,B: set_Product_unit] :
% 2.39/2.71 ( ( ( inf_in4660618365625256667t_unit @ A @ B )
% 2.39/2.71 = top_to1996260823553986621t_unit )
% 2.39/2.71 = ( ( A = top_to1996260823553986621t_unit )
% 2.39/2.71 & ( B = top_to1996260823553986621t_unit ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_top.eq_neutr_iff
% 2.39/2.71 thf(fact_364_top__eq__inf__iff,axiom,
% 2.39/2.71 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 2.39/2.71 ( ( top_to4669805908274784177at_nat
% 2.39/2.71 = ( inf_in2572325071724192079at_nat @ X @ Y ) )
% 2.39/2.71 = ( ( X = top_to4669805908274784177at_nat )
% 2.39/2.71 & ( Y = top_to4669805908274784177at_nat ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % top_eq_inf_iff
% 2.39/2.71 thf(fact_365_top__eq__inf__iff,axiom,
% 2.39/2.71 ! [X: set_nat,Y: set_nat] :
% 2.39/2.71 ( ( top_top_set_nat
% 2.39/2.71 = ( inf_inf_set_nat @ X @ Y ) )
% 2.39/2.71 = ( ( X = top_top_set_nat )
% 2.39/2.71 & ( Y = top_top_set_nat ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % top_eq_inf_iff
% 2.39/2.71 thf(fact_366_top__eq__inf__iff,axiom,
% 2.39/2.71 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 2.39/2.71 ( ( top_to1578927101902068148_int_o
% 2.39/2.71 = ( inf_in3604695632404883862_int_o @ X @ Y ) )
% 2.39/2.71 = ( ( X = top_to1578927101902068148_int_o )
% 2.39/2.71 & ( Y = top_to1578927101902068148_int_o ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % top_eq_inf_iff
% 2.39/2.71 thf(fact_367_top__eq__inf__iff,axiom,
% 2.39/2.71 ! [X: assn,Y: assn] :
% 2.39/2.71 ( ( top_top_assn
% 2.39/2.71 = ( inf_inf_assn @ X @ Y ) )
% 2.39/2.71 = ( ( X = top_top_assn )
% 2.39/2.71 & ( Y = top_top_assn ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % top_eq_inf_iff
% 2.39/2.71 thf(fact_368_top__eq__inf__iff,axiom,
% 2.39/2.71 ! [X: set_Product_unit,Y: set_Product_unit] :
% 2.39/2.71 ( ( top_to1996260823553986621t_unit
% 2.39/2.71 = ( inf_in4660618365625256667t_unit @ X @ Y ) )
% 2.39/2.71 = ( ( X = top_to1996260823553986621t_unit )
% 2.39/2.71 & ( Y = top_to1996260823553986621t_unit ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % top_eq_inf_iff
% 2.39/2.71 thf(fact_369_inf__eq__top__iff,axiom,
% 2.39/2.71 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 2.39/2.71 ( ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 2.39/2.71 = top_to4669805908274784177at_nat )
% 2.39/2.71 = ( ( X = top_to4669805908274784177at_nat )
% 2.39/2.71 & ( Y = top_to4669805908274784177at_nat ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_eq_top_iff
% 2.39/2.71 thf(fact_370_inf__eq__top__iff,axiom,
% 2.39/2.71 ! [X: set_nat,Y: set_nat] :
% 2.39/2.71 ( ( ( inf_inf_set_nat @ X @ Y )
% 2.39/2.71 = top_top_set_nat )
% 2.39/2.71 = ( ( X = top_top_set_nat )
% 2.39/2.71 & ( Y = top_top_set_nat ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_eq_top_iff
% 2.39/2.71 thf(fact_371_inf__eq__top__iff,axiom,
% 2.39/2.71 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 2.39/2.71 ( ( ( inf_in3604695632404883862_int_o @ X @ Y )
% 2.39/2.71 = top_to1578927101902068148_int_o )
% 2.39/2.71 = ( ( X = top_to1578927101902068148_int_o )
% 2.39/2.71 & ( Y = top_to1578927101902068148_int_o ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_eq_top_iff
% 2.39/2.71 thf(fact_372_inf__eq__top__iff,axiom,
% 2.39/2.71 ! [X: assn,Y: assn] :
% 2.39/2.71 ( ( ( inf_inf_assn @ X @ Y )
% 2.39/2.71 = top_top_assn )
% 2.39/2.71 = ( ( X = top_top_assn )
% 2.39/2.71 & ( Y = top_top_assn ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_eq_top_iff
% 2.39/2.71 thf(fact_373_inf__eq__top__iff,axiom,
% 2.39/2.71 ! [X: set_Product_unit,Y: set_Product_unit] :
% 2.39/2.71 ( ( ( inf_in4660618365625256667t_unit @ X @ Y )
% 2.39/2.71 = top_to1996260823553986621t_unit )
% 2.39/2.71 = ( ( X = top_to1996260823553986621t_unit )
% 2.39/2.71 & ( Y = top_to1996260823553986621t_unit ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % inf_eq_top_iff
% 2.39/2.71 thf(fact_374_inf__top__right,axiom,
% 2.39/2.71 ! [X: set_Pr1261947904930325089at_nat] :
% 2.39/2.71 ( ( inf_in2572325071724192079at_nat @ X @ top_to4669805908274784177at_nat )
% 2.39/2.71 = X ) ).
% 2.39/2.71
% 2.39/2.71 % inf_top_right
% 2.39/2.71 thf(fact_375_inf__top__right,axiom,
% 2.39/2.71 ! [X: set_nat] :
% 2.39/2.71 ( ( inf_inf_set_nat @ X @ top_top_set_nat )
% 2.39/2.71 = X ) ).
% 2.39/2.71
% 2.39/2.71 % inf_top_right
% 2.39/2.71 thf(fact_376_inf__top__right,axiom,
% 2.39/2.71 ! [X: product_prod_int_int > $o] :
% 2.39/2.71 ( ( inf_in3604695632404883862_int_o @ X @ top_to1578927101902068148_int_o )
% 2.39/2.71 = X ) ).
% 2.39/2.71
% 2.39/2.71 % inf_top_right
% 2.39/2.71 thf(fact_377_inf__top__right,axiom,
% 2.39/2.71 ! [X: assn] :
% 2.39/2.71 ( ( inf_inf_assn @ X @ top_top_assn )
% 2.39/2.71 = X ) ).
% 2.39/2.71
% 2.39/2.71 % inf_top_right
% 2.39/2.71 thf(fact_378_inf__top__right,axiom,
% 2.39/2.71 ! [X: set_Product_unit] :
% 2.39/2.71 ( ( inf_in4660618365625256667t_unit @ X @ top_to1996260823553986621t_unit )
% 2.39/2.71 = X ) ).
% 2.39/2.71
% 2.39/2.71 % inf_top_right
% 2.39/2.71 thf(fact_379_inf__top__left,axiom,
% 2.39/2.71 ! [X: set_Pr1261947904930325089at_nat] :
% 2.39/2.71 ( ( inf_in2572325071724192079at_nat @ top_to4669805908274784177at_nat @ X )
% 2.39/2.71 = X ) ).
% 2.39/2.71
% 2.39/2.71 % inf_top_left
% 2.39/2.71 thf(fact_380_inf__top__left,axiom,
% 2.39/2.71 ! [X: set_nat] :
% 2.39/2.71 ( ( inf_inf_set_nat @ top_top_set_nat @ X )
% 2.39/2.71 = X ) ).
% 2.39/2.71
% 2.39/2.71 % inf_top_left
% 2.39/2.71 thf(fact_381_inf__top__left,axiom,
% 2.39/2.71 ! [X: product_prod_int_int > $o] :
% 2.39/2.71 ( ( inf_in3604695632404883862_int_o @ top_to1578927101902068148_int_o @ X )
% 2.39/2.71 = X ) ).
% 2.39/2.71
% 2.39/2.71 % inf_top_left
% 2.39/2.71 thf(fact_382_inf__top__left,axiom,
% 2.39/2.71 ! [X: assn] :
% 2.39/2.71 ( ( inf_inf_assn @ top_top_assn @ X )
% 2.39/2.71 = X ) ).
% 2.39/2.71
% 2.39/2.71 % inf_top_left
% 2.39/2.71 thf(fact_383_inf__top__left,axiom,
% 2.39/2.71 ! [X: set_Product_unit] :
% 2.39/2.71 ( ( inf_in4660618365625256667t_unit @ top_to1996260823553986621t_unit @ X )
% 2.39/2.71 = X ) ).
% 2.39/2.71
% 2.39/2.71 % inf_top_left
% 2.39/2.71 thf(fact_384_merge__true__star,axiom,
% 2.39/2.71 ( ( times_times_assn @ top_top_assn @ top_top_assn )
% 2.39/2.71 = top_top_assn ) ).
% 2.39/2.71
% 2.39/2.71 % merge_true_star
% 2.39/2.71 thf(fact_385_star__false__right,axiom,
% 2.39/2.71 ! [P2: assn] :
% 2.39/2.71 ( ( times_times_assn @ P2 @ bot_bot_assn )
% 2.39/2.71 = bot_bot_assn ) ).
% 2.39/2.71
% 2.39/2.71 % star_false_right
% 2.39/2.71 thf(fact_386_star__false__left,axiom,
% 2.39/2.71 ! [P2: assn] :
% 2.39/2.71 ( ( times_times_assn @ bot_bot_assn @ P2 )
% 2.39/2.71 = bot_bot_assn ) ).
% 2.39/2.71
% 2.39/2.71 % star_false_left
% 2.39/2.71 thf(fact_387_pure__false,axiom,
% 2.39/2.71 ( ( pure_assn @ $false )
% 2.39/2.71 = bot_bot_assn ) ).
% 2.39/2.71
% 2.39/2.71 % pure_false
% 2.39/2.71 thf(fact_388_pure__assn__eq__false__iff,axiom,
% 2.39/2.71 ! [P2: $o] :
% 2.39/2.71 ( ( ( pure_assn @ P2 )
% 2.39/2.71 = bot_bot_assn )
% 2.39/2.71 = ~ P2 ) ).
% 2.39/2.71
% 2.39/2.71 % pure_assn_eq_false_iff
% 2.39/2.71 thf(fact_389_assn__basic__inequalities_I1_J,axiom,
% 2.39/2.71 top_top_assn != one_one_assn ).
% 2.39/2.71
% 2.39/2.71 % assn_basic_inequalities(1)
% 2.39/2.71 thf(fact_390_assn__basic__inequalities_I5_J,axiom,
% 2.39/2.71 top_top_assn != bot_bot_assn ).
% 2.39/2.71
% 2.39/2.71 % assn_basic_inequalities(5)
% 2.39/2.71 thf(fact_391_assn__basic__inequalities_I3_J,axiom,
% 2.39/2.71 bot_bot_assn != one_one_assn ).
% 2.39/2.71
% 2.39/2.71 % assn_basic_inequalities(3)
% 2.39/2.71 thf(fact_392_inf__top_Ocomm__monoid__axioms,axiom,
% 2.39/2.71 comm_m5709050211238513046at_nat @ inf_in2572325071724192079at_nat @ top_to4669805908274784177at_nat ).
% 2.39/2.71
% 2.39/2.71 % inf_top.comm_monoid_axioms
% 2.39/2.71 thf(fact_393_inf__top_Ocomm__monoid__axioms,axiom,
% 2.39/2.71 comm_monoid_set_nat @ inf_inf_set_nat @ top_top_set_nat ).
% 2.39/2.71
% 2.39/2.71 % inf_top.comm_monoid_axioms
% 2.39/2.71 thf(fact_394_inf__top_Ocomm__monoid__axioms,axiom,
% 2.39/2.71 comm_m5839176995973721103_int_o @ inf_in3604695632404883862_int_o @ top_to1578927101902068148_int_o ).
% 2.39/2.71
% 2.39/2.71 % inf_top.comm_monoid_axioms
% 2.39/2.71 thf(fact_395_inf__top_Ocomm__monoid__axioms,axiom,
% 2.39/2.71 comm_monoid_assn @ inf_inf_assn @ top_top_assn ).
% 2.39/2.71
% 2.39/2.71 % inf_top.comm_monoid_axioms
% 2.39/2.71 thf(fact_396_inf__top_Ocomm__monoid__axioms,axiom,
% 2.39/2.71 comm_m7591727228438362018t_unit @ inf_in4660618365625256667t_unit @ top_to1996260823553986621t_unit ).
% 2.39/2.71
% 2.39/2.71 % inf_top.comm_monoid_axioms
% 2.39/2.71 thf(fact_397_boolean__algebra_Oconj__one__right,axiom,
% 2.39/2.71 ! [X: set_Pr1261947904930325089at_nat] :
% 2.39/2.71 ( ( inf_in2572325071724192079at_nat @ X @ top_to4669805908274784177at_nat )
% 2.39/2.71 = X ) ).
% 2.39/2.71
% 2.39/2.71 % boolean_algebra.conj_one_right
% 2.39/2.71 thf(fact_398_boolean__algebra_Oconj__one__right,axiom,
% 2.39/2.71 ! [X: set_nat] :
% 2.39/2.71 ( ( inf_inf_set_nat @ X @ top_top_set_nat )
% 2.39/2.71 = X ) ).
% 2.39/2.71
% 2.39/2.71 % boolean_algebra.conj_one_right
% 2.39/2.71 thf(fact_399_boolean__algebra_Oconj__one__right,axiom,
% 2.39/2.71 ! [X: product_prod_int_int > $o] :
% 2.39/2.71 ( ( inf_in3604695632404883862_int_o @ X @ top_to1578927101902068148_int_o )
% 2.39/2.71 = X ) ).
% 2.39/2.71
% 2.39/2.71 % boolean_algebra.conj_one_right
% 2.39/2.71 thf(fact_400_boolean__algebra_Oconj__one__right,axiom,
% 2.39/2.71 ! [X: assn] :
% 2.39/2.71 ( ( inf_inf_assn @ X @ top_top_assn )
% 2.39/2.71 = X ) ).
% 2.39/2.71
% 2.39/2.71 % boolean_algebra.conj_one_right
% 2.39/2.71 thf(fact_401_boolean__algebra_Oconj__one__right,axiom,
% 2.39/2.71 ! [X: set_Product_unit] :
% 2.39/2.71 ( ( inf_in4660618365625256667t_unit @ X @ top_to1996260823553986621t_unit )
% 2.39/2.71 = X ) ).
% 2.39/2.71
% 2.39/2.71 % boolean_algebra.conj_one_right
% 2.39/2.71 thf(fact_402_inf__top_Omonoid__axioms,axiom,
% 2.39/2.71 monoid1519094961268053602at_nat @ inf_in2572325071724192079at_nat @ top_to4669805908274784177at_nat ).
% 2.39/2.71
% 2.39/2.71 % inf_top.monoid_axioms
% 2.39/2.71 thf(fact_403_inf__top_Omonoid__axioms,axiom,
% 2.39/2.71 monoid_set_nat @ inf_inf_set_nat @ top_top_set_nat ).
% 2.39/2.71
% 2.39/2.71 % inf_top.monoid_axioms
% 2.39/2.71 thf(fact_404_inf__top_Omonoid__axioms,axiom,
% 2.39/2.71 monoid6910981727789844035_int_o @ inf_in3604695632404883862_int_o @ top_to1578927101902068148_int_o ).
% 2.39/2.71
% 2.39/2.71 % inf_top.monoid_axioms
% 2.39/2.71 thf(fact_405_inf__top_Omonoid__axioms,axiom,
% 2.39/2.71 monoid_assn @ inf_inf_assn @ top_top_assn ).
% 2.39/2.71
% 2.39/2.71 % inf_top.monoid_axioms
% 2.39/2.71 thf(fact_406_inf__top_Omonoid__axioms,axiom,
% 2.39/2.71 monoid202360481972076142t_unit @ inf_in4660618365625256667t_unit @ top_to1996260823553986621t_unit ).
% 2.39/2.71
% 2.39/2.71 % inf_top.monoid_axioms
% 2.39/2.71 thf(fact_407_merge__true__star__ctx,axiom,
% 2.39/2.71 ! [P2: assn] :
% 2.39/2.71 ( ( times_times_assn @ top_top_assn @ ( times_times_assn @ top_top_assn @ P2 ) )
% 2.39/2.71 = ( times_times_assn @ top_top_assn @ P2 ) ) ).
% 2.39/2.71
% 2.39/2.71 % merge_true_star_ctx
% 2.39/2.71 thf(fact_408_mod__false,axiom,
% 2.39/2.71 ! [H2: produc3658429121746597890et_nat] :
% 2.39/2.71 ~ ( rep_assn @ bot_bot_assn @ H2 ) ).
% 2.39/2.71
% 2.39/2.71 % mod_false
% 2.39/2.71 thf(fact_409_ent__false,axiom,
% 2.39/2.71 ! [P2: assn] : ( entails @ bot_bot_assn @ P2 ) ).
% 2.39/2.71
% 2.39/2.71 % ent_false
% 2.39/2.71 thf(fact_410_ent__true,axiom,
% 2.39/2.71 ! [P2: assn] : ( entails @ P2 @ top_top_assn ) ).
% 2.39/2.71
% 2.39/2.71 % ent_true
% 2.39/2.71 thf(fact_411_norm__assertion__simps_I9_J,axiom,
% 2.39/2.71 ! [X: assn] :
% 2.39/2.71 ( ( inf_inf_assn @ bot_bot_assn @ X )
% 2.39/2.71 = bot_bot_assn ) ).
% 2.39/2.71
% 2.39/2.71 % norm_assertion_simps(9)
% 2.39/2.71 thf(fact_412_norm__assertion__simps_I10_J,axiom,
% 2.39/2.71 ! [X: assn] :
% 2.39/2.71 ( ( inf_inf_assn @ X @ bot_bot_assn )
% 2.39/2.71 = bot_bot_assn ) ).
% 2.39/2.71
% 2.39/2.71 % norm_assertion_simps(10)
% 2.39/2.71 thf(fact_413_norm__assertion__simps_I3_J,axiom,
% 2.39/2.71 ! [X: assn] :
% 2.39/2.71 ( ( inf_inf_assn @ top_top_assn @ X )
% 2.39/2.71 = X ) ).
% 2.39/2.71
% 2.39/2.71 % norm_assertion_simps(3)
% 2.39/2.71 thf(fact_414_norm__assertion__simps_I4_J,axiom,
% 2.39/2.71 ! [X: assn] :
% 2.39/2.71 ( ( inf_inf_assn @ X @ top_top_assn )
% 2.39/2.71 = X ) ).
% 2.39/2.71
% 2.39/2.71 % norm_assertion_simps(4)
% 2.39/2.71 thf(fact_415_is__pure__assn__basic__simps_I1_J,axiom,
% 2.39/2.71 is_pure_assn @ bot_bot_assn ).
% 2.39/2.71
% 2.39/2.71 % is_pure_assn_basic_simps(1)
% 2.39/2.71 thf(fact_416_rotate1_Osimps_I1_J,axiom,
% 2.39/2.71 ( ( rotate328796349445179396n_assn @ nil_Pr5671120429643327159n_assn )
% 2.39/2.71 = nil_Pr5671120429643327159n_assn ) ).
% 2.39/2.71
% 2.39/2.71 % rotate1.simps(1)
% 2.39/2.71 thf(fact_417_rotate1_Osimps_I1_J,axiom,
% 2.39/2.71 ( ( rotate1_int @ nil_int )
% 2.39/2.71 = nil_int ) ).
% 2.39/2.71
% 2.39/2.71 % rotate1.simps(1)
% 2.39/2.71 thf(fact_418_rotate1_Osimps_I1_J,axiom,
% 2.39/2.71 ( ( rotate1_nat @ nil_nat )
% 2.39/2.71 = nil_nat ) ).
% 2.39/2.71
% 2.39/2.71 % rotate1.simps(1)
% 2.39/2.71 thf(fact_419_splice_Osimps_I1_J,axiom,
% 2.39/2.71 ! [Ys: list_P8527749157015355191n_assn] :
% 2.39/2.71 ( ( splice4588524007259616650n_assn @ nil_Pr5671120429643327159n_assn @ Ys )
% 2.39/2.71 = Ys ) ).
% 2.39/2.71
% 2.39/2.71 % splice.simps(1)
% 2.39/2.71 thf(fact_420_splice_Osimps_I1_J,axiom,
% 2.39/2.71 ! [Ys: list_int] :
% 2.39/2.71 ( ( splice_int @ nil_int @ Ys )
% 2.39/2.71 = Ys ) ).
% 2.39/2.71
% 2.39/2.71 % splice.simps(1)
% 2.39/2.71 thf(fact_421_splice_Osimps_I1_J,axiom,
% 2.39/2.71 ! [Ys: list_nat] :
% 2.39/2.71 ( ( splice_nat @ nil_nat @ Ys )
% 2.39/2.71 = Ys ) ).
% 2.39/2.71
% 2.39/2.71 % splice.simps(1)
% 2.39/2.71 thf(fact_422_entt__def__true,axiom,
% 2.39/2.71 ( entailst
% 2.39/2.71 = ( ^ [P: assn,Q: assn] : ( entails @ ( times_times_assn @ P @ top_top_assn ) @ ( times_times_assn @ Q @ top_top_assn ) ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % entt_def_true
% 2.39/2.71 thf(fact_423_entailst__def,axiom,
% 2.39/2.71 ( entailst
% 2.39/2.71 = ( ^ [A4: assn,B4: assn] : ( entails @ A4 @ ( times_times_assn @ B4 @ top_top_assn ) ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % entailst_def
% 2.39/2.71 thf(fact_424_enttI__true,axiom,
% 2.39/2.71 ! [P2: assn,Q2: assn] :
% 2.39/2.71 ( ( entails @ ( times_times_assn @ P2 @ top_top_assn ) @ ( times_times_assn @ Q2 @ top_top_assn ) )
% 2.39/2.71 => ( entailst @ P2 @ Q2 ) ) ).
% 2.39/2.71
% 2.39/2.71 % enttI_true
% 2.39/2.71 thf(fact_425_enttI,axiom,
% 2.39/2.71 ! [A3: assn,B3: assn] :
% 2.39/2.71 ( ( entails @ A3 @ ( times_times_assn @ B3 @ top_top_assn ) )
% 2.39/2.71 => ( entailst @ A3 @ B3 ) ) ).
% 2.39/2.71
% 2.39/2.71 % enttI
% 2.39/2.71 thf(fact_426_enttD,axiom,
% 2.39/2.71 ! [A3: assn,B3: assn] :
% 2.39/2.71 ( ( entailst @ A3 @ B3 )
% 2.39/2.71 => ( entails @ A3 @ ( times_times_assn @ B3 @ top_top_assn ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % enttD
% 2.39/2.71 thf(fact_427_entt__star__true__simp_I2_J,axiom,
% 2.39/2.71 ! [A3: assn,B3: assn] :
% 2.39/2.71 ( ( entailst @ ( times_times_assn @ A3 @ top_top_assn ) @ B3 )
% 2.39/2.71 = ( entailst @ A3 @ B3 ) ) ).
% 2.39/2.71
% 2.39/2.71 % entt_star_true_simp(2)
% 2.39/2.71 thf(fact_428_entt__star__true__simp_I1_J,axiom,
% 2.39/2.71 ! [A3: assn,B3: assn] :
% 2.39/2.71 ( ( entailst @ A3 @ ( times_times_assn @ B3 @ top_top_assn ) )
% 2.39/2.71 = ( entailst @ A3 @ B3 ) ) ).
% 2.39/2.71
% 2.39/2.71 % entt_star_true_simp(1)
% 2.39/2.71 thf(fact_429_inf__top_Osemilattice__neutr__axioms,axiom,
% 2.39/2.71 semila858173770281612099at_nat @ inf_in2572325071724192079at_nat @ top_to4669805908274784177at_nat ).
% 2.39/2.71
% 2.39/2.71 % inf_top.semilattice_neutr_axioms
% 2.39/2.71 thf(fact_430_inf__top_Osemilattice__neutr__axioms,axiom,
% 2.39/2.71 semila1241773964035338532et_nat @ inf_inf_set_nat @ top_top_set_nat ).
% 2.39/2.71
% 2.39/2.71 % inf_top.semilattice_neutr_axioms
% 2.39/2.71 thf(fact_431_inf__top_Osemilattice__neutr__axioms,axiom,
% 2.39/2.71 semila6538661356715008162_int_o @ inf_in3604695632404883862_int_o @ top_to1578927101902068148_int_o ).
% 2.39/2.71
% 2.39/2.71 % inf_top.semilattice_neutr_axioms
% 2.39/2.71 thf(fact_432_inf__top_Osemilattice__neutr__axioms,axiom,
% 2.39/2.71 semila5388846958306562758r_assn @ inf_inf_assn @ top_top_assn ).
% 2.39/2.71
% 2.39/2.71 % inf_top.semilattice_neutr_axioms
% 2.39/2.71 thf(fact_433_inf__top_Osemilattice__neutr__axioms,axiom,
% 2.39/2.71 semila7638931295954862799t_unit @ inf_in4660618365625256667t_unit @ top_to1996260823553986621t_unit ).
% 2.39/2.71
% 2.39/2.71 % inf_top.semilattice_neutr_axioms
% 2.39/2.71 thf(fact_434_entt__refl,axiom,
% 2.39/2.71 ! [A3: assn] : ( entailst @ A3 @ A3 ) ).
% 2.39/2.71
% 2.39/2.71 % entt_refl
% 2.39/2.71 thf(fact_435_entt__true,axiom,
% 2.39/2.71 ! [A3: assn] : ( entailst @ A3 @ top_top_assn ) ).
% 2.39/2.71
% 2.39/2.71 % entt_true
% 2.39/2.71 thf(fact_436_entt__emp,axiom,
% 2.39/2.71 ! [A3: assn] : ( entailst @ A3 @ one_one_assn ) ).
% 2.39/2.71
% 2.39/2.71 % entt_emp
% 2.39/2.71 thf(fact_437_entt__trans,axiom,
% 2.39/2.71 ! [A3: assn,B3: assn,C2: assn] :
% 2.39/2.71 ( ( entailst @ A3 @ B3 )
% 2.39/2.71 => ( ( entailst @ B3 @ C2 )
% 2.39/2.71 => ( entailst @ A3 @ C2 ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % entt_trans
% 2.39/2.71 thf(fact_438_entt__frame__fwd,axiom,
% 2.39/2.71 ! [P2: assn,Q2: assn,A3: assn,F4: assn,B3: assn] :
% 2.39/2.71 ( ( entailst @ P2 @ Q2 )
% 2.39/2.71 => ( ( entailst @ A3 @ ( times_times_assn @ P2 @ F4 ) )
% 2.39/2.71 => ( ( entailst @ ( times_times_assn @ Q2 @ F4 ) @ B3 )
% 2.39/2.71 => ( entailst @ A3 @ B3 ) ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % entt_frame_fwd
% 2.39/2.71 thf(fact_439_entt__star__mono,axiom,
% 2.39/2.71 ! [A3: assn,B3: assn,C2: assn,D: assn] :
% 2.39/2.71 ( ( entailst @ A3 @ B3 )
% 2.39/2.71 => ( ( entailst @ C2 @ D )
% 2.39/2.71 => ( entailst @ ( times_times_assn @ A3 @ C2 ) @ ( times_times_assn @ B3 @ D ) ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % entt_star_mono
% 2.39/2.71 thf(fact_440_ent__imp__entt,axiom,
% 2.39/2.71 ! [P2: assn,Q2: assn] :
% 2.39/2.71 ( ( entails @ P2 @ Q2 )
% 2.39/2.71 => ( entailst @ P2 @ Q2 ) ) ).
% 2.39/2.71
% 2.39/2.71 % ent_imp_entt
% 2.39/2.71 thf(fact_441_mod__true,axiom,
% 2.39/2.71 ! [H2: produc3658429121746597890et_nat] :
% 2.39/2.71 ( ( rep_assn @ top_top_assn @ H2 )
% 2.39/2.71 = ( in_range @ H2 ) ) ).
% 2.39/2.71
% 2.39/2.71 % mod_true
% 2.39/2.71 thf(fact_442_mod__h__bot__iff_I6_J,axiom,
% 2.39/2.71 ! [P2: assn,Q2: assn,H2: heap_e7401611519738050253t_unit] :
% 2.39/2.71 ( ( rep_assn @ ( inf_inf_assn @ P2 @ Q2 ) @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) )
% 2.39/2.71 = ( ( rep_assn @ P2 @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) )
% 2.39/2.71 & ( rep_assn @ Q2 @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % mod_h_bot_iff(6)
% 2.39/2.71 thf(fact_443_mod__h__bot__iff_I1_J,axiom,
% 2.39/2.71 ! [B: $o,H2: heap_e7401611519738050253t_unit] :
% 2.39/2.71 ( ( rep_assn @ ( pure_assn @ B ) @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) )
% 2.39/2.71 = B ) ).
% 2.39/2.71
% 2.39/2.71 % mod_h_bot_iff(1)
% 2.39/2.71 thf(fact_444_in__range__empty,axiom,
% 2.39/2.71 ! [H2: heap_e7401611519738050253t_unit] : ( in_range @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) ) ).
% 2.39/2.71
% 2.39/2.71 % in_range_empty
% 2.39/2.71 thf(fact_445_mod__h__bot__iff_I5_J,axiom,
% 2.39/2.71 ! [P2: assn,Q2: assn,H2: heap_e7401611519738050253t_unit] :
% 2.39/2.71 ( ( rep_assn @ ( times_times_assn @ P2 @ Q2 ) @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) )
% 2.39/2.71 = ( ( rep_assn @ P2 @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) )
% 2.39/2.71 & ( rep_assn @ Q2 @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % mod_h_bot_iff(5)
% 2.39/2.71 thf(fact_446_one__assn__raw_Ocases,axiom,
% 2.39/2.71 ! [X: produc3658429121746597890et_nat] :
% 2.39/2.71 ~ ! [H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.39/2.71 ( X
% 2.39/2.71 != ( produc7507926704131184380et_nat @ H3 @ As ) ) ).
% 2.39/2.71
% 2.39/2.71 % one_assn_raw.cases
% 2.39/2.71 thf(fact_447_mod__h__bot__indep,axiom,
% 2.39/2.71 ! [P2: assn,H2: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit] :
% 2.39/2.71 ( ( rep_assn @ P2 @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) )
% 2.39/2.71 = ( rep_assn @ P2 @ ( produc7507926704131184380et_nat @ H5 @ bot_bot_set_nat ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % mod_h_bot_indep
% 2.39/2.71 thf(fact_448_mult_Oabel__semigroup__axioms,axiom,
% 2.39/2.71 abel_semigroup_assn @ times_times_assn ).
% 2.39/2.71
% 2.39/2.71 % mult.abel_semigroup_axioms
% 2.39/2.71 thf(fact_449_mult_Oabel__semigroup__axioms,axiom,
% 2.39/2.71 abel_semigroup_nat @ times_times_nat ).
% 2.39/2.71
% 2.39/2.71 % mult.abel_semigroup_axioms
% 2.39/2.71 thf(fact_450_mult_Oabel__semigroup__axioms,axiom,
% 2.39/2.71 abel_semigroup_int @ times_times_int ).
% 2.39/2.71
% 2.39/2.71 % mult.abel_semigroup_axioms
% 2.39/2.71 thf(fact_451_mult_Oabel__semigroup__axioms,axiom,
% 2.39/2.71 abel_s8772020223019846471nteger @ times_3573771949741848930nteger ).
% 2.39/2.71
% 2.39/2.71 % mult.abel_semigroup_axioms
% 2.39/2.71 thf(fact_452_mult_Oabel__semigroup__axioms,axiom,
% 2.39/2.71 abel_s7595615374776563986atural @ times_2397367101498566445atural ).
% 2.39/2.71
% 2.39/2.71 % mult.abel_semigroup_axioms
% 2.39/2.71 thf(fact_453_models__in__range,axiom,
% 2.39/2.71 ! [P2: assn,H2: produc3658429121746597890et_nat] :
% 2.39/2.71 ( ( rep_assn @ P2 @ H2 )
% 2.39/2.71 => ( in_range @ H2 ) ) ).
% 2.39/2.71
% 2.39/2.71 % models_in_range
% 2.39/2.71 thf(fact_454_inf_Oabel__semigroup__axioms,axiom,
% 2.39/2.71 abel_semigroup_assn @ inf_inf_assn ).
% 2.39/2.71
% 2.39/2.71 % inf.abel_semigroup_axioms
% 2.39/2.71 thf(fact_455_inf_Oabel__semigroup__axioms,axiom,
% 2.39/2.71 abel_s1357164767337380599at_nat @ inf_in2572325071724192079at_nat ).
% 2.39/2.71
% 2.39/2.71 % inf.abel_semigroup_axioms
% 2.39/2.71 thf(fact_456_inf_Oabel__semigroup__axioms,axiom,
% 2.39/2.71 abel_s3907380067910933104et_nat @ inf_inf_set_nat ).
% 2.39/2.71
% 2.39/2.71 % inf.abel_semigroup_axioms
% 2.39/2.71 thf(fact_457_inf_Oabel__semigroup__axioms,axiom,
% 2.39/2.71 abel_semigroup_nat @ inf_inf_nat ).
% 2.39/2.71
% 2.39/2.71 % inf.abel_semigroup_axioms
% 2.39/2.71 thf(fact_458_inf_Oabel__semigroup__axioms,axiom,
% 2.39/2.71 abel_s3861158783995384302_int_o @ inf_in3604695632404883862_int_o ).
% 2.39/2.71
% 2.39/2.71 % inf.abel_semigroup_axioms
% 2.39/2.71 thf(fact_459_mult_Osemigroup__axioms,axiom,
% 2.39/2.71 semigroup_assn @ times_times_assn ).
% 2.39/2.71
% 2.39/2.71 % mult.semigroup_axioms
% 2.39/2.71 thf(fact_460_mult_Osemigroup__axioms,axiom,
% 2.39/2.71 semigroup_nat @ times_times_nat ).
% 2.39/2.71
% 2.39/2.71 % mult.semigroup_axioms
% 2.39/2.71 thf(fact_461_mult_Osemigroup__axioms,axiom,
% 2.39/2.71 semigroup_int @ times_times_int ).
% 2.39/2.71
% 2.39/2.71 % mult.semigroup_axioms
% 2.39/2.71 thf(fact_462_mult_Osemigroup__axioms,axiom,
% 2.39/2.71 semigr7036097719740861967nteger @ times_3573771949741848930nteger ).
% 2.39/2.71
% 2.39/2.71 % mult.semigroup_axioms
% 2.39/2.71 thf(fact_463_mult_Osemigroup__axioms,axiom,
% 2.39/2.71 semigr5859692871497579482atural @ times_2397367101498566445atural ).
% 2.39/2.71
% 2.39/2.71 % mult.semigroup_axioms
% 2.39/2.71 thf(fact_464_inf_Osemilattice__axioms,axiom,
% 2.39/2.71 semilattice_assn @ inf_inf_assn ).
% 2.39/2.71
% 2.39/2.71 % inf.semilattice_axioms
% 2.39/2.71 thf(fact_465_inf_Osemilattice__axioms,axiom,
% 2.39/2.71 semila6306352305301525377at_nat @ inf_in2572325071724192079at_nat ).
% 2.39/2.71
% 2.39/2.71 % inf.semilattice_axioms
% 2.39/2.71 thf(fact_466_inf_Osemilattice__axioms,axiom,
% 2.39/2.71 semilattice_set_nat @ inf_inf_set_nat ).
% 2.39/2.71
% 2.39/2.71 % inf.semilattice_axioms
% 2.39/2.71 thf(fact_467_inf_Osemilattice__axioms,axiom,
% 2.39/2.71 semilattice_nat @ inf_inf_nat ).
% 2.39/2.71
% 2.39/2.71 % inf.semilattice_axioms
% 2.39/2.71 thf(fact_468_inf_Osemilattice__axioms,axiom,
% 2.39/2.71 semila1175464891343163876_int_o @ inf_in3604695632404883862_int_o ).
% 2.39/2.71
% 2.39/2.71 % inf.semilattice_axioms
% 2.39/2.71 thf(fact_469_inf_Osemigroup__axioms,axiom,
% 2.39/2.71 semigroup_assn @ inf_inf_assn ).
% 2.39/2.71
% 2.39/2.71 % inf.semigroup_axioms
% 2.39/2.71 thf(fact_470_inf_Osemigroup__axioms,axiom,
% 2.39/2.71 semigr3814207799437385263at_nat @ inf_in2572325071724192079at_nat ).
% 2.39/2.71
% 2.39/2.71 % inf.semigroup_axioms
% 2.39/2.71 thf(fact_471_inf_Osemigroup__axioms,axiom,
% 2.39/2.71 semigroup_set_nat @ inf_inf_set_nat ).
% 2.39/2.71
% 2.39/2.71 % inf.semigroup_axioms
% 2.39/2.71 thf(fact_472_inf_Osemigroup__axioms,axiom,
% 2.39/2.71 semigroup_nat @ inf_inf_nat ).
% 2.39/2.71
% 2.39/2.71 % inf.semigroup_axioms
% 2.39/2.71 thf(fact_473_inf_Osemigroup__axioms,axiom,
% 2.39/2.71 semigr8095932293087610038_int_o @ inf_in3604695632404883862_int_o ).
% 2.39/2.71
% 2.39/2.71 % inf.semigroup_axioms
% 2.39/2.71 thf(fact_474_mod__h__bot__iff_I2_J,axiom,
% 2.39/2.71 ! [H2: heap_e7401611519738050253t_unit] : ( rep_assn @ top_top_assn @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) ) ).
% 2.39/2.71
% 2.39/2.71 % mod_h_bot_iff(2)
% 2.39/2.71 thf(fact_475_mod__emp__simp,axiom,
% 2.39/2.71 ! [H2: heap_e7401611519738050253t_unit] : ( rep_assn @ one_one_assn @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) ) ).
% 2.39/2.71
% 2.39/2.71 % mod_emp_simp
% 2.39/2.71 thf(fact_476_pure__assn__raw_Oelims_I3_J,axiom,
% 2.39/2.71 ! [X: $o,Xa: produc3658429121746597890et_nat] :
% 2.39/2.71 ( ~ ( pure_a825153325127701367it_nat @ X @ Xa )
% 2.39/2.71 => ~ ! [H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.39/2.71 ( ( Xa
% 2.39/2.71 = ( produc7507926704131184380et_nat @ H3 @ As ) )
% 2.39/2.71 => ( ( As = bot_bot_set_nat )
% 2.39/2.71 & X ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % pure_assn_raw.elims(3)
% 2.39/2.71 thf(fact_477_pure__assn__raw_Oelims_I2_J,axiom,
% 2.39/2.71 ! [X: $o,Xa: produc3658429121746597890et_nat] :
% 2.39/2.71 ( ( pure_a825153325127701367it_nat @ X @ Xa )
% 2.39/2.71 => ~ ! [H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.39/2.71 ( ( Xa
% 2.39/2.71 = ( produc7507926704131184380et_nat @ H3 @ As ) )
% 2.39/2.71 => ~ ( ( As = bot_bot_set_nat )
% 2.39/2.71 & X ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % pure_assn_raw.elims(2)
% 2.39/2.71 thf(fact_478_pure__assn__raw_Oelims_I1_J,axiom,
% 2.39/2.71 ! [X: $o,Xa: produc3658429121746597890et_nat,Y: $o] :
% 2.39/2.71 ( ( ( pure_a825153325127701367it_nat @ X @ Xa )
% 2.39/2.71 = Y )
% 2.39/2.71 => ~ ! [H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.39/2.71 ( ( Xa
% 2.39/2.71 = ( produc7507926704131184380et_nat @ H3 @ As ) )
% 2.39/2.71 => ( Y
% 2.39/2.71 = ( ~ ( ( As = bot_bot_set_nat )
% 2.39/2.71 & X ) ) ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % pure_assn_raw.elims(1)
% 2.39/2.71 thf(fact_479_pure__assn__raw_Osimps,axiom,
% 2.39/2.71 ! [B: $o,H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 2.39/2.71 ( ( pure_a825153325127701367it_nat @ B @ ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 2.39/2.71 = ( ( As2 = bot_bot_set_nat )
% 2.39/2.71 & B ) ) ).
% 2.39/2.71
% 2.39/2.71 % pure_assn_raw.simps
% 2.39/2.71 thf(fact_480_mod__star__conv,axiom,
% 2.39/2.71 ! [A3: assn,B3: assn,H2: produc3658429121746597890et_nat] :
% 2.39/2.71 ( ( rep_assn @ ( times_times_assn @ A3 @ B3 ) @ H2 )
% 2.39/2.71 = ( ? [Hr: heap_e7401611519738050253t_unit,As1: set_nat,As22: set_nat] :
% 2.39/2.71 ( ( H2
% 2.39/2.71 = ( produc7507926704131184380et_nat @ Hr @ ( sup_sup_set_nat @ As1 @ As22 ) ) )
% 2.39/2.71 & ( ( inf_inf_set_nat @ As1 @ As22 )
% 2.39/2.71 = bot_bot_set_nat )
% 2.39/2.71 & ( rep_assn @ A3 @ ( produc7507926704131184380et_nat @ Hr @ As1 ) )
% 2.39/2.71 & ( rep_assn @ B3 @ ( produc7507926704131184380et_nat @ Hr @ As22 ) ) ) ) ) ).
% 2.39/2.71
% 2.39/2.71 % mod_star_conv
% 2.39/2.71 thf(fact_481_star__assnI,axiom,
% 2.39/2.71 ! [P2: assn,H2: heap_e7401611519738050253t_unit,As2: set_nat,Q2: assn,As3: set_nat] :
% 2.39/2.71 ( ( rep_assn @ P2 @ ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 2.39/2.72 => ( ( rep_assn @ Q2 @ ( produc7507926704131184380et_nat @ H2 @ As3 ) )
% 2.39/2.72 => ( ( ( inf_inf_set_nat @ As2 @ As3 )
% 2.39/2.72 = bot_bot_set_nat )
% 2.39/2.72 => ( rep_assn @ ( times_times_assn @ P2 @ Q2 ) @ ( produc7507926704131184380et_nat @ H2 @ ( sup_sup_set_nat @ As2 @ As3 ) ) ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % star_assnI
% 2.39/2.72 thf(fact_482_one__assn__raw_Oelims_I3_J,axiom,
% 2.39/2.72 ! [X: produc3658429121746597890et_nat] :
% 2.39/2.72 ( ~ ( one_assn_raw @ X )
% 2.39/2.72 => ~ ! [H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.39/2.72 ( ( X
% 2.39/2.72 = ( produc7507926704131184380et_nat @ H3 @ As ) )
% 2.39/2.72 => ( As = bot_bot_set_nat ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % one_assn_raw.elims(3)
% 2.39/2.72 thf(fact_483_sup_Oright__idem,axiom,
% 2.39/2.72 ! [A: set_nat,B: set_nat] :
% 2.39/2.72 ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ A @ B ) @ B )
% 2.39/2.72 = ( sup_sup_set_nat @ A @ B ) ) ).
% 2.39/2.72
% 2.39/2.72 % sup.right_idem
% 2.39/2.72 thf(fact_484_sup_Oright__idem,axiom,
% 2.39/2.72 ! [A: assn,B: assn] :
% 2.39/2.72 ( ( sup_sup_assn @ ( sup_sup_assn @ A @ B ) @ B )
% 2.39/2.72 = ( sup_sup_assn @ A @ B ) ) ).
% 2.39/2.72
% 2.39/2.72 % sup.right_idem
% 2.39/2.72 thf(fact_485_sup__left__idem,axiom,
% 2.39/2.72 ! [X: set_nat,Y: set_nat] :
% 2.39/2.72 ( ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ X @ Y ) )
% 2.39/2.72 = ( sup_sup_set_nat @ X @ Y ) ) ).
% 2.39/2.72
% 2.39/2.72 % sup_left_idem
% 2.39/2.72 thf(fact_486_sup__left__idem,axiom,
% 2.39/2.72 ! [X: assn,Y: assn] :
% 2.39/2.72 ( ( sup_sup_assn @ X @ ( sup_sup_assn @ X @ Y ) )
% 2.39/2.72 = ( sup_sup_assn @ X @ Y ) ) ).
% 2.39/2.72
% 2.39/2.72 % sup_left_idem
% 2.39/2.72 thf(fact_487_sup_Oleft__idem,axiom,
% 2.39/2.72 ! [A: set_nat,B: set_nat] :
% 2.39/2.72 ( ( sup_sup_set_nat @ A @ ( sup_sup_set_nat @ A @ B ) )
% 2.39/2.72 = ( sup_sup_set_nat @ A @ B ) ) ).
% 2.39/2.72
% 2.39/2.72 % sup.left_idem
% 2.39/2.72 thf(fact_488_sup_Oleft__idem,axiom,
% 2.39/2.72 ! [A: assn,B: assn] :
% 2.39/2.72 ( ( sup_sup_assn @ A @ ( sup_sup_assn @ A @ B ) )
% 2.39/2.72 = ( sup_sup_assn @ A @ B ) ) ).
% 2.39/2.72
% 2.39/2.72 % sup.left_idem
% 2.39/2.72 thf(fact_489_sup__idem,axiom,
% 2.39/2.72 ! [X: set_nat] :
% 2.39/2.72 ( ( sup_sup_set_nat @ X @ X )
% 2.39/2.72 = X ) ).
% 2.39/2.72
% 2.39/2.72 % sup_idem
% 2.39/2.72 thf(fact_490_sup__idem,axiom,
% 2.39/2.72 ! [X: assn] :
% 2.39/2.72 ( ( sup_sup_assn @ X @ X )
% 2.39/2.72 = X ) ).
% 2.39/2.72
% 2.39/2.72 % sup_idem
% 2.39/2.72 thf(fact_491_sup_Oidem,axiom,
% 2.39/2.72 ! [A: set_nat] :
% 2.39/2.72 ( ( sup_sup_set_nat @ A @ A )
% 2.39/2.72 = A ) ).
% 2.39/2.72
% 2.39/2.72 % sup.idem
% 2.39/2.72 thf(fact_492_sup_Oidem,axiom,
% 2.39/2.72 ! [A: assn] :
% 2.39/2.72 ( ( sup_sup_assn @ A @ A )
% 2.39/2.72 = A ) ).
% 2.39/2.72
% 2.39/2.72 % sup.idem
% 2.39/2.72 thf(fact_493_sup__bot_Oright__neutral,axiom,
% 2.39/2.72 ! [A: assn] :
% 2.39/2.72 ( ( sup_sup_assn @ A @ bot_bot_assn )
% 2.39/2.72 = A ) ).
% 2.39/2.72
% 2.39/2.72 % sup_bot.right_neutral
% 2.39/2.72 thf(fact_494_sup__bot_Oright__neutral,axiom,
% 2.39/2.72 ! [A: set_nat] :
% 2.39/2.72 ( ( sup_sup_set_nat @ A @ bot_bot_set_nat )
% 2.39/2.72 = A ) ).
% 2.39/2.72
% 2.39/2.72 % sup_bot.right_neutral
% 2.39/2.72 thf(fact_495_sup__bot_Oright__neutral,axiom,
% 2.39/2.72 ! [A: set_int] :
% 2.39/2.72 ( ( sup_sup_set_int @ A @ bot_bot_set_int )
% 2.39/2.72 = A ) ).
% 2.39/2.72
% 2.39/2.72 % sup_bot.right_neutral
% 2.39/2.72 thf(fact_496_sup__bot_Oneutr__eq__iff,axiom,
% 2.39/2.72 ! [A: assn,B: assn] :
% 2.39/2.72 ( ( bot_bot_assn
% 2.39/2.72 = ( sup_sup_assn @ A @ B ) )
% 2.39/2.72 = ( ( A = bot_bot_assn )
% 2.39/2.72 & ( B = bot_bot_assn ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % sup_bot.neutr_eq_iff
% 2.39/2.72 thf(fact_497_sup__bot_Oneutr__eq__iff,axiom,
% 2.39/2.72 ! [A: set_nat,B: set_nat] :
% 2.39/2.72 ( ( bot_bot_set_nat
% 2.39/2.72 = ( sup_sup_set_nat @ A @ B ) )
% 2.39/2.72 = ( ( A = bot_bot_set_nat )
% 2.39/2.72 & ( B = bot_bot_set_nat ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % sup_bot.neutr_eq_iff
% 2.39/2.72 thf(fact_498_sup__bot_Oneutr__eq__iff,axiom,
% 2.39/2.72 ! [A: set_int,B: set_int] :
% 2.39/2.72 ( ( bot_bot_set_int
% 2.39/2.72 = ( sup_sup_set_int @ A @ B ) )
% 2.39/2.72 = ( ( A = bot_bot_set_int )
% 2.39/2.72 & ( B = bot_bot_set_int ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % sup_bot.neutr_eq_iff
% 2.39/2.72 thf(fact_499_sup__bot_Oleft__neutral,axiom,
% 2.39/2.72 ! [A: assn] :
% 2.39/2.72 ( ( sup_sup_assn @ bot_bot_assn @ A )
% 2.39/2.72 = A ) ).
% 2.39/2.72
% 2.39/2.72 % sup_bot.left_neutral
% 2.39/2.72 thf(fact_500_sup__bot_Oleft__neutral,axiom,
% 2.39/2.72 ! [A: set_nat] :
% 2.39/2.72 ( ( sup_sup_set_nat @ bot_bot_set_nat @ A )
% 2.39/2.72 = A ) ).
% 2.39/2.72
% 2.39/2.72 % sup_bot.left_neutral
% 2.39/2.72 thf(fact_501_sup__bot_Oleft__neutral,axiom,
% 2.39/2.72 ! [A: set_int] :
% 2.39/2.72 ( ( sup_sup_set_int @ bot_bot_set_int @ A )
% 2.39/2.72 = A ) ).
% 2.39/2.72
% 2.39/2.72 % sup_bot.left_neutral
% 2.39/2.72 thf(fact_502_sup__bot_Oeq__neutr__iff,axiom,
% 2.39/2.72 ! [A: assn,B: assn] :
% 2.39/2.72 ( ( ( sup_sup_assn @ A @ B )
% 2.39/2.72 = bot_bot_assn )
% 2.39/2.72 = ( ( A = bot_bot_assn )
% 2.39/2.72 & ( B = bot_bot_assn ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % sup_bot.eq_neutr_iff
% 2.39/2.72 thf(fact_503_sup__bot_Oeq__neutr__iff,axiom,
% 2.39/2.72 ! [A: set_nat,B: set_nat] :
% 2.39/2.72 ( ( ( sup_sup_set_nat @ A @ B )
% 2.39/2.72 = bot_bot_set_nat )
% 2.39/2.72 = ( ( A = bot_bot_set_nat )
% 2.39/2.72 & ( B = bot_bot_set_nat ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % sup_bot.eq_neutr_iff
% 2.39/2.72 thf(fact_504_sup__bot_Oeq__neutr__iff,axiom,
% 2.39/2.72 ! [A: set_int,B: set_int] :
% 2.39/2.72 ( ( ( sup_sup_set_int @ A @ B )
% 2.39/2.72 = bot_bot_set_int )
% 2.39/2.72 = ( ( A = bot_bot_set_int )
% 2.39/2.72 & ( B = bot_bot_set_int ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % sup_bot.eq_neutr_iff
% 2.39/2.72 thf(fact_505_sup__eq__bot__iff,axiom,
% 2.39/2.72 ! [X: assn,Y: assn] :
% 2.39/2.72 ( ( ( sup_sup_assn @ X @ Y )
% 2.39/2.72 = bot_bot_assn )
% 2.39/2.72 = ( ( X = bot_bot_assn )
% 2.39/2.72 & ( Y = bot_bot_assn ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % sup_eq_bot_iff
% 2.39/2.72 thf(fact_506_sup__eq__bot__iff,axiom,
% 2.39/2.72 ! [X: set_nat,Y: set_nat] :
% 2.39/2.72 ( ( ( sup_sup_set_nat @ X @ Y )
% 2.39/2.72 = bot_bot_set_nat )
% 2.39/2.72 = ( ( X = bot_bot_set_nat )
% 2.39/2.72 & ( Y = bot_bot_set_nat ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % sup_eq_bot_iff
% 2.39/2.72 thf(fact_507_sup__eq__bot__iff,axiom,
% 2.39/2.72 ! [X: set_int,Y: set_int] :
% 2.39/2.72 ( ( ( sup_sup_set_int @ X @ Y )
% 2.39/2.72 = bot_bot_set_int )
% 2.39/2.72 = ( ( X = bot_bot_set_int )
% 2.39/2.72 & ( Y = bot_bot_set_int ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % sup_eq_bot_iff
% 2.39/2.72 thf(fact_508_bot__eq__sup__iff,axiom,
% 2.39/2.72 ! [X: assn,Y: assn] :
% 2.39/2.72 ( ( bot_bot_assn
% 2.39/2.72 = ( sup_sup_assn @ X @ Y ) )
% 2.39/2.72 = ( ( X = bot_bot_assn )
% 2.39/2.72 & ( Y = bot_bot_assn ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % bot_eq_sup_iff
% 2.39/2.72 thf(fact_509_bot__eq__sup__iff,axiom,
% 2.39/2.72 ! [X: set_nat,Y: set_nat] :
% 2.39/2.72 ( ( bot_bot_set_nat
% 2.39/2.72 = ( sup_sup_set_nat @ X @ Y ) )
% 2.39/2.72 = ( ( X = bot_bot_set_nat )
% 2.39/2.72 & ( Y = bot_bot_set_nat ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % bot_eq_sup_iff
% 2.39/2.72 thf(fact_510_bot__eq__sup__iff,axiom,
% 2.39/2.72 ! [X: set_int,Y: set_int] :
% 2.39/2.72 ( ( bot_bot_set_int
% 2.39/2.72 = ( sup_sup_set_int @ X @ Y ) )
% 2.39/2.72 = ( ( X = bot_bot_set_int )
% 2.39/2.72 & ( Y = bot_bot_set_int ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % bot_eq_sup_iff
% 2.39/2.72 thf(fact_511_sup__bot__right,axiom,
% 2.39/2.72 ! [X: assn] :
% 2.39/2.72 ( ( sup_sup_assn @ X @ bot_bot_assn )
% 2.39/2.72 = X ) ).
% 2.39/2.72
% 2.39/2.72 % sup_bot_right
% 2.39/2.72 thf(fact_512_sup__bot__right,axiom,
% 2.39/2.72 ! [X: set_nat] :
% 2.39/2.72 ( ( sup_sup_set_nat @ X @ bot_bot_set_nat )
% 2.39/2.72 = X ) ).
% 2.39/2.72
% 2.39/2.72 % sup_bot_right
% 2.39/2.72 thf(fact_513_sup__bot__right,axiom,
% 2.39/2.72 ! [X: set_int] :
% 2.39/2.72 ( ( sup_sup_set_int @ X @ bot_bot_set_int )
% 2.39/2.72 = X ) ).
% 2.39/2.72
% 2.39/2.72 % sup_bot_right
% 2.39/2.72 thf(fact_514_sup__bot__left,axiom,
% 2.39/2.72 ! [X: assn] :
% 2.39/2.72 ( ( sup_sup_assn @ bot_bot_assn @ X )
% 2.39/2.72 = X ) ).
% 2.39/2.72
% 2.39/2.72 % sup_bot_left
% 2.39/2.72 thf(fact_515_sup__bot__left,axiom,
% 2.39/2.72 ! [X: set_nat] :
% 2.39/2.72 ( ( sup_sup_set_nat @ bot_bot_set_nat @ X )
% 2.39/2.72 = X ) ).
% 2.39/2.72
% 2.39/2.72 % sup_bot_left
% 2.39/2.72 thf(fact_516_sup__bot__left,axiom,
% 2.39/2.72 ! [X: set_int] :
% 2.39/2.72 ( ( sup_sup_set_int @ bot_bot_set_int @ X )
% 2.39/2.72 = X ) ).
% 2.39/2.72
% 2.39/2.72 % sup_bot_left
% 2.39/2.72 thf(fact_517_sup__top__right,axiom,
% 2.39/2.72 ! [X: set_nat] :
% 2.39/2.72 ( ( sup_sup_set_nat @ X @ top_top_set_nat )
% 2.39/2.72 = top_top_set_nat ) ).
% 2.39/2.72
% 2.39/2.72 % sup_top_right
% 2.39/2.72 thf(fact_518_sup__top__right,axiom,
% 2.39/2.72 ! [X: assn] :
% 2.39/2.72 ( ( sup_sup_assn @ X @ top_top_assn )
% 2.39/2.72 = top_top_assn ) ).
% 2.39/2.72
% 2.39/2.72 % sup_top_right
% 2.39/2.72 thf(fact_519_sup__top__right,axiom,
% 2.39/2.72 ! [X: set_Product_unit] :
% 2.39/2.72 ( ( sup_su793286257634532545t_unit @ X @ top_to1996260823553986621t_unit )
% 2.39/2.72 = top_to1996260823553986621t_unit ) ).
% 2.39/2.72
% 2.39/2.72 % sup_top_right
% 2.39/2.72 thf(fact_520_sup__top__left,axiom,
% 2.39/2.72 ! [X: set_nat] :
% 2.39/2.72 ( ( sup_sup_set_nat @ top_top_set_nat @ X )
% 2.39/2.72 = top_top_set_nat ) ).
% 2.39/2.72
% 2.39/2.72 % sup_top_left
% 2.39/2.72 thf(fact_521_sup__top__left,axiom,
% 2.39/2.72 ! [X: assn] :
% 2.39/2.72 ( ( sup_sup_assn @ top_top_assn @ X )
% 2.39/2.72 = top_top_assn ) ).
% 2.39/2.72
% 2.39/2.72 % sup_top_left
% 2.39/2.72 thf(fact_522_sup__top__left,axiom,
% 2.39/2.72 ! [X: set_Product_unit] :
% 2.39/2.72 ( ( sup_su793286257634532545t_unit @ top_to1996260823553986621t_unit @ X )
% 2.39/2.72 = top_to1996260823553986621t_unit ) ).
% 2.39/2.72
% 2.39/2.72 % sup_top_left
% 2.39/2.72 thf(fact_523_inf__sup__absorb,axiom,
% 2.39/2.72 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( inf_in2572325071724192079at_nat @ X @ ( sup_su6327502436637775413at_nat @ X @ Y ) )
% 2.39/2.72 = X ) ).
% 2.39/2.72
% 2.39/2.72 % inf_sup_absorb
% 2.39/2.72 thf(fact_524_inf__sup__absorb,axiom,
% 2.39/2.72 ! [X: nat,Y: nat] :
% 2.39/2.72 ( ( inf_inf_nat @ X @ ( sup_sup_nat @ X @ Y ) )
% 2.39/2.72 = X ) ).
% 2.39/2.72
% 2.39/2.72 % inf_sup_absorb
% 2.39/2.72 thf(fact_525_inf__sup__absorb,axiom,
% 2.39/2.72 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 2.39/2.72 ( ( inf_in3604695632404883862_int_o @ X @ ( sup_su8463660629351352368_int_o @ X @ Y ) )
% 2.39/2.72 = X ) ).
% 2.39/2.72
% 2.39/2.72 % inf_sup_absorb
% 2.39/2.72 thf(fact_526_inf__sup__absorb,axiom,
% 2.39/2.72 ! [X: set_nat,Y: set_nat] :
% 2.39/2.72 ( ( inf_inf_set_nat @ X @ ( sup_sup_set_nat @ X @ Y ) )
% 2.39/2.72 = X ) ).
% 2.39/2.72
% 2.39/2.72 % inf_sup_absorb
% 2.39/2.72 thf(fact_527_inf__sup__absorb,axiom,
% 2.39/2.72 ! [X: assn,Y: assn] :
% 2.39/2.72 ( ( inf_inf_assn @ X @ ( sup_sup_assn @ X @ Y ) )
% 2.39/2.72 = X ) ).
% 2.39/2.72
% 2.39/2.72 % inf_sup_absorb
% 2.39/2.72 thf(fact_528_sup__inf__absorb,axiom,
% 2.39/2.72 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( sup_su6327502436637775413at_nat @ X @ ( inf_in2572325071724192079at_nat @ X @ Y ) )
% 2.39/2.72 = X ) ).
% 2.39/2.72
% 2.39/2.72 % sup_inf_absorb
% 2.39/2.72 thf(fact_529_sup__inf__absorb,axiom,
% 2.39/2.72 ! [X: nat,Y: nat] :
% 2.39/2.72 ( ( sup_sup_nat @ X @ ( inf_inf_nat @ X @ Y ) )
% 2.39/2.72 = X ) ).
% 2.39/2.72
% 2.39/2.72 % sup_inf_absorb
% 2.39/2.72 thf(fact_530_sup__inf__absorb,axiom,
% 2.39/2.72 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 2.39/2.72 ( ( sup_su8463660629351352368_int_o @ X @ ( inf_in3604695632404883862_int_o @ X @ Y ) )
% 2.39/2.72 = X ) ).
% 2.39/2.72
% 2.39/2.72 % sup_inf_absorb
% 2.39/2.72 thf(fact_531_sup__inf__absorb,axiom,
% 2.39/2.72 ! [X: set_nat,Y: set_nat] :
% 2.39/2.72 ( ( sup_sup_set_nat @ X @ ( inf_inf_set_nat @ X @ Y ) )
% 2.39/2.72 = X ) ).
% 2.39/2.72
% 2.39/2.72 % sup_inf_absorb
% 2.39/2.72 thf(fact_532_sup__inf__absorb,axiom,
% 2.39/2.72 ! [X: assn,Y: assn] :
% 2.39/2.72 ( ( sup_sup_assn @ X @ ( inf_inf_assn @ X @ Y ) )
% 2.39/2.72 = X ) ).
% 2.39/2.72
% 2.39/2.72 % sup_inf_absorb
% 2.39/2.72 thf(fact_533_in__range__dist__union,axiom,
% 2.39/2.72 ! [H2: heap_e7401611519738050253t_unit,As2: set_nat,As3: set_nat] :
% 2.39/2.72 ( ( in_range @ ( produc7507926704131184380et_nat @ H2 @ ( sup_sup_set_nat @ As2 @ As3 ) ) )
% 2.39/2.72 = ( ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 2.39/2.72 & ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As3 ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % in_range_dist_union
% 2.39/2.72 thf(fact_534_sup__left__commute,axiom,
% 2.39/2.72 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 2.39/2.72 ( ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) )
% 2.39/2.72 = ( sup_sup_set_nat @ Y @ ( sup_sup_set_nat @ X @ Z ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % sup_left_commute
% 2.39/2.72 thf(fact_535_sup__left__commute,axiom,
% 2.39/2.72 ! [X: assn,Y: assn,Z: assn] :
% 2.39/2.72 ( ( sup_sup_assn @ X @ ( sup_sup_assn @ Y @ Z ) )
% 2.39/2.72 = ( sup_sup_assn @ Y @ ( sup_sup_assn @ X @ Z ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % sup_left_commute
% 2.39/2.72 thf(fact_536_sup_Oleft__commute,axiom,
% 2.39/2.72 ! [B: set_nat,A: set_nat,C: set_nat] :
% 2.39/2.72 ( ( sup_sup_set_nat @ B @ ( sup_sup_set_nat @ A @ C ) )
% 2.39/2.72 = ( sup_sup_set_nat @ A @ ( sup_sup_set_nat @ B @ C ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % sup.left_commute
% 2.39/2.72 thf(fact_537_sup_Oleft__commute,axiom,
% 2.39/2.72 ! [B: assn,A: assn,C: assn] :
% 2.39/2.72 ( ( sup_sup_assn @ B @ ( sup_sup_assn @ A @ C ) )
% 2.39/2.72 = ( sup_sup_assn @ A @ ( sup_sup_assn @ B @ C ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % sup.left_commute
% 2.39/2.72 thf(fact_538_sup__commute,axiom,
% 2.39/2.72 ( sup_sup_set_nat
% 2.39/2.72 = ( ^ [X2: set_nat,Y2: set_nat] : ( sup_sup_set_nat @ Y2 @ X2 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % sup_commute
% 2.39/2.72 thf(fact_539_sup__commute,axiom,
% 2.39/2.72 ( sup_sup_assn
% 2.39/2.72 = ( ^ [X2: assn,Y2: assn] : ( sup_sup_assn @ Y2 @ X2 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % sup_commute
% 2.39/2.72 thf(fact_540_sup_Ocommute,axiom,
% 2.39/2.72 ( sup_sup_set_nat
% 2.39/2.72 = ( ^ [A2: set_nat,B2: set_nat] : ( sup_sup_set_nat @ B2 @ A2 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % sup.commute
% 2.39/2.72 thf(fact_541_sup_Ocommute,axiom,
% 2.39/2.72 ( sup_sup_assn
% 2.39/2.72 = ( ^ [A2: assn,B2: assn] : ( sup_sup_assn @ B2 @ A2 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % sup.commute
% 2.39/2.72 thf(fact_542_sup__assoc,axiom,
% 2.39/2.72 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 2.39/2.72 ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ Z )
% 2.39/2.72 = ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % sup_assoc
% 2.39/2.72 thf(fact_543_sup__assoc,axiom,
% 2.39/2.72 ! [X: assn,Y: assn,Z: assn] :
% 2.39/2.72 ( ( sup_sup_assn @ ( sup_sup_assn @ X @ Y ) @ Z )
% 2.39/2.72 = ( sup_sup_assn @ X @ ( sup_sup_assn @ Y @ Z ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % sup_assoc
% 2.39/2.72 thf(fact_544_sup_Oassoc,axiom,
% 2.39/2.72 ! [A: set_nat,B: set_nat,C: set_nat] :
% 2.39/2.72 ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ A @ B ) @ C )
% 2.39/2.72 = ( sup_sup_set_nat @ A @ ( sup_sup_set_nat @ B @ C ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % sup.assoc
% 2.39/2.72 thf(fact_545_sup_Oassoc,axiom,
% 2.39/2.72 ! [A: assn,B: assn,C: assn] :
% 2.39/2.72 ( ( sup_sup_assn @ ( sup_sup_assn @ A @ B ) @ C )
% 2.39/2.72 = ( sup_sup_assn @ A @ ( sup_sup_assn @ B @ C ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % sup.assoc
% 2.39/2.72 thf(fact_546_inf__sup__aci_I5_J,axiom,
% 2.39/2.72 ( sup_sup_set_nat
% 2.39/2.72 = ( ^ [X2: set_nat,Y2: set_nat] : ( sup_sup_set_nat @ Y2 @ X2 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % inf_sup_aci(5)
% 2.39/2.72 thf(fact_547_inf__sup__aci_I5_J,axiom,
% 2.39/2.72 ( sup_sup_assn
% 2.39/2.72 = ( ^ [X2: assn,Y2: assn] : ( sup_sup_assn @ Y2 @ X2 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % inf_sup_aci(5)
% 2.39/2.72 thf(fact_548_inf__sup__aci_I6_J,axiom,
% 2.39/2.72 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 2.39/2.72 ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ Z )
% 2.39/2.72 = ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % inf_sup_aci(6)
% 2.39/2.72 thf(fact_549_inf__sup__aci_I6_J,axiom,
% 2.39/2.72 ! [X: assn,Y: assn,Z: assn] :
% 2.39/2.72 ( ( sup_sup_assn @ ( sup_sup_assn @ X @ Y ) @ Z )
% 2.39/2.72 = ( sup_sup_assn @ X @ ( sup_sup_assn @ Y @ Z ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % inf_sup_aci(6)
% 2.39/2.72 thf(fact_550_inf__sup__aci_I7_J,axiom,
% 2.39/2.72 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 2.39/2.72 ( ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) )
% 2.39/2.72 = ( sup_sup_set_nat @ Y @ ( sup_sup_set_nat @ X @ Z ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % inf_sup_aci(7)
% 2.39/2.72 thf(fact_551_inf__sup__aci_I7_J,axiom,
% 2.39/2.72 ! [X: assn,Y: assn,Z: assn] :
% 2.39/2.72 ( ( sup_sup_assn @ X @ ( sup_sup_assn @ Y @ Z ) )
% 2.39/2.72 = ( sup_sup_assn @ Y @ ( sup_sup_assn @ X @ Z ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % inf_sup_aci(7)
% 2.39/2.72 thf(fact_552_inf__sup__aci_I8_J,axiom,
% 2.39/2.72 ! [X: set_nat,Y: set_nat] :
% 2.39/2.72 ( ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ X @ Y ) )
% 2.39/2.72 = ( sup_sup_set_nat @ X @ Y ) ) ).
% 2.39/2.72
% 2.39/2.72 % inf_sup_aci(8)
% 2.39/2.72 thf(fact_553_inf__sup__aci_I8_J,axiom,
% 2.39/2.72 ! [X: assn,Y: assn] :
% 2.39/2.72 ( ( sup_sup_assn @ X @ ( sup_sup_assn @ X @ Y ) )
% 2.39/2.72 = ( sup_sup_assn @ X @ Y ) ) ).
% 2.39/2.72
% 2.39/2.72 % inf_sup_aci(8)
% 2.39/2.72 thf(fact_554_distrib__imp1,axiom,
% 2.39/2.72 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,Z2: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( inf_in2572325071724192079at_nat @ X3 @ ( sup_su6327502436637775413at_nat @ Y3 @ Z2 ) )
% 2.39/2.72 = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ X3 @ Y3 ) @ ( inf_in2572325071724192079at_nat @ X3 @ Z2 ) ) )
% 2.39/2.72 => ( ( sup_su6327502436637775413at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) )
% 2.39/2.72 = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ X @ Y ) @ ( sup_su6327502436637775413at_nat @ X @ Z ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % distrib_imp1
% 2.39/2.72 thf(fact_555_distrib__imp1,axiom,
% 2.39/2.72 ! [X: nat,Y: nat,Z: nat] :
% 2.39/2.72 ( ! [X3: nat,Y3: nat,Z2: nat] :
% 2.39/2.72 ( ( inf_inf_nat @ X3 @ ( sup_sup_nat @ Y3 @ Z2 ) )
% 2.39/2.72 = ( sup_sup_nat @ ( inf_inf_nat @ X3 @ Y3 ) @ ( inf_inf_nat @ X3 @ Z2 ) ) )
% 2.39/2.72 => ( ( sup_sup_nat @ X @ ( inf_inf_nat @ Y @ Z ) )
% 2.39/2.72 = ( inf_inf_nat @ ( sup_sup_nat @ X @ Y ) @ ( sup_sup_nat @ X @ Z ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % distrib_imp1
% 2.39/2.72 thf(fact_556_distrib__imp1,axiom,
% 2.39/2.72 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 2.39/2.72 ( ! [X3: product_prod_int_int > $o,Y3: product_prod_int_int > $o,Z2: product_prod_int_int > $o] :
% 2.39/2.72 ( ( inf_in3604695632404883862_int_o @ X3 @ ( sup_su8463660629351352368_int_o @ Y3 @ Z2 ) )
% 2.39/2.72 = ( sup_su8463660629351352368_int_o @ ( inf_in3604695632404883862_int_o @ X3 @ Y3 ) @ ( inf_in3604695632404883862_int_o @ X3 @ Z2 ) ) )
% 2.39/2.72 => ( ( sup_su8463660629351352368_int_o @ X @ ( inf_in3604695632404883862_int_o @ Y @ Z ) )
% 2.39/2.72 = ( inf_in3604695632404883862_int_o @ ( sup_su8463660629351352368_int_o @ X @ Y ) @ ( sup_su8463660629351352368_int_o @ X @ Z ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % distrib_imp1
% 2.39/2.72 thf(fact_557_distrib__imp1,axiom,
% 2.39/2.72 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 2.39/2.72 ( ! [X3: set_nat,Y3: set_nat,Z2: set_nat] :
% 2.39/2.72 ( ( inf_inf_set_nat @ X3 @ ( sup_sup_set_nat @ Y3 @ Z2 ) )
% 2.39/2.72 = ( sup_sup_set_nat @ ( inf_inf_set_nat @ X3 @ Y3 ) @ ( inf_inf_set_nat @ X3 @ Z2 ) ) )
% 2.39/2.72 => ( ( sup_sup_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) )
% 2.39/2.72 = ( inf_inf_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ ( sup_sup_set_nat @ X @ Z ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % distrib_imp1
% 2.39/2.72 thf(fact_558_distrib__imp1,axiom,
% 2.39/2.72 ! [X: assn,Y: assn,Z: assn] :
% 2.39/2.72 ( ! [X3: assn,Y3: assn,Z2: assn] :
% 2.39/2.72 ( ( inf_inf_assn @ X3 @ ( sup_sup_assn @ Y3 @ Z2 ) )
% 2.39/2.72 = ( sup_sup_assn @ ( inf_inf_assn @ X3 @ Y3 ) @ ( inf_inf_assn @ X3 @ Z2 ) ) )
% 2.39/2.72 => ( ( sup_sup_assn @ X @ ( inf_inf_assn @ Y @ Z ) )
% 2.39/2.72 = ( inf_inf_assn @ ( sup_sup_assn @ X @ Y ) @ ( sup_sup_assn @ X @ Z ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % distrib_imp1
% 2.39/2.72 thf(fact_559_distrib__imp2,axiom,
% 2.39/2.72 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,Z2: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( sup_su6327502436637775413at_nat @ X3 @ ( inf_in2572325071724192079at_nat @ Y3 @ Z2 ) )
% 2.39/2.72 = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ X3 @ Y3 ) @ ( sup_su6327502436637775413at_nat @ X3 @ Z2 ) ) )
% 2.39/2.72 => ( ( inf_in2572325071724192079at_nat @ X @ ( sup_su6327502436637775413at_nat @ Y @ Z ) )
% 2.39/2.72 = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ ( inf_in2572325071724192079at_nat @ X @ Z ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % distrib_imp2
% 2.39/2.72 thf(fact_560_distrib__imp2,axiom,
% 2.39/2.72 ! [X: nat,Y: nat,Z: nat] :
% 2.39/2.72 ( ! [X3: nat,Y3: nat,Z2: nat] :
% 2.39/2.72 ( ( sup_sup_nat @ X3 @ ( inf_inf_nat @ Y3 @ Z2 ) )
% 2.39/2.72 = ( inf_inf_nat @ ( sup_sup_nat @ X3 @ Y3 ) @ ( sup_sup_nat @ X3 @ Z2 ) ) )
% 2.39/2.72 => ( ( inf_inf_nat @ X @ ( sup_sup_nat @ Y @ Z ) )
% 2.39/2.72 = ( sup_sup_nat @ ( inf_inf_nat @ X @ Y ) @ ( inf_inf_nat @ X @ Z ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % distrib_imp2
% 2.39/2.72 thf(fact_561_distrib__imp2,axiom,
% 2.39/2.72 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 2.39/2.72 ( ! [X3: product_prod_int_int > $o,Y3: product_prod_int_int > $o,Z2: product_prod_int_int > $o] :
% 2.39/2.72 ( ( sup_su8463660629351352368_int_o @ X3 @ ( inf_in3604695632404883862_int_o @ Y3 @ Z2 ) )
% 2.39/2.72 = ( inf_in3604695632404883862_int_o @ ( sup_su8463660629351352368_int_o @ X3 @ Y3 ) @ ( sup_su8463660629351352368_int_o @ X3 @ Z2 ) ) )
% 2.39/2.72 => ( ( inf_in3604695632404883862_int_o @ X @ ( sup_su8463660629351352368_int_o @ Y @ Z ) )
% 2.39/2.72 = ( sup_su8463660629351352368_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ ( inf_in3604695632404883862_int_o @ X @ Z ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % distrib_imp2
% 2.39/2.72 thf(fact_562_distrib__imp2,axiom,
% 2.39/2.72 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 2.39/2.72 ( ! [X3: set_nat,Y3: set_nat,Z2: set_nat] :
% 2.39/2.72 ( ( sup_sup_set_nat @ X3 @ ( inf_inf_set_nat @ Y3 @ Z2 ) )
% 2.39/2.72 = ( inf_inf_set_nat @ ( sup_sup_set_nat @ X3 @ Y3 ) @ ( sup_sup_set_nat @ X3 @ Z2 ) ) )
% 2.39/2.72 => ( ( inf_inf_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) )
% 2.39/2.72 = ( sup_sup_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ ( inf_inf_set_nat @ X @ Z ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % distrib_imp2
% 2.39/2.72 thf(fact_563_distrib__imp2,axiom,
% 2.39/2.72 ! [X: assn,Y: assn,Z: assn] :
% 2.39/2.72 ( ! [X3: assn,Y3: assn,Z2: assn] :
% 2.39/2.72 ( ( sup_sup_assn @ X3 @ ( inf_inf_assn @ Y3 @ Z2 ) )
% 2.39/2.72 = ( inf_inf_assn @ ( sup_sup_assn @ X3 @ Y3 ) @ ( sup_sup_assn @ X3 @ Z2 ) ) )
% 2.39/2.72 => ( ( inf_inf_assn @ X @ ( sup_sup_assn @ Y @ Z ) )
% 2.39/2.72 = ( sup_sup_assn @ ( inf_inf_assn @ X @ Y ) @ ( inf_inf_assn @ X @ Z ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % distrib_imp2
% 2.39/2.72 thf(fact_564_inf__sup__distrib1,axiom,
% 2.39/2.72 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( inf_in2572325071724192079at_nat @ X @ ( sup_su6327502436637775413at_nat @ Y @ Z ) )
% 2.39/2.72 = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ ( inf_in2572325071724192079at_nat @ X @ Z ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % inf_sup_distrib1
% 2.39/2.72 thf(fact_565_inf__sup__distrib1,axiom,
% 2.39/2.72 ! [X: nat,Y: nat,Z: nat] :
% 2.39/2.72 ( ( inf_inf_nat @ X @ ( sup_sup_nat @ Y @ Z ) )
% 2.39/2.72 = ( sup_sup_nat @ ( inf_inf_nat @ X @ Y ) @ ( inf_inf_nat @ X @ Z ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % inf_sup_distrib1
% 2.39/2.72 thf(fact_566_inf__sup__distrib1,axiom,
% 2.39/2.72 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 2.39/2.72 ( ( inf_in3604695632404883862_int_o @ X @ ( sup_su8463660629351352368_int_o @ Y @ Z ) )
% 2.39/2.72 = ( sup_su8463660629351352368_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ ( inf_in3604695632404883862_int_o @ X @ Z ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % inf_sup_distrib1
% 2.39/2.72 thf(fact_567_inf__sup__distrib1,axiom,
% 2.39/2.72 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 2.39/2.72 ( ( inf_inf_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) )
% 2.39/2.72 = ( sup_sup_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ ( inf_inf_set_nat @ X @ Z ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % inf_sup_distrib1
% 2.39/2.72 thf(fact_568_inf__sup__distrib1,axiom,
% 2.39/2.72 ! [X: assn,Y: assn,Z: assn] :
% 2.39/2.72 ( ( inf_inf_assn @ X @ ( sup_sup_assn @ Y @ Z ) )
% 2.39/2.72 = ( sup_sup_assn @ ( inf_inf_assn @ X @ Y ) @ ( inf_inf_assn @ X @ Z ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % inf_sup_distrib1
% 2.39/2.72 thf(fact_569_inf__sup__distrib2,axiom,
% 2.39/2.72 ! [Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ Y @ Z ) @ X )
% 2.39/2.72 = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ Y @ X ) @ ( inf_in2572325071724192079at_nat @ Z @ X ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % inf_sup_distrib2
% 2.39/2.72 thf(fact_570_inf__sup__distrib2,axiom,
% 2.39/2.72 ! [Y: nat,Z: nat,X: nat] :
% 2.39/2.72 ( ( inf_inf_nat @ ( sup_sup_nat @ Y @ Z ) @ X )
% 2.39/2.72 = ( sup_sup_nat @ ( inf_inf_nat @ Y @ X ) @ ( inf_inf_nat @ Z @ X ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % inf_sup_distrib2
% 2.39/2.72 thf(fact_571_inf__sup__distrib2,axiom,
% 2.39/2.72 ! [Y: product_prod_int_int > $o,Z: product_prod_int_int > $o,X: product_prod_int_int > $o] :
% 2.39/2.72 ( ( inf_in3604695632404883862_int_o @ ( sup_su8463660629351352368_int_o @ Y @ Z ) @ X )
% 2.39/2.72 = ( sup_su8463660629351352368_int_o @ ( inf_in3604695632404883862_int_o @ Y @ X ) @ ( inf_in3604695632404883862_int_o @ Z @ X ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % inf_sup_distrib2
% 2.39/2.72 thf(fact_572_inf__sup__distrib2,axiom,
% 2.39/2.72 ! [Y: set_nat,Z: set_nat,X: set_nat] :
% 2.39/2.72 ( ( inf_inf_set_nat @ ( sup_sup_set_nat @ Y @ Z ) @ X )
% 2.39/2.72 = ( sup_sup_set_nat @ ( inf_inf_set_nat @ Y @ X ) @ ( inf_inf_set_nat @ Z @ X ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % inf_sup_distrib2
% 2.39/2.72 thf(fact_573_inf__sup__distrib2,axiom,
% 2.39/2.72 ! [Y: assn,Z: assn,X: assn] :
% 2.39/2.72 ( ( inf_inf_assn @ ( sup_sup_assn @ Y @ Z ) @ X )
% 2.39/2.72 = ( sup_sup_assn @ ( inf_inf_assn @ Y @ X ) @ ( inf_inf_assn @ Z @ X ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % inf_sup_distrib2
% 2.39/2.72 thf(fact_574_sup__inf__distrib1,axiom,
% 2.39/2.72 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( sup_su6327502436637775413at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) )
% 2.39/2.72 = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ X @ Y ) @ ( sup_su6327502436637775413at_nat @ X @ Z ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % sup_inf_distrib1
% 2.39/2.72 thf(fact_575_sup__inf__distrib1,axiom,
% 2.39/2.72 ! [X: nat,Y: nat,Z: nat] :
% 2.39/2.72 ( ( sup_sup_nat @ X @ ( inf_inf_nat @ Y @ Z ) )
% 2.39/2.72 = ( inf_inf_nat @ ( sup_sup_nat @ X @ Y ) @ ( sup_sup_nat @ X @ Z ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % sup_inf_distrib1
% 2.39/2.72 thf(fact_576_sup__inf__distrib1,axiom,
% 2.39/2.72 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 2.39/2.72 ( ( sup_su8463660629351352368_int_o @ X @ ( inf_in3604695632404883862_int_o @ Y @ Z ) )
% 2.39/2.72 = ( inf_in3604695632404883862_int_o @ ( sup_su8463660629351352368_int_o @ X @ Y ) @ ( sup_su8463660629351352368_int_o @ X @ Z ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % sup_inf_distrib1
% 2.39/2.72 thf(fact_577_sup__inf__distrib1,axiom,
% 2.39/2.72 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 2.39/2.72 ( ( sup_sup_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) )
% 2.39/2.72 = ( inf_inf_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ ( sup_sup_set_nat @ X @ Z ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % sup_inf_distrib1
% 2.39/2.72 thf(fact_578_sup__inf__distrib1,axiom,
% 2.39/2.72 ! [X: assn,Y: assn,Z: assn] :
% 2.39/2.72 ( ( sup_sup_assn @ X @ ( inf_inf_assn @ Y @ Z ) )
% 2.39/2.72 = ( inf_inf_assn @ ( sup_sup_assn @ X @ Y ) @ ( sup_sup_assn @ X @ Z ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % sup_inf_distrib1
% 2.39/2.72 thf(fact_579_sup__inf__distrib2,axiom,
% 2.39/2.72 ! [Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ Y @ Z ) @ X )
% 2.39/2.72 = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ Y @ X ) @ ( sup_su6327502436637775413at_nat @ Z @ X ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % sup_inf_distrib2
% 2.39/2.72 thf(fact_580_sup__inf__distrib2,axiom,
% 2.39/2.72 ! [Y: nat,Z: nat,X: nat] :
% 2.39/2.72 ( ( sup_sup_nat @ ( inf_inf_nat @ Y @ Z ) @ X )
% 2.39/2.72 = ( inf_inf_nat @ ( sup_sup_nat @ Y @ X ) @ ( sup_sup_nat @ Z @ X ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % sup_inf_distrib2
% 2.39/2.72 thf(fact_581_sup__inf__distrib2,axiom,
% 2.39/2.72 ! [Y: product_prod_int_int > $o,Z: product_prod_int_int > $o,X: product_prod_int_int > $o] :
% 2.39/2.72 ( ( sup_su8463660629351352368_int_o @ ( inf_in3604695632404883862_int_o @ Y @ Z ) @ X )
% 2.39/2.72 = ( inf_in3604695632404883862_int_o @ ( sup_su8463660629351352368_int_o @ Y @ X ) @ ( sup_su8463660629351352368_int_o @ Z @ X ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % sup_inf_distrib2
% 2.39/2.72 thf(fact_582_sup__inf__distrib2,axiom,
% 2.39/2.72 ! [Y: set_nat,Z: set_nat,X: set_nat] :
% 2.39/2.72 ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ Y @ Z ) @ X )
% 2.39/2.72 = ( inf_inf_set_nat @ ( sup_sup_set_nat @ Y @ X ) @ ( sup_sup_set_nat @ Z @ X ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % sup_inf_distrib2
% 2.39/2.72 thf(fact_583_sup__inf__distrib2,axiom,
% 2.39/2.72 ! [Y: assn,Z: assn,X: assn] :
% 2.39/2.72 ( ( sup_sup_assn @ ( inf_inf_assn @ Y @ Z ) @ X )
% 2.39/2.72 = ( inf_inf_assn @ ( sup_sup_assn @ Y @ X ) @ ( sup_sup_assn @ Z @ X ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % sup_inf_distrib2
% 2.39/2.72 thf(fact_584_boolean__algebra_Oconj__disj__distrib,axiom,
% 2.39/2.72 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( inf_in2572325071724192079at_nat @ X @ ( sup_su6327502436637775413at_nat @ Y @ Z ) )
% 2.39/2.72 = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ ( inf_in2572325071724192079at_nat @ X @ Z ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.conj_disj_distrib
% 2.39/2.72 thf(fact_585_boolean__algebra_Oconj__disj__distrib,axiom,
% 2.39/2.72 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 2.39/2.72 ( ( inf_in3604695632404883862_int_o @ X @ ( sup_su8463660629351352368_int_o @ Y @ Z ) )
% 2.39/2.72 = ( sup_su8463660629351352368_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ ( inf_in3604695632404883862_int_o @ X @ Z ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.conj_disj_distrib
% 2.39/2.72 thf(fact_586_boolean__algebra_Oconj__disj__distrib,axiom,
% 2.39/2.72 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 2.39/2.72 ( ( inf_inf_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) )
% 2.39/2.72 = ( sup_sup_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ ( inf_inf_set_nat @ X @ Z ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.conj_disj_distrib
% 2.39/2.72 thf(fact_587_boolean__algebra_Oconj__disj__distrib,axiom,
% 2.39/2.72 ! [X: assn,Y: assn,Z: assn] :
% 2.39/2.72 ( ( inf_inf_assn @ X @ ( sup_sup_assn @ Y @ Z ) )
% 2.39/2.72 = ( sup_sup_assn @ ( inf_inf_assn @ X @ Y ) @ ( inf_inf_assn @ X @ Z ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.conj_disj_distrib
% 2.39/2.72 thf(fact_588_boolean__algebra_Odisj__conj__distrib,axiom,
% 2.39/2.72 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( sup_su6327502436637775413at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) )
% 2.39/2.72 = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ X @ Y ) @ ( sup_su6327502436637775413at_nat @ X @ Z ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.disj_conj_distrib
% 2.39/2.72 thf(fact_589_boolean__algebra_Odisj__conj__distrib,axiom,
% 2.39/2.72 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 2.39/2.72 ( ( sup_su8463660629351352368_int_o @ X @ ( inf_in3604695632404883862_int_o @ Y @ Z ) )
% 2.39/2.72 = ( inf_in3604695632404883862_int_o @ ( sup_su8463660629351352368_int_o @ X @ Y ) @ ( sup_su8463660629351352368_int_o @ X @ Z ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.disj_conj_distrib
% 2.39/2.72 thf(fact_590_boolean__algebra_Odisj__conj__distrib,axiom,
% 2.39/2.72 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 2.39/2.72 ( ( sup_sup_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) )
% 2.39/2.72 = ( inf_inf_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ ( sup_sup_set_nat @ X @ Z ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.disj_conj_distrib
% 2.39/2.72 thf(fact_591_boolean__algebra_Odisj__conj__distrib,axiom,
% 2.39/2.72 ! [X: assn,Y: assn,Z: assn] :
% 2.39/2.72 ( ( sup_sup_assn @ X @ ( inf_inf_assn @ Y @ Z ) )
% 2.39/2.72 = ( inf_inf_assn @ ( sup_sup_assn @ X @ Y ) @ ( sup_sup_assn @ X @ Z ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.disj_conj_distrib
% 2.39/2.72 thf(fact_592_boolean__algebra_Oconj__disj__distrib2,axiom,
% 2.39/2.72 ! [Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ Y @ Z ) @ X )
% 2.39/2.72 = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ Y @ X ) @ ( inf_in2572325071724192079at_nat @ Z @ X ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.conj_disj_distrib2
% 2.39/2.72 thf(fact_593_boolean__algebra_Oconj__disj__distrib2,axiom,
% 2.39/2.72 ! [Y: product_prod_int_int > $o,Z: product_prod_int_int > $o,X: product_prod_int_int > $o] :
% 2.39/2.72 ( ( inf_in3604695632404883862_int_o @ ( sup_su8463660629351352368_int_o @ Y @ Z ) @ X )
% 2.39/2.72 = ( sup_su8463660629351352368_int_o @ ( inf_in3604695632404883862_int_o @ Y @ X ) @ ( inf_in3604695632404883862_int_o @ Z @ X ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.conj_disj_distrib2
% 2.39/2.72 thf(fact_594_boolean__algebra_Oconj__disj__distrib2,axiom,
% 2.39/2.72 ! [Y: set_nat,Z: set_nat,X: set_nat] :
% 2.39/2.72 ( ( inf_inf_set_nat @ ( sup_sup_set_nat @ Y @ Z ) @ X )
% 2.39/2.72 = ( sup_sup_set_nat @ ( inf_inf_set_nat @ Y @ X ) @ ( inf_inf_set_nat @ Z @ X ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.conj_disj_distrib2
% 2.39/2.72 thf(fact_595_boolean__algebra_Oconj__disj__distrib2,axiom,
% 2.39/2.72 ! [Y: assn,Z: assn,X: assn] :
% 2.39/2.72 ( ( inf_inf_assn @ ( sup_sup_assn @ Y @ Z ) @ X )
% 2.39/2.72 = ( sup_sup_assn @ ( inf_inf_assn @ Y @ X ) @ ( inf_inf_assn @ Z @ X ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.conj_disj_distrib2
% 2.39/2.72 thf(fact_596_boolean__algebra_Odisj__conj__distrib2,axiom,
% 2.39/2.72 ! [Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ Y @ Z ) @ X )
% 2.39/2.72 = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ Y @ X ) @ ( sup_su6327502436637775413at_nat @ Z @ X ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.disj_conj_distrib2
% 2.39/2.72 thf(fact_597_boolean__algebra_Odisj__conj__distrib2,axiom,
% 2.39/2.72 ! [Y: product_prod_int_int > $o,Z: product_prod_int_int > $o,X: product_prod_int_int > $o] :
% 2.39/2.72 ( ( sup_su8463660629351352368_int_o @ ( inf_in3604695632404883862_int_o @ Y @ Z ) @ X )
% 2.39/2.72 = ( inf_in3604695632404883862_int_o @ ( sup_su8463660629351352368_int_o @ Y @ X ) @ ( sup_su8463660629351352368_int_o @ Z @ X ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.disj_conj_distrib2
% 2.39/2.72 thf(fact_598_boolean__algebra_Odisj__conj__distrib2,axiom,
% 2.39/2.72 ! [Y: set_nat,Z: set_nat,X: set_nat] :
% 2.39/2.72 ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ Y @ Z ) @ X )
% 2.39/2.72 = ( inf_inf_set_nat @ ( sup_sup_set_nat @ Y @ X ) @ ( sup_sup_set_nat @ Z @ X ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.disj_conj_distrib2
% 2.39/2.72 thf(fact_599_boolean__algebra_Odisj__conj__distrib2,axiom,
% 2.39/2.72 ! [Y: assn,Z: assn,X: assn] :
% 2.39/2.72 ( ( sup_sup_assn @ ( inf_inf_assn @ Y @ Z ) @ X )
% 2.39/2.72 = ( inf_inf_assn @ ( sup_sup_assn @ Y @ X ) @ ( sup_sup_assn @ Z @ X ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.disj_conj_distrib2
% 2.39/2.72 thf(fact_600_sup_Oabel__semigroup__axioms,axiom,
% 2.39/2.72 abel_s3907380067910933104et_nat @ sup_sup_set_nat ).
% 2.39/2.72
% 2.39/2.72 % sup.abel_semigroup_axioms
% 2.39/2.72 thf(fact_601_sup_Oabel__semigroup__axioms,axiom,
% 2.39/2.72 abel_semigroup_assn @ sup_sup_assn ).
% 2.39/2.72
% 2.39/2.72 % sup.abel_semigroup_axioms
% 2.39/2.72 thf(fact_602_sup_Osemilattice__axioms,axiom,
% 2.39/2.72 semilattice_set_nat @ sup_sup_set_nat ).
% 2.39/2.72
% 2.39/2.72 % sup.semilattice_axioms
% 2.39/2.72 thf(fact_603_sup_Osemilattice__axioms,axiom,
% 2.39/2.72 semilattice_assn @ sup_sup_assn ).
% 2.39/2.72
% 2.39/2.72 % sup.semilattice_axioms
% 2.39/2.72 thf(fact_604_sup_Osemigroup__axioms,axiom,
% 2.39/2.72 semigroup_set_nat @ sup_sup_set_nat ).
% 2.39/2.72
% 2.39/2.72 % sup.semigroup_axioms
% 2.39/2.72 thf(fact_605_sup_Osemigroup__axioms,axiom,
% 2.39/2.72 semigroup_assn @ sup_sup_assn ).
% 2.39/2.72
% 2.39/2.72 % sup.semigroup_axioms
% 2.39/2.72 thf(fact_606_sup__bot_Ocomm__monoid__axioms,axiom,
% 2.39/2.72 comm_monoid_assn @ sup_sup_assn @ bot_bot_assn ).
% 2.39/2.72
% 2.39/2.72 % sup_bot.comm_monoid_axioms
% 2.39/2.72 thf(fact_607_sup__bot_Ocomm__monoid__axioms,axiom,
% 2.39/2.72 comm_monoid_set_nat @ sup_sup_set_nat @ bot_bot_set_nat ).
% 2.39/2.72
% 2.39/2.72 % sup_bot.comm_monoid_axioms
% 2.39/2.72 thf(fact_608_sup__bot_Ocomm__monoid__axioms,axiom,
% 2.39/2.72 comm_monoid_set_int @ sup_sup_set_int @ bot_bot_set_int ).
% 2.39/2.72
% 2.39/2.72 % sup_bot.comm_monoid_axioms
% 2.39/2.72 thf(fact_609_sup__bot_Omonoid__axioms,axiom,
% 2.39/2.72 monoid_assn @ sup_sup_assn @ bot_bot_assn ).
% 2.39/2.72
% 2.39/2.72 % sup_bot.monoid_axioms
% 2.39/2.72 thf(fact_610_sup__bot_Omonoid__axioms,axiom,
% 2.39/2.72 monoid_set_nat @ sup_sup_set_nat @ bot_bot_set_nat ).
% 2.39/2.72
% 2.39/2.72 % sup_bot.monoid_axioms
% 2.39/2.72 thf(fact_611_sup__bot_Omonoid__axioms,axiom,
% 2.39/2.72 monoid_set_int @ sup_sup_set_int @ bot_bot_set_int ).
% 2.39/2.72
% 2.39/2.72 % sup_bot.monoid_axioms
% 2.39/2.72 thf(fact_612_sup__bot_Osemilattice__neutr__axioms,axiom,
% 2.39/2.72 semila5388846958306562758r_assn @ sup_sup_assn @ bot_bot_assn ).
% 2.39/2.72
% 2.39/2.72 % sup_bot.semilattice_neutr_axioms
% 2.39/2.72 thf(fact_613_sup__bot_Osemilattice__neutr__axioms,axiom,
% 2.39/2.72 semila1241773964035338532et_nat @ sup_sup_set_nat @ bot_bot_set_nat ).
% 2.39/2.72
% 2.39/2.72 % sup_bot.semilattice_neutr_axioms
% 2.39/2.72 thf(fact_614_sup__bot_Osemilattice__neutr__axioms,axiom,
% 2.39/2.72 semila6287294981380917632et_int @ sup_sup_set_int @ bot_bot_set_int ).
% 2.39/2.72
% 2.39/2.72 % sup_bot.semilattice_neutr_axioms
% 2.39/2.72 thf(fact_615_boolean__algebra_Ocomplement__unique,axiom,
% 2.39/2.72 ! [A: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( ( inf_in2572325071724192079at_nat @ A @ X )
% 2.39/2.72 = bot_bo2099793752762293965at_nat )
% 2.39/2.72 => ( ( ( sup_su6327502436637775413at_nat @ A @ X )
% 2.39/2.72 = top_to4669805908274784177at_nat )
% 2.39/2.72 => ( ( ( inf_in2572325071724192079at_nat @ A @ Y )
% 2.39/2.72 = bot_bo2099793752762293965at_nat )
% 2.39/2.72 => ( ( ( sup_su6327502436637775413at_nat @ A @ Y )
% 2.39/2.72 = top_to4669805908274784177at_nat )
% 2.39/2.72 => ( X = Y ) ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.complement_unique
% 2.39/2.72 thf(fact_616_boolean__algebra_Ocomplement__unique,axiom,
% 2.39/2.72 ! [A: product_prod_int_int > $o,X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 2.39/2.72 ( ( ( inf_in3604695632404883862_int_o @ A @ X )
% 2.39/2.72 = bot_bo8147686125503663512_int_o )
% 2.39/2.72 => ( ( ( sup_su8463660629351352368_int_o @ A @ X )
% 2.39/2.72 = top_to1578927101902068148_int_o )
% 2.39/2.72 => ( ( ( inf_in3604695632404883862_int_o @ A @ Y )
% 2.39/2.72 = bot_bo8147686125503663512_int_o )
% 2.39/2.72 => ( ( ( sup_su8463660629351352368_int_o @ A @ Y )
% 2.39/2.72 = top_to1578927101902068148_int_o )
% 2.39/2.72 => ( X = Y ) ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.complement_unique
% 2.39/2.72 thf(fact_617_boolean__algebra_Ocomplement__unique,axiom,
% 2.39/2.72 ! [A: set_nat,X: set_nat,Y: set_nat] :
% 2.39/2.72 ( ( ( inf_inf_set_nat @ A @ X )
% 2.39/2.72 = bot_bot_set_nat )
% 2.39/2.72 => ( ( ( sup_sup_set_nat @ A @ X )
% 2.39/2.72 = top_top_set_nat )
% 2.39/2.72 => ( ( ( inf_inf_set_nat @ A @ Y )
% 2.39/2.72 = bot_bot_set_nat )
% 2.39/2.72 => ( ( ( sup_sup_set_nat @ A @ Y )
% 2.39/2.72 = top_top_set_nat )
% 2.39/2.72 => ( X = Y ) ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.complement_unique
% 2.39/2.72 thf(fact_618_boolean__algebra_Ocomplement__unique,axiom,
% 2.39/2.72 ! [A: set_int,X: set_int,Y: set_int] :
% 2.39/2.72 ( ( ( inf_inf_set_int @ A @ X )
% 2.39/2.72 = bot_bot_set_int )
% 2.39/2.72 => ( ( ( sup_sup_set_int @ A @ X )
% 2.39/2.72 = top_top_set_int )
% 2.39/2.72 => ( ( ( inf_inf_set_int @ A @ Y )
% 2.39/2.72 = bot_bot_set_int )
% 2.39/2.72 => ( ( ( sup_sup_set_int @ A @ Y )
% 2.39/2.72 = top_top_set_int )
% 2.39/2.72 => ( X = Y ) ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.complement_unique
% 2.39/2.72 thf(fact_619_boolean__algebra_Ocomplement__unique,axiom,
% 2.39/2.72 ! [A: assn,X: assn,Y: assn] :
% 2.39/2.72 ( ( ( inf_inf_assn @ A @ X )
% 2.39/2.72 = bot_bot_assn )
% 2.39/2.72 => ( ( ( sup_sup_assn @ A @ X )
% 2.39/2.72 = top_top_assn )
% 2.39/2.72 => ( ( ( inf_inf_assn @ A @ Y )
% 2.39/2.72 = bot_bot_assn )
% 2.39/2.72 => ( ( ( sup_sup_assn @ A @ Y )
% 2.39/2.72 = top_top_assn )
% 2.39/2.72 => ( X = Y ) ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.complement_unique
% 2.39/2.72 thf(fact_620_boolean__algebra_Ocomplement__unique,axiom,
% 2.39/2.72 ! [A: set_Product_unit,X: set_Product_unit,Y: set_Product_unit] :
% 2.39/2.72 ( ( ( inf_in4660618365625256667t_unit @ A @ X )
% 2.39/2.72 = bot_bo3957492148770167129t_unit )
% 2.39/2.72 => ( ( ( sup_su793286257634532545t_unit @ A @ X )
% 2.39/2.72 = top_to1996260823553986621t_unit )
% 2.39/2.72 => ( ( ( inf_in4660618365625256667t_unit @ A @ Y )
% 2.39/2.72 = bot_bo3957492148770167129t_unit )
% 2.39/2.72 => ( ( ( sup_su793286257634532545t_unit @ A @ Y )
% 2.39/2.72 = top_to1996260823553986621t_unit )
% 2.39/2.72 => ( X = Y ) ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.complement_unique
% 2.39/2.72 thf(fact_621_one__assn__raw_Osimps,axiom,
% 2.39/2.72 ! [H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 2.39/2.72 ( ( one_assn_raw @ ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 2.39/2.72 = ( As2 = bot_bot_set_nat ) ) ).
% 2.39/2.72
% 2.39/2.72 % one_assn_raw.simps
% 2.39/2.72 thf(fact_622_one__assn__raw_Oelims_I1_J,axiom,
% 2.39/2.72 ! [X: produc3658429121746597890et_nat,Y: $o] :
% 2.39/2.72 ( ( ( one_assn_raw @ X )
% 2.39/2.72 = Y )
% 2.39/2.72 => ~ ! [H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.39/2.72 ( ( X
% 2.39/2.72 = ( produc7507926704131184380et_nat @ H3 @ As ) )
% 2.39/2.72 => ( Y
% 2.39/2.72 = ( As != bot_bot_set_nat ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % one_assn_raw.elims(1)
% 2.39/2.72 thf(fact_623_one__assn__raw_Oelims_I2_J,axiom,
% 2.39/2.72 ! [X: produc3658429121746597890et_nat] :
% 2.39/2.72 ( ( one_assn_raw @ X )
% 2.39/2.72 => ~ ! [H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.39/2.72 ( ( X
% 2.39/2.72 = ( produc7507926704131184380et_nat @ H3 @ As ) )
% 2.39/2.72 => ( As != bot_bot_set_nat ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % one_assn_raw.elims(2)
% 2.39/2.72 thf(fact_624_Int__Un__eq_I4_J,axiom,
% 2.39/2.72 ! [T: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( sup_su6327502436637775413at_nat @ T @ ( inf_in2572325071724192079at_nat @ S @ T ) )
% 2.39/2.72 = T ) ).
% 2.39/2.72
% 2.39/2.72 % Int_Un_eq(4)
% 2.39/2.72 thf(fact_625_Int__Un__eq_I4_J,axiom,
% 2.39/2.72 ! [T: set_nat,S: set_nat] :
% 2.39/2.72 ( ( sup_sup_set_nat @ T @ ( inf_inf_set_nat @ S @ T ) )
% 2.39/2.72 = T ) ).
% 2.39/2.72
% 2.39/2.72 % Int_Un_eq(4)
% 2.39/2.72 thf(fact_626_Int__Un__eq_I3_J,axiom,
% 2.39/2.72 ! [S: set_Pr1261947904930325089at_nat,T: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( sup_su6327502436637775413at_nat @ S @ ( inf_in2572325071724192079at_nat @ S @ T ) )
% 2.39/2.72 = S ) ).
% 2.39/2.72
% 2.39/2.72 % Int_Un_eq(3)
% 2.39/2.72 thf(fact_627_Int__Un__eq_I3_J,axiom,
% 2.39/2.72 ! [S: set_nat,T: set_nat] :
% 2.39/2.72 ( ( sup_sup_set_nat @ S @ ( inf_inf_set_nat @ S @ T ) )
% 2.39/2.72 = S ) ).
% 2.39/2.72
% 2.39/2.72 % Int_Un_eq(3)
% 2.39/2.72 thf(fact_628_Int__Un__eq_I2_J,axiom,
% 2.39/2.72 ! [S: set_Pr1261947904930325089at_nat,T: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ S @ T ) @ T )
% 2.39/2.72 = T ) ).
% 2.39/2.72
% 2.39/2.72 % Int_Un_eq(2)
% 2.39/2.72 thf(fact_629_Int__Un__eq_I2_J,axiom,
% 2.39/2.72 ! [S: set_nat,T: set_nat] :
% 2.39/2.72 ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ S @ T ) @ T )
% 2.39/2.72 = T ) ).
% 2.39/2.72
% 2.39/2.72 % Int_Un_eq(2)
% 2.39/2.72 thf(fact_630_Int__Un__eq_I1_J,axiom,
% 2.39/2.72 ! [S: set_Pr1261947904930325089at_nat,T: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ S @ T ) @ S )
% 2.39/2.72 = S ) ).
% 2.39/2.72
% 2.39/2.72 % Int_Un_eq(1)
% 2.39/2.72 thf(fact_631_Int__Un__eq_I1_J,axiom,
% 2.39/2.72 ! [S: set_nat,T: set_nat] :
% 2.39/2.72 ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ S @ T ) @ S )
% 2.39/2.72 = S ) ).
% 2.39/2.72
% 2.39/2.72 % Int_Un_eq(1)
% 2.39/2.72 thf(fact_632_Un__Int__eq_I4_J,axiom,
% 2.39/2.72 ! [T: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( inf_in2572325071724192079at_nat @ T @ ( sup_su6327502436637775413at_nat @ S @ T ) )
% 2.39/2.72 = T ) ).
% 2.39/2.72
% 2.39/2.72 % Un_Int_eq(4)
% 2.39/2.72 thf(fact_633_Un__Int__eq_I4_J,axiom,
% 2.39/2.72 ! [T: set_nat,S: set_nat] :
% 2.39/2.72 ( ( inf_inf_set_nat @ T @ ( sup_sup_set_nat @ S @ T ) )
% 2.39/2.72 = T ) ).
% 2.39/2.72
% 2.39/2.72 % Un_Int_eq(4)
% 2.39/2.72 thf(fact_634_Un__Int__eq_I3_J,axiom,
% 2.39/2.72 ! [S: set_Pr1261947904930325089at_nat,T: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( inf_in2572325071724192079at_nat @ S @ ( sup_su6327502436637775413at_nat @ S @ T ) )
% 2.39/2.72 = S ) ).
% 2.39/2.72
% 2.39/2.72 % Un_Int_eq(3)
% 2.39/2.72 thf(fact_635_Un__Int__eq_I3_J,axiom,
% 2.39/2.72 ! [S: set_nat,T: set_nat] :
% 2.39/2.72 ( ( inf_inf_set_nat @ S @ ( sup_sup_set_nat @ S @ T ) )
% 2.39/2.72 = S ) ).
% 2.39/2.72
% 2.39/2.72 % Un_Int_eq(3)
% 2.39/2.72 thf(fact_636_Un__Int__eq_I2_J,axiom,
% 2.39/2.72 ! [S: set_Pr1261947904930325089at_nat,T: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ S @ T ) @ T )
% 2.39/2.72 = T ) ).
% 2.39/2.72
% 2.39/2.72 % Un_Int_eq(2)
% 2.39/2.72 thf(fact_637_Un__Int__eq_I2_J,axiom,
% 2.39/2.72 ! [S: set_nat,T: set_nat] :
% 2.39/2.72 ( ( inf_inf_set_nat @ ( sup_sup_set_nat @ S @ T ) @ T )
% 2.39/2.72 = T ) ).
% 2.39/2.72
% 2.39/2.72 % Un_Int_eq(2)
% 2.39/2.72 thf(fact_638_Un__Int__eq_I1_J,axiom,
% 2.39/2.72 ! [S: set_Pr1261947904930325089at_nat,T: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ S @ T ) @ S )
% 2.39/2.72 = S ) ).
% 2.39/2.72
% 2.39/2.72 % Un_Int_eq(1)
% 2.39/2.72 thf(fact_639_Un__Int__eq_I1_J,axiom,
% 2.39/2.72 ! [S: set_nat,T: set_nat] :
% 2.39/2.72 ( ( inf_inf_set_nat @ ( sup_sup_set_nat @ S @ T ) @ S )
% 2.39/2.72 = S ) ).
% 2.39/2.72
% 2.39/2.72 % Un_Int_eq(1)
% 2.39/2.72 thf(fact_640_wand__assnI,axiom,
% 2.39/2.72 ! [H2: heap_e7401611519738050253t_unit,As2: set_nat,Q2: assn,R: assn] :
% 2.39/2.72 ( ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 2.39/2.72 => ( ! [H4: heap_e7401611519738050253t_unit,As4: set_nat] :
% 2.39/2.72 ( ( ( inf_inf_set_nat @ As2 @ As4 )
% 2.39/2.72 = bot_bot_set_nat )
% 2.39/2.72 => ( ( relH @ As2 @ H2 @ H4 )
% 2.39/2.72 => ( ( in_range @ ( produc7507926704131184380et_nat @ H4 @ As2 ) )
% 2.39/2.72 => ( ( rep_assn @ Q2 @ ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 2.39/2.72 => ( rep_assn @ R @ ( produc7507926704131184380et_nat @ H4 @ ( sup_sup_set_nat @ As2 @ As4 ) ) ) ) ) ) )
% 2.39/2.72 => ( rep_assn @ ( wand_assn @ Q2 @ R ) @ ( produc7507926704131184380et_nat @ H2 @ As2 ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % wand_assnI
% 2.39/2.72 thf(fact_641_IntI,axiom,
% 2.39/2.72 ! [C: produc3658429121746597890et_nat > $o,A3: set_Pr4532377907799695533_nat_o,B3: set_Pr4532377907799695533_nat_o] :
% 2.39/2.72 ( ( member6576561426505652726_nat_o @ C @ A3 )
% 2.39/2.72 => ( ( member6576561426505652726_nat_o @ C @ B3 )
% 2.39/2.72 => ( member6576561426505652726_nat_o @ C @ ( inf_in1906310914598751387_nat_o @ A3 @ B3 ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % IntI
% 2.39/2.72 thf(fact_642_IntI,axiom,
% 2.39/2.72 ! [C: int,A3: set_int,B3: set_int] :
% 2.39/2.72 ( ( member_int2 @ C @ A3 )
% 2.39/2.72 => ( ( member_int2 @ C @ B3 )
% 2.39/2.72 => ( member_int2 @ C @ ( inf_inf_set_int @ A3 @ B3 ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % IntI
% 2.39/2.72 thf(fact_643_IntI,axiom,
% 2.39/2.72 ! [C: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( member8440522571783428010at_nat @ C @ A3 )
% 2.39/2.72 => ( ( member8440522571783428010at_nat @ C @ B3 )
% 2.39/2.72 => ( member8440522571783428010at_nat @ C @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % IntI
% 2.39/2.72 thf(fact_644_IntI,axiom,
% 2.39/2.72 ! [C: nat,A3: set_nat,B3: set_nat] :
% 2.39/2.72 ( ( member_nat2 @ C @ A3 )
% 2.39/2.72 => ( ( member_nat2 @ C @ B3 )
% 2.39/2.72 => ( member_nat2 @ C @ ( inf_inf_set_nat @ A3 @ B3 ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % IntI
% 2.39/2.72 thf(fact_645_Int__iff,axiom,
% 2.39/2.72 ! [C: produc3658429121746597890et_nat > $o,A3: set_Pr4532377907799695533_nat_o,B3: set_Pr4532377907799695533_nat_o] :
% 2.39/2.72 ( ( member6576561426505652726_nat_o @ C @ ( inf_in1906310914598751387_nat_o @ A3 @ B3 ) )
% 2.39/2.72 = ( ( member6576561426505652726_nat_o @ C @ A3 )
% 2.39/2.72 & ( member6576561426505652726_nat_o @ C @ B3 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % Int_iff
% 2.39/2.72 thf(fact_646_Int__iff,axiom,
% 2.39/2.72 ! [C: int,A3: set_int,B3: set_int] :
% 2.39/2.72 ( ( member_int2 @ C @ ( inf_inf_set_int @ A3 @ B3 ) )
% 2.39/2.72 = ( ( member_int2 @ C @ A3 )
% 2.39/2.72 & ( member_int2 @ C @ B3 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % Int_iff
% 2.39/2.72 thf(fact_647_Int__iff,axiom,
% 2.39/2.72 ! [C: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( member8440522571783428010at_nat @ C @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) )
% 2.39/2.72 = ( ( member8440522571783428010at_nat @ C @ A3 )
% 2.39/2.72 & ( member8440522571783428010at_nat @ C @ B3 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % Int_iff
% 2.39/2.72 thf(fact_648_Int__iff,axiom,
% 2.39/2.72 ! [C: nat,A3: set_nat,B3: set_nat] :
% 2.39/2.72 ( ( member_nat2 @ C @ ( inf_inf_set_nat @ A3 @ B3 ) )
% 2.39/2.72 = ( ( member_nat2 @ C @ A3 )
% 2.39/2.72 & ( member_nat2 @ C @ B3 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % Int_iff
% 2.39/2.72 thf(fact_649_Int__UNIV,axiom,
% 2.39/2.72 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( ( inf_in2572325071724192079at_nat @ A3 @ B3 )
% 2.39/2.72 = top_to4669805908274784177at_nat )
% 2.39/2.72 = ( ( A3 = top_to4669805908274784177at_nat )
% 2.39/2.72 & ( B3 = top_to4669805908274784177at_nat ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % Int_UNIV
% 2.39/2.72 thf(fact_650_Int__UNIV,axiom,
% 2.39/2.72 ! [A3: set_nat,B3: set_nat] :
% 2.39/2.72 ( ( ( inf_inf_set_nat @ A3 @ B3 )
% 2.39/2.72 = top_top_set_nat )
% 2.39/2.72 = ( ( A3 = top_top_set_nat )
% 2.39/2.72 & ( B3 = top_top_set_nat ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % Int_UNIV
% 2.39/2.72 thf(fact_651_Int__UNIV,axiom,
% 2.39/2.72 ! [A3: set_Product_unit,B3: set_Product_unit] :
% 2.39/2.72 ( ( ( inf_in4660618365625256667t_unit @ A3 @ B3 )
% 2.39/2.72 = top_to1996260823553986621t_unit )
% 2.39/2.72 = ( ( A3 = top_to1996260823553986621t_unit )
% 2.39/2.72 & ( B3 = top_to1996260823553986621t_unit ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % Int_UNIV
% 2.39/2.72 thf(fact_652_mod__or__dist,axiom,
% 2.39/2.72 ! [P2: assn,Q2: assn,H2: produc3658429121746597890et_nat] :
% 2.39/2.72 ( ( rep_assn @ ( sup_sup_assn @ P2 @ Q2 ) @ H2 )
% 2.39/2.72 = ( ( rep_assn @ P2 @ H2 )
% 2.39/2.72 | ( rep_assn @ Q2 @ H2 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % mod_or_dist
% 2.39/2.72 thf(fact_653_merge__pure__or,axiom,
% 2.39/2.72 ! [A: $o,B: $o] :
% 2.39/2.72 ( ( sup_sup_assn @ ( pure_assn @ A ) @ ( pure_assn @ B ) )
% 2.39/2.72 = ( pure_assn
% 2.39/2.72 @ ( A
% 2.39/2.72 | B ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % merge_pure_or
% 2.39/2.72 thf(fact_654_relH__dist__union,axiom,
% 2.39/2.72 ! [As2: set_nat,As3: set_nat,H2: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit] :
% 2.39/2.72 ( ( relH @ ( sup_sup_set_nat @ As2 @ As3 ) @ H2 @ H5 )
% 2.39/2.72 = ( ( relH @ As2 @ H2 @ H5 )
% 2.39/2.72 & ( relH @ As3 @ H2 @ H5 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % relH_dist_union
% 2.39/2.72 thf(fact_655_mod__h__bot__iff_I7_J,axiom,
% 2.39/2.72 ! [P2: assn,Q2: assn,H2: heap_e7401611519738050253t_unit] :
% 2.39/2.72 ( ( rep_assn @ ( sup_sup_assn @ P2 @ Q2 ) @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) )
% 2.39/2.72 = ( ( rep_assn @ P2 @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) )
% 2.39/2.72 | ( rep_assn @ Q2 @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % mod_h_bot_iff(7)
% 2.39/2.72 thf(fact_656_relH__sym,axiom,
% 2.39/2.72 ! [As2: set_nat,H2: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit] :
% 2.39/2.72 ( ( relH @ As2 @ H2 @ H5 )
% 2.39/2.72 => ( relH @ As2 @ H5 @ H2 ) ) ).
% 2.39/2.72
% 2.39/2.72 % relH_sym
% 2.39/2.72 thf(fact_657_relH__trans,axiom,
% 2.39/2.72 ! [As2: set_nat,H12: heap_e7401611519738050253t_unit,H23: heap_e7401611519738050253t_unit,H32: heap_e7401611519738050253t_unit] :
% 2.39/2.72 ( ( relH @ As2 @ H12 @ H23 )
% 2.39/2.72 => ( ( relH @ As2 @ H23 @ H32 )
% 2.39/2.72 => ( relH @ As2 @ H12 @ H32 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % relH_trans
% 2.39/2.72 thf(fact_658_star__or__dist2,axiom,
% 2.39/2.72 ! [C2: assn,A3: assn,B3: assn] :
% 2.39/2.72 ( ( times_times_assn @ C2 @ ( sup_sup_assn @ A3 @ B3 ) )
% 2.39/2.72 = ( sup_sup_assn @ ( times_times_assn @ C2 @ A3 ) @ ( times_times_assn @ C2 @ B3 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % star_or_dist2
% 2.39/2.72 thf(fact_659_star__or__dist1,axiom,
% 2.39/2.72 ! [A3: assn,B3: assn,C2: assn] :
% 2.39/2.72 ( ( times_times_assn @ ( sup_sup_assn @ A3 @ B3 ) @ C2 )
% 2.39/2.72 = ( sup_sup_assn @ ( times_times_assn @ A3 @ C2 ) @ ( times_times_assn @ B3 @ C2 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % star_or_dist1
% 2.39/2.72 thf(fact_660_ent__disjI2__direct,axiom,
% 2.39/2.72 ! [B3: assn,A3: assn] : ( entails @ B3 @ ( sup_sup_assn @ A3 @ B3 ) ) ).
% 2.39/2.72
% 2.39/2.72 % ent_disjI2_direct
% 2.39/2.72 thf(fact_661_ent__disjI1__direct,axiom,
% 2.39/2.72 ! [A3: assn,B3: assn] : ( entails @ A3 @ ( sup_sup_assn @ A3 @ B3 ) ) ).
% 2.39/2.72
% 2.39/2.72 % ent_disjI1_direct
% 2.39/2.72 thf(fact_662_ent__disjI2_H,axiom,
% 2.39/2.72 ! [A3: assn,C2: assn,B3: assn] :
% 2.39/2.72 ( ( entails @ A3 @ C2 )
% 2.39/2.72 => ( entails @ A3 @ ( sup_sup_assn @ B3 @ C2 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % ent_disjI2'
% 2.39/2.72 thf(fact_663_ent__disjI1_H,axiom,
% 2.39/2.72 ! [A3: assn,B3: assn,C2: assn] :
% 2.39/2.72 ( ( entails @ A3 @ B3 )
% 2.39/2.72 => ( entails @ A3 @ ( sup_sup_assn @ B3 @ C2 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % ent_disjI1'
% 2.39/2.72 thf(fact_664_ent__disjI2,axiom,
% 2.39/2.72 ! [P2: assn,Q2: assn,R: assn] :
% 2.39/2.72 ( ( entails @ ( sup_sup_assn @ P2 @ Q2 ) @ R )
% 2.39/2.72 => ( entails @ Q2 @ R ) ) ).
% 2.39/2.72
% 2.39/2.72 % ent_disjI2
% 2.39/2.72 thf(fact_665_ent__disjI1,axiom,
% 2.39/2.72 ! [P2: assn,Q2: assn,R: assn] :
% 2.39/2.72 ( ( entails @ ( sup_sup_assn @ P2 @ Q2 ) @ R )
% 2.39/2.72 => ( entails @ P2 @ R ) ) ).
% 2.39/2.72
% 2.39/2.72 % ent_disjI1
% 2.39/2.72 thf(fact_666_ent__disjE,axiom,
% 2.39/2.72 ! [A3: assn,C2: assn,B3: assn] :
% 2.39/2.72 ( ( entails @ A3 @ C2 )
% 2.39/2.72 => ( ( entails @ B3 @ C2 )
% 2.39/2.72 => ( entails @ ( sup_sup_assn @ A3 @ B3 ) @ C2 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % ent_disjE
% 2.39/2.72 thf(fact_667_entt__disjE,axiom,
% 2.39/2.72 ! [A3: assn,M: assn,B3: assn] :
% 2.39/2.72 ( ( entailst @ A3 @ M )
% 2.39/2.72 => ( ( entailst @ B3 @ M )
% 2.39/2.72 => ( entailst @ ( sup_sup_assn @ A3 @ B3 ) @ M ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % entt_disjE
% 2.39/2.72 thf(fact_668_entt__disjD1,axiom,
% 2.39/2.72 ! [A3: assn,B3: assn,C2: assn] :
% 2.39/2.72 ( ( entailst @ ( sup_sup_assn @ A3 @ B3 ) @ C2 )
% 2.39/2.72 => ( entailst @ A3 @ C2 ) ) ).
% 2.39/2.72
% 2.39/2.72 % entt_disjD1
% 2.39/2.72 thf(fact_669_entt__disjD2,axiom,
% 2.39/2.72 ! [A3: assn,B3: assn,C2: assn] :
% 2.39/2.72 ( ( entailst @ ( sup_sup_assn @ A3 @ B3 ) @ C2 )
% 2.39/2.72 => ( entailst @ B3 @ C2 ) ) ).
% 2.39/2.72
% 2.39/2.72 % entt_disjD2
% 2.39/2.72 thf(fact_670_entt__disjI1_H,axiom,
% 2.39/2.72 ! [A3: assn,B3: assn,C2: assn] :
% 2.39/2.72 ( ( entailst @ A3 @ B3 )
% 2.39/2.72 => ( entailst @ A3 @ ( sup_sup_assn @ B3 @ C2 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % entt_disjI1'
% 2.39/2.72 thf(fact_671_entt__disjI2_H,axiom,
% 2.39/2.72 ! [A3: assn,C2: assn,B3: assn] :
% 2.39/2.72 ( ( entailst @ A3 @ C2 )
% 2.39/2.72 => ( entailst @ A3 @ ( sup_sup_assn @ B3 @ C2 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % entt_disjI2'
% 2.39/2.72 thf(fact_672_entt__disjI1__direct,axiom,
% 2.39/2.72 ! [A3: assn,B3: assn] : ( entailst @ A3 @ ( sup_sup_assn @ A3 @ B3 ) ) ).
% 2.39/2.72
% 2.39/2.72 % entt_disjI1_direct
% 2.39/2.72 thf(fact_673_entt__disjI2__direct,axiom,
% 2.39/2.72 ! [B3: assn,A3: assn] : ( entailst @ B3 @ ( sup_sup_assn @ A3 @ B3 ) ) ).
% 2.39/2.72
% 2.39/2.72 % entt_disjI2_direct
% 2.39/2.72 thf(fact_674_norm__assertion__simps_I11_J,axiom,
% 2.39/2.72 ! [X: assn] :
% 2.39/2.72 ( ( sup_sup_assn @ top_top_assn @ X )
% 2.39/2.72 = top_top_assn ) ).
% 2.39/2.72
% 2.39/2.72 % norm_assertion_simps(11)
% 2.39/2.72 thf(fact_675_norm__assertion__simps_I12_J,axiom,
% 2.39/2.72 ! [X: assn] :
% 2.39/2.72 ( ( sup_sup_assn @ X @ top_top_assn )
% 2.39/2.72 = top_top_assn ) ).
% 2.39/2.72
% 2.39/2.72 % norm_assertion_simps(12)
% 2.39/2.72 thf(fact_676_norm__assertion__simps_I5_J,axiom,
% 2.39/2.72 ! [X: assn] :
% 2.39/2.72 ( ( sup_sup_assn @ bot_bot_assn @ X )
% 2.39/2.72 = X ) ).
% 2.39/2.72
% 2.39/2.72 % norm_assertion_simps(5)
% 2.39/2.72 thf(fact_677_norm__assertion__simps_I6_J,axiom,
% 2.39/2.72 ! [X: assn] :
% 2.39/2.72 ( ( sup_sup_assn @ X @ bot_bot_assn )
% 2.39/2.72 = X ) ).
% 2.39/2.72
% 2.39/2.72 % norm_assertion_simps(6)
% 2.39/2.72 thf(fact_678_mod__relH,axiom,
% 2.39/2.72 ! [As2: set_nat,H2: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit,P2: assn] :
% 2.39/2.72 ( ( relH @ As2 @ H2 @ H5 )
% 2.39/2.72 => ( ( rep_assn @ P2 @ ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 2.39/2.72 = ( rep_assn @ P2 @ ( produc7507926704131184380et_nat @ H5 @ As2 ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % mod_relH
% 2.39/2.72 thf(fact_679_relH__in__rangeI_I2_J,axiom,
% 2.39/2.72 ! [As2: set_nat,H2: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit] :
% 2.39/2.72 ( ( relH @ As2 @ H2 @ H5 )
% 2.39/2.72 => ( in_range @ ( produc7507926704131184380et_nat @ H5 @ As2 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % relH_in_rangeI(2)
% 2.39/2.72 thf(fact_680_relH__in__rangeI_I1_J,axiom,
% 2.39/2.72 ! [As2: set_nat,H2: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit] :
% 2.39/2.72 ( ( relH @ As2 @ H2 @ H5 )
% 2.39/2.72 => ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As2 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % relH_in_rangeI(1)
% 2.39/2.72 thf(fact_681_relH__refl,axiom,
% 2.39/2.72 ! [H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 2.39/2.72 ( ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 2.39/2.72 => ( relH @ As2 @ H2 @ H2 ) ) ).
% 2.39/2.72
% 2.39/2.72 % relH_refl
% 2.39/2.72 thf(fact_682_Int__UNIV__right,axiom,
% 2.39/2.72 ! [A3: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( inf_in2572325071724192079at_nat @ A3 @ top_to4669805908274784177at_nat )
% 2.39/2.72 = A3 ) ).
% 2.39/2.72
% 2.39/2.72 % Int_UNIV_right
% 2.39/2.72 thf(fact_683_Int__UNIV__right,axiom,
% 2.39/2.72 ! [A3: set_nat] :
% 2.39/2.72 ( ( inf_inf_set_nat @ A3 @ top_top_set_nat )
% 2.39/2.72 = A3 ) ).
% 2.39/2.72
% 2.39/2.72 % Int_UNIV_right
% 2.39/2.72 thf(fact_684_Int__UNIV__right,axiom,
% 2.39/2.72 ! [A3: set_Product_unit] :
% 2.39/2.72 ( ( inf_in4660618365625256667t_unit @ A3 @ top_to1996260823553986621t_unit )
% 2.39/2.72 = A3 ) ).
% 2.39/2.72
% 2.39/2.72 % Int_UNIV_right
% 2.39/2.72 thf(fact_685_Int__UNIV__left,axiom,
% 2.39/2.72 ! [B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( inf_in2572325071724192079at_nat @ top_to4669805908274784177at_nat @ B3 )
% 2.39/2.72 = B3 ) ).
% 2.39/2.72
% 2.39/2.72 % Int_UNIV_left
% 2.39/2.72 thf(fact_686_Int__UNIV__left,axiom,
% 2.39/2.72 ! [B3: set_nat] :
% 2.39/2.72 ( ( inf_inf_set_nat @ top_top_set_nat @ B3 )
% 2.39/2.72 = B3 ) ).
% 2.39/2.72
% 2.39/2.72 % Int_UNIV_left
% 2.39/2.72 thf(fact_687_Int__UNIV__left,axiom,
% 2.39/2.72 ! [B3: set_Product_unit] :
% 2.39/2.72 ( ( inf_in4660618365625256667t_unit @ top_to1996260823553986621t_unit @ B3 )
% 2.39/2.72 = B3 ) ).
% 2.39/2.72
% 2.39/2.72 % Int_UNIV_left
% 2.39/2.72 thf(fact_688_Int__left__commute,axiom,
% 2.39/2.72 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( inf_in2572325071724192079at_nat @ A3 @ ( inf_in2572325071724192079at_nat @ B3 @ C2 ) )
% 2.39/2.72 = ( inf_in2572325071724192079at_nat @ B3 @ ( inf_in2572325071724192079at_nat @ A3 @ C2 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % Int_left_commute
% 2.39/2.72 thf(fact_689_Int__left__commute,axiom,
% 2.39/2.72 ! [A3: set_nat,B3: set_nat,C2: set_nat] :
% 2.39/2.72 ( ( inf_inf_set_nat @ A3 @ ( inf_inf_set_nat @ B3 @ C2 ) )
% 2.39/2.72 = ( inf_inf_set_nat @ B3 @ ( inf_inf_set_nat @ A3 @ C2 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % Int_left_commute
% 2.39/2.72 thf(fact_690_Int__left__absorb,axiom,
% 2.39/2.72 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( inf_in2572325071724192079at_nat @ A3 @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) )
% 2.39/2.72 = ( inf_in2572325071724192079at_nat @ A3 @ B3 ) ) ).
% 2.39/2.72
% 2.39/2.72 % Int_left_absorb
% 2.39/2.72 thf(fact_691_Int__left__absorb,axiom,
% 2.39/2.72 ! [A3: set_nat,B3: set_nat] :
% 2.39/2.72 ( ( inf_inf_set_nat @ A3 @ ( inf_inf_set_nat @ A3 @ B3 ) )
% 2.39/2.72 = ( inf_inf_set_nat @ A3 @ B3 ) ) ).
% 2.39/2.72
% 2.39/2.72 % Int_left_absorb
% 2.39/2.72 thf(fact_692_Int__commute,axiom,
% 2.39/2.72 ( inf_in2572325071724192079at_nat
% 2.39/2.72 = ( ^ [A4: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat] : ( inf_in2572325071724192079at_nat @ B4 @ A4 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % Int_commute
% 2.39/2.72 thf(fact_693_Int__commute,axiom,
% 2.39/2.72 ( inf_inf_set_nat
% 2.39/2.72 = ( ^ [A4: set_nat,B4: set_nat] : ( inf_inf_set_nat @ B4 @ A4 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % Int_commute
% 2.39/2.72 thf(fact_694_Int__absorb,axiom,
% 2.39/2.72 ! [A3: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( inf_in2572325071724192079at_nat @ A3 @ A3 )
% 2.39/2.72 = A3 ) ).
% 2.39/2.72
% 2.39/2.72 % Int_absorb
% 2.39/2.72 thf(fact_695_Int__absorb,axiom,
% 2.39/2.72 ! [A3: set_nat] :
% 2.39/2.72 ( ( inf_inf_set_nat @ A3 @ A3 )
% 2.39/2.72 = A3 ) ).
% 2.39/2.72
% 2.39/2.72 % Int_absorb
% 2.39/2.72 thf(fact_696_Int__assoc,axiom,
% 2.39/2.72 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) @ C2 )
% 2.39/2.72 = ( inf_in2572325071724192079at_nat @ A3 @ ( inf_in2572325071724192079at_nat @ B3 @ C2 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % Int_assoc
% 2.39/2.72 thf(fact_697_Int__assoc,axiom,
% 2.39/2.72 ! [A3: set_nat,B3: set_nat,C2: set_nat] :
% 2.39/2.72 ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ A3 @ B3 ) @ C2 )
% 2.39/2.72 = ( inf_inf_set_nat @ A3 @ ( inf_inf_set_nat @ B3 @ C2 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % Int_assoc
% 2.39/2.72 thf(fact_698_IntD2,axiom,
% 2.39/2.72 ! [C: produc3658429121746597890et_nat > $o,A3: set_Pr4532377907799695533_nat_o,B3: set_Pr4532377907799695533_nat_o] :
% 2.39/2.72 ( ( member6576561426505652726_nat_o @ C @ ( inf_in1906310914598751387_nat_o @ A3 @ B3 ) )
% 2.39/2.72 => ( member6576561426505652726_nat_o @ C @ B3 ) ) ).
% 2.39/2.72
% 2.39/2.72 % IntD2
% 2.39/2.72 thf(fact_699_IntD2,axiom,
% 2.39/2.72 ! [C: int,A3: set_int,B3: set_int] :
% 2.39/2.72 ( ( member_int2 @ C @ ( inf_inf_set_int @ A3 @ B3 ) )
% 2.39/2.72 => ( member_int2 @ C @ B3 ) ) ).
% 2.39/2.72
% 2.39/2.72 % IntD2
% 2.39/2.72 thf(fact_700_IntD2,axiom,
% 2.39/2.72 ! [C: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( member8440522571783428010at_nat @ C @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) )
% 2.39/2.72 => ( member8440522571783428010at_nat @ C @ B3 ) ) ).
% 2.39/2.72
% 2.39/2.72 % IntD2
% 2.39/2.72 thf(fact_701_IntD2,axiom,
% 2.39/2.72 ! [C: nat,A3: set_nat,B3: set_nat] :
% 2.39/2.72 ( ( member_nat2 @ C @ ( inf_inf_set_nat @ A3 @ B3 ) )
% 2.39/2.72 => ( member_nat2 @ C @ B3 ) ) ).
% 2.39/2.72
% 2.39/2.72 % IntD2
% 2.39/2.72 thf(fact_702_IntD1,axiom,
% 2.39/2.72 ! [C: produc3658429121746597890et_nat > $o,A3: set_Pr4532377907799695533_nat_o,B3: set_Pr4532377907799695533_nat_o] :
% 2.39/2.72 ( ( member6576561426505652726_nat_o @ C @ ( inf_in1906310914598751387_nat_o @ A3 @ B3 ) )
% 2.39/2.72 => ( member6576561426505652726_nat_o @ C @ A3 ) ) ).
% 2.39/2.72
% 2.39/2.72 % IntD1
% 2.39/2.72 thf(fact_703_IntD1,axiom,
% 2.39/2.72 ! [C: int,A3: set_int,B3: set_int] :
% 2.39/2.72 ( ( member_int2 @ C @ ( inf_inf_set_int @ A3 @ B3 ) )
% 2.39/2.72 => ( member_int2 @ C @ A3 ) ) ).
% 2.39/2.72
% 2.39/2.72 % IntD1
% 2.39/2.72 thf(fact_704_IntD1,axiom,
% 2.39/2.72 ! [C: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( member8440522571783428010at_nat @ C @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) )
% 2.39/2.72 => ( member8440522571783428010at_nat @ C @ A3 ) ) ).
% 2.39/2.72
% 2.39/2.72 % IntD1
% 2.39/2.72 thf(fact_705_IntD1,axiom,
% 2.39/2.72 ! [C: nat,A3: set_nat,B3: set_nat] :
% 2.39/2.72 ( ( member_nat2 @ C @ ( inf_inf_set_nat @ A3 @ B3 ) )
% 2.39/2.72 => ( member_nat2 @ C @ A3 ) ) ).
% 2.39/2.72
% 2.39/2.72 % IntD1
% 2.39/2.72 thf(fact_706_IntE,axiom,
% 2.39/2.72 ! [C: produc3658429121746597890et_nat > $o,A3: set_Pr4532377907799695533_nat_o,B3: set_Pr4532377907799695533_nat_o] :
% 2.39/2.72 ( ( member6576561426505652726_nat_o @ C @ ( inf_in1906310914598751387_nat_o @ A3 @ B3 ) )
% 2.39/2.72 => ~ ( ( member6576561426505652726_nat_o @ C @ A3 )
% 2.39/2.72 => ~ ( member6576561426505652726_nat_o @ C @ B3 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % IntE
% 2.39/2.72 thf(fact_707_IntE,axiom,
% 2.39/2.72 ! [C: int,A3: set_int,B3: set_int] :
% 2.39/2.72 ( ( member_int2 @ C @ ( inf_inf_set_int @ A3 @ B3 ) )
% 2.39/2.72 => ~ ( ( member_int2 @ C @ A3 )
% 2.39/2.72 => ~ ( member_int2 @ C @ B3 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % IntE
% 2.39/2.72 thf(fact_708_IntE,axiom,
% 2.39/2.72 ! [C: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( member8440522571783428010at_nat @ C @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) )
% 2.39/2.72 => ~ ( ( member8440522571783428010at_nat @ C @ A3 )
% 2.39/2.72 => ~ ( member8440522571783428010at_nat @ C @ B3 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % IntE
% 2.39/2.72 thf(fact_709_IntE,axiom,
% 2.39/2.72 ! [C: nat,A3: set_nat,B3: set_nat] :
% 2.39/2.72 ( ( member_nat2 @ C @ ( inf_inf_set_nat @ A3 @ B3 ) )
% 2.39/2.72 => ~ ( ( member_nat2 @ C @ A3 )
% 2.39/2.72 => ~ ( member_nat2 @ C @ B3 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % IntE
% 2.39/2.72 thf(fact_710_disjoint__iff__not__equal,axiom,
% 2.39/2.72 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( ( inf_in2572325071724192079at_nat @ A3 @ B3 )
% 2.39/2.72 = bot_bo2099793752762293965at_nat )
% 2.39/2.72 = ( ! [X2: product_prod_nat_nat] :
% 2.39/2.72 ( ( member8440522571783428010at_nat @ X2 @ A3 )
% 2.39/2.72 => ! [Y2: product_prod_nat_nat] :
% 2.39/2.72 ( ( member8440522571783428010at_nat @ Y2 @ B3 )
% 2.39/2.72 => ( X2 != Y2 ) ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % disjoint_iff_not_equal
% 2.39/2.72 thf(fact_711_disjoint__iff__not__equal,axiom,
% 2.39/2.72 ! [A3: set_nat,B3: set_nat] :
% 2.39/2.72 ( ( ( inf_inf_set_nat @ A3 @ B3 )
% 2.39/2.72 = bot_bot_set_nat )
% 2.39/2.72 = ( ! [X2: nat] :
% 2.39/2.72 ( ( member_nat2 @ X2 @ A3 )
% 2.39/2.72 => ! [Y2: nat] :
% 2.39/2.72 ( ( member_nat2 @ Y2 @ B3 )
% 2.39/2.72 => ( X2 != Y2 ) ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % disjoint_iff_not_equal
% 2.39/2.72 thf(fact_712_disjoint__iff__not__equal,axiom,
% 2.39/2.72 ! [A3: set_int,B3: set_int] :
% 2.39/2.72 ( ( ( inf_inf_set_int @ A3 @ B3 )
% 2.39/2.72 = bot_bot_set_int )
% 2.39/2.72 = ( ! [X2: int] :
% 2.39/2.72 ( ( member_int2 @ X2 @ A3 )
% 2.39/2.72 => ! [Y2: int] :
% 2.39/2.72 ( ( member_int2 @ Y2 @ B3 )
% 2.39/2.72 => ( X2 != Y2 ) ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % disjoint_iff_not_equal
% 2.39/2.72 thf(fact_713_Int__empty__right,axiom,
% 2.39/2.72 ! [A3: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( inf_in2572325071724192079at_nat @ A3 @ bot_bo2099793752762293965at_nat )
% 2.39/2.72 = bot_bo2099793752762293965at_nat ) ).
% 2.39/2.72
% 2.39/2.72 % Int_empty_right
% 2.39/2.72 thf(fact_714_Int__empty__right,axiom,
% 2.39/2.72 ! [A3: set_nat] :
% 2.39/2.72 ( ( inf_inf_set_nat @ A3 @ bot_bot_set_nat )
% 2.39/2.72 = bot_bot_set_nat ) ).
% 2.39/2.72
% 2.39/2.72 % Int_empty_right
% 2.39/2.72 thf(fact_715_Int__empty__right,axiom,
% 2.39/2.72 ! [A3: set_int] :
% 2.39/2.72 ( ( inf_inf_set_int @ A3 @ bot_bot_set_int )
% 2.39/2.72 = bot_bot_set_int ) ).
% 2.39/2.72
% 2.39/2.72 % Int_empty_right
% 2.39/2.72 thf(fact_716_Int__empty__left,axiom,
% 2.39/2.72 ! [B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( inf_in2572325071724192079at_nat @ bot_bo2099793752762293965at_nat @ B3 )
% 2.39/2.72 = bot_bo2099793752762293965at_nat ) ).
% 2.39/2.72
% 2.39/2.72 % Int_empty_left
% 2.39/2.72 thf(fact_717_Int__empty__left,axiom,
% 2.39/2.72 ! [B3: set_nat] :
% 2.39/2.72 ( ( inf_inf_set_nat @ bot_bot_set_nat @ B3 )
% 2.39/2.72 = bot_bot_set_nat ) ).
% 2.39/2.72
% 2.39/2.72 % Int_empty_left
% 2.39/2.72 thf(fact_718_Int__empty__left,axiom,
% 2.39/2.72 ! [B3: set_int] :
% 2.39/2.72 ( ( inf_inf_set_int @ bot_bot_set_int @ B3 )
% 2.39/2.72 = bot_bot_set_int ) ).
% 2.39/2.72
% 2.39/2.72 % Int_empty_left
% 2.39/2.72 thf(fact_719_disjoint__iff,axiom,
% 2.39/2.72 ! [A3: set_Pr4532377907799695533_nat_o,B3: set_Pr4532377907799695533_nat_o] :
% 2.39/2.72 ( ( ( inf_in1906310914598751387_nat_o @ A3 @ B3 )
% 2.39/2.72 = bot_bo7824918357723582233_nat_o )
% 2.39/2.72 = ( ! [X2: produc3658429121746597890et_nat > $o] :
% 2.39/2.72 ( ( member6576561426505652726_nat_o @ X2 @ A3 )
% 2.39/2.72 => ~ ( member6576561426505652726_nat_o @ X2 @ B3 ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % disjoint_iff
% 2.39/2.72 thf(fact_720_disjoint__iff,axiom,
% 2.39/2.72 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( ( inf_in2572325071724192079at_nat @ A3 @ B3 )
% 2.39/2.72 = bot_bo2099793752762293965at_nat )
% 2.39/2.72 = ( ! [X2: product_prod_nat_nat] :
% 2.39/2.72 ( ( member8440522571783428010at_nat @ X2 @ A3 )
% 2.39/2.72 => ~ ( member8440522571783428010at_nat @ X2 @ B3 ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % disjoint_iff
% 2.39/2.72 thf(fact_721_disjoint__iff,axiom,
% 2.39/2.72 ! [A3: set_nat,B3: set_nat] :
% 2.39/2.72 ( ( ( inf_inf_set_nat @ A3 @ B3 )
% 2.39/2.72 = bot_bot_set_nat )
% 2.39/2.72 = ( ! [X2: nat] :
% 2.39/2.72 ( ( member_nat2 @ X2 @ A3 )
% 2.39/2.72 => ~ ( member_nat2 @ X2 @ B3 ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % disjoint_iff
% 2.39/2.72 thf(fact_722_disjoint__iff,axiom,
% 2.39/2.72 ! [A3: set_int,B3: set_int] :
% 2.39/2.72 ( ( ( inf_inf_set_int @ A3 @ B3 )
% 2.39/2.72 = bot_bot_set_int )
% 2.39/2.72 = ( ! [X2: int] :
% 2.39/2.72 ( ( member_int2 @ X2 @ A3 )
% 2.39/2.72 => ~ ( member_int2 @ X2 @ B3 ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % disjoint_iff
% 2.39/2.72 thf(fact_723_Int__emptyI,axiom,
% 2.39/2.72 ! [A3: set_Pr4532377907799695533_nat_o,B3: set_Pr4532377907799695533_nat_o] :
% 2.39/2.72 ( ! [X3: produc3658429121746597890et_nat > $o] :
% 2.39/2.72 ( ( member6576561426505652726_nat_o @ X3 @ A3 )
% 2.39/2.72 => ~ ( member6576561426505652726_nat_o @ X3 @ B3 ) )
% 2.39/2.72 => ( ( inf_in1906310914598751387_nat_o @ A3 @ B3 )
% 2.39/2.72 = bot_bo7824918357723582233_nat_o ) ) ).
% 2.39/2.72
% 2.39/2.72 % Int_emptyI
% 2.39/2.72 thf(fact_724_Int__emptyI,axiom,
% 2.39/2.72 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ! [X3: product_prod_nat_nat] :
% 2.39/2.72 ( ( member8440522571783428010at_nat @ X3 @ A3 )
% 2.39/2.72 => ~ ( member8440522571783428010at_nat @ X3 @ B3 ) )
% 2.39/2.72 => ( ( inf_in2572325071724192079at_nat @ A3 @ B3 )
% 2.39/2.72 = bot_bo2099793752762293965at_nat ) ) ).
% 2.39/2.72
% 2.39/2.72 % Int_emptyI
% 2.39/2.72 thf(fact_725_Int__emptyI,axiom,
% 2.39/2.72 ! [A3: set_nat,B3: set_nat] :
% 2.39/2.72 ( ! [X3: nat] :
% 2.39/2.72 ( ( member_nat2 @ X3 @ A3 )
% 2.39/2.72 => ~ ( member_nat2 @ X3 @ B3 ) )
% 2.39/2.72 => ( ( inf_inf_set_nat @ A3 @ B3 )
% 2.39/2.72 = bot_bot_set_nat ) ) ).
% 2.39/2.72
% 2.39/2.72 % Int_emptyI
% 2.39/2.72 thf(fact_726_Int__emptyI,axiom,
% 2.39/2.72 ! [A3: set_int,B3: set_int] :
% 2.39/2.72 ( ! [X3: int] :
% 2.39/2.72 ( ( member_int2 @ X3 @ A3 )
% 2.39/2.72 => ~ ( member_int2 @ X3 @ B3 ) )
% 2.39/2.72 => ( ( inf_inf_set_int @ A3 @ B3 )
% 2.39/2.72 = bot_bot_set_int ) ) ).
% 2.39/2.72
% 2.39/2.72 % Int_emptyI
% 2.39/2.72 thf(fact_727_Un__Int__distrib2,axiom,
% 2.39/2.72 ! [B3: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ B3 @ C2 ) @ A3 )
% 2.39/2.72 = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ B3 @ A3 ) @ ( sup_su6327502436637775413at_nat @ C2 @ A3 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % Un_Int_distrib2
% 2.39/2.72 thf(fact_728_Un__Int__distrib2,axiom,
% 2.39/2.72 ! [B3: set_nat,C2: set_nat,A3: set_nat] :
% 2.39/2.72 ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ B3 @ C2 ) @ A3 )
% 2.39/2.72 = ( inf_inf_set_nat @ ( sup_sup_set_nat @ B3 @ A3 ) @ ( sup_sup_set_nat @ C2 @ A3 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % Un_Int_distrib2
% 2.39/2.72 thf(fact_729_Int__Un__distrib2,axiom,
% 2.39/2.72 ! [B3: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ B3 @ C2 ) @ A3 )
% 2.39/2.72 = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ B3 @ A3 ) @ ( inf_in2572325071724192079at_nat @ C2 @ A3 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % Int_Un_distrib2
% 2.39/2.72 thf(fact_730_Int__Un__distrib2,axiom,
% 2.39/2.72 ! [B3: set_nat,C2: set_nat,A3: set_nat] :
% 2.39/2.72 ( ( inf_inf_set_nat @ ( sup_sup_set_nat @ B3 @ C2 ) @ A3 )
% 2.39/2.72 = ( sup_sup_set_nat @ ( inf_inf_set_nat @ B3 @ A3 ) @ ( inf_inf_set_nat @ C2 @ A3 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % Int_Un_distrib2
% 2.39/2.72 thf(fact_731_Un__Int__distrib,axiom,
% 2.39/2.72 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( sup_su6327502436637775413at_nat @ A3 @ ( inf_in2572325071724192079at_nat @ B3 @ C2 ) )
% 2.39/2.72 = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ A3 @ B3 ) @ ( sup_su6327502436637775413at_nat @ A3 @ C2 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % Un_Int_distrib
% 2.39/2.72 thf(fact_732_Un__Int__distrib,axiom,
% 2.39/2.72 ! [A3: set_nat,B3: set_nat,C2: set_nat] :
% 2.39/2.72 ( ( sup_sup_set_nat @ A3 @ ( inf_inf_set_nat @ B3 @ C2 ) )
% 2.39/2.72 = ( inf_inf_set_nat @ ( sup_sup_set_nat @ A3 @ B3 ) @ ( sup_sup_set_nat @ A3 @ C2 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % Un_Int_distrib
% 2.39/2.72 thf(fact_733_Int__Un__distrib,axiom,
% 2.39/2.72 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( inf_in2572325071724192079at_nat @ A3 @ ( sup_su6327502436637775413at_nat @ B3 @ C2 ) )
% 2.39/2.72 = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) @ ( inf_in2572325071724192079at_nat @ A3 @ C2 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % Int_Un_distrib
% 2.39/2.72 thf(fact_734_Int__Un__distrib,axiom,
% 2.39/2.72 ! [A3: set_nat,B3: set_nat,C2: set_nat] :
% 2.39/2.72 ( ( inf_inf_set_nat @ A3 @ ( sup_sup_set_nat @ B3 @ C2 ) )
% 2.39/2.72 = ( sup_sup_set_nat @ ( inf_inf_set_nat @ A3 @ B3 ) @ ( inf_inf_set_nat @ A3 @ C2 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % Int_Un_distrib
% 2.39/2.72 thf(fact_735_Un__Int__crazy,axiom,
% 2.39/2.72 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( sup_su6327502436637775413at_nat @ ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) @ ( inf_in2572325071724192079at_nat @ B3 @ C2 ) ) @ ( inf_in2572325071724192079at_nat @ C2 @ A3 ) )
% 2.39/2.72 = ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ A3 @ B3 ) @ ( sup_su6327502436637775413at_nat @ B3 @ C2 ) ) @ ( sup_su6327502436637775413at_nat @ C2 @ A3 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % Un_Int_crazy
% 2.39/2.72 thf(fact_736_Un__Int__crazy,axiom,
% 2.39/2.72 ! [A3: set_nat,B3: set_nat,C2: set_nat] :
% 2.39/2.72 ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ ( inf_inf_set_nat @ A3 @ B3 ) @ ( inf_inf_set_nat @ B3 @ C2 ) ) @ ( inf_inf_set_nat @ C2 @ A3 ) )
% 2.39/2.72 = ( inf_inf_set_nat @ ( inf_inf_set_nat @ ( sup_sup_set_nat @ A3 @ B3 ) @ ( sup_sup_set_nat @ B3 @ C2 ) ) @ ( sup_sup_set_nat @ C2 @ A3 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % Un_Int_crazy
% 2.39/2.72 thf(fact_737_wand__raw_Oelims_I3_J,axiom,
% 2.39/2.72 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 2.39/2.72 ( ~ ( wand_raw @ X @ Xa @ Xb )
% 2.39/2.72 => ~ ! [H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.39/2.72 ( ( Xb
% 2.39/2.72 = ( produc7507926704131184380et_nat @ H3 @ As ) )
% 2.39/2.72 => ( ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As ) )
% 2.39/2.72 & ! [H4: heap_e7401611519738050253t_unit,As4: set_nat] :
% 2.39/2.72 ( ( ( ( inf_inf_set_nat @ As @ As4 )
% 2.39/2.72 = bot_bot_set_nat )
% 2.39/2.72 & ( relH @ As @ H3 @ H4 )
% 2.39/2.72 & ( in_range @ ( produc7507926704131184380et_nat @ H4 @ As ) )
% 2.39/2.72 & ( X @ ( produc7507926704131184380et_nat @ H4 @ As4 ) ) )
% 2.39/2.72 => ( Xa @ ( produc7507926704131184380et_nat @ H4 @ ( sup_sup_set_nat @ As @ As4 ) ) ) ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % wand_raw.elims(3)
% 2.39/2.72 thf(fact_738_wand__raw_Oelims_I2_J,axiom,
% 2.39/2.72 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 2.39/2.72 ( ( wand_raw @ X @ Xa @ Xb )
% 2.39/2.72 => ~ ! [H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.39/2.72 ( ( Xb
% 2.39/2.72 = ( produc7507926704131184380et_nat @ H3 @ As ) )
% 2.39/2.72 => ~ ( ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As ) )
% 2.39/2.72 & ! [H6: heap_e7401611519738050253t_unit,As5: set_nat] :
% 2.39/2.72 ( ( ( ( inf_inf_set_nat @ As @ As5 )
% 2.39/2.72 = bot_bot_set_nat )
% 2.39/2.72 & ( relH @ As @ H3 @ H6 )
% 2.39/2.72 & ( in_range @ ( produc7507926704131184380et_nat @ H6 @ As ) )
% 2.39/2.72 & ( X @ ( produc7507926704131184380et_nat @ H6 @ As5 ) ) )
% 2.39/2.72 => ( Xa @ ( produc7507926704131184380et_nat @ H6 @ ( sup_sup_set_nat @ As @ As5 ) ) ) ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % wand_raw.elims(2)
% 2.39/2.72 thf(fact_739_wand__raw_Oelims_I1_J,axiom,
% 2.39/2.72 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat,Y: $o] :
% 2.39/2.72 ( ( ( wand_raw @ X @ Xa @ Xb )
% 2.39/2.72 = Y )
% 2.39/2.72 => ~ ! [H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.39/2.72 ( ( Xb
% 2.39/2.72 = ( produc7507926704131184380et_nat @ H3 @ As ) )
% 2.39/2.72 => ( Y
% 2.39/2.72 = ( ~ ( ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As ) )
% 2.39/2.72 & ! [H7: heap_e7401611519738050253t_unit,As6: set_nat] :
% 2.39/2.72 ( ( ( ( inf_inf_set_nat @ As @ As6 )
% 2.39/2.72 = bot_bot_set_nat )
% 2.39/2.72 & ( relH @ As @ H3 @ H7 )
% 2.39/2.72 & ( in_range @ ( produc7507926704131184380et_nat @ H7 @ As ) )
% 2.39/2.72 & ( X @ ( produc7507926704131184380et_nat @ H7 @ As6 ) ) )
% 2.39/2.72 => ( Xa @ ( produc7507926704131184380et_nat @ H7 @ ( sup_sup_set_nat @ As @ As6 ) ) ) ) ) ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % wand_raw.elims(1)
% 2.39/2.72 thf(fact_740_wand__raw_Osimps,axiom,
% 2.39/2.72 ! [P2: produc3658429121746597890et_nat > $o,Q2: produc3658429121746597890et_nat > $o,H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 2.39/2.72 ( ( wand_raw @ P2 @ Q2 @ ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 2.39/2.72 = ( ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 2.39/2.72 & ! [H7: heap_e7401611519738050253t_unit,As6: set_nat] :
% 2.39/2.72 ( ( ( ( inf_inf_set_nat @ As2 @ As6 )
% 2.39/2.72 = bot_bot_set_nat )
% 2.39/2.72 & ( relH @ As2 @ H2 @ H7 )
% 2.39/2.72 & ( in_range @ ( produc7507926704131184380et_nat @ H7 @ As2 ) )
% 2.39/2.72 & ( P2 @ ( produc7507926704131184380et_nat @ H7 @ As6 ) ) )
% 2.39/2.72 => ( Q2 @ ( produc7507926704131184380et_nat @ H7 @ ( sup_sup_set_nat @ As2 @ As6 ) ) ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % wand_raw.simps
% 2.39/2.72 thf(fact_741_times__assn__raw_Oelims_I3_J,axiom,
% 2.39/2.72 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 2.39/2.72 ( ~ ( times_assn_raw @ X @ Xa @ Xb )
% 2.39/2.72 => ~ ! [H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.39/2.72 ( ( Xb
% 2.39/2.72 = ( produc7507926704131184380et_nat @ H3 @ As ) )
% 2.39/2.72 => ? [As12: set_nat,As23: set_nat] :
% 2.39/2.72 ( ( As
% 2.39/2.72 = ( sup_sup_set_nat @ As12 @ As23 ) )
% 2.39/2.72 & ( ( inf_inf_set_nat @ As12 @ As23 )
% 2.39/2.72 = bot_bot_set_nat )
% 2.39/2.72 & ( X @ ( produc7507926704131184380et_nat @ H3 @ As12 ) )
% 2.39/2.72 & ( Xa @ ( produc7507926704131184380et_nat @ H3 @ As23 ) ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % times_assn_raw.elims(3)
% 2.39/2.72 thf(fact_742_times__assn__raw_Oelims_I2_J,axiom,
% 2.39/2.72 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 2.39/2.72 ( ( times_assn_raw @ X @ Xa @ Xb )
% 2.39/2.72 => ~ ! [H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.39/2.72 ( ( Xb
% 2.39/2.72 = ( produc7507926704131184380et_nat @ H3 @ As ) )
% 2.39/2.72 => ~ ? [As13: set_nat,As24: set_nat] :
% 2.39/2.72 ( ( As
% 2.39/2.72 = ( sup_sup_set_nat @ As13 @ As24 ) )
% 2.39/2.72 & ( ( inf_inf_set_nat @ As13 @ As24 )
% 2.39/2.72 = bot_bot_set_nat )
% 2.39/2.72 & ( X @ ( produc7507926704131184380et_nat @ H3 @ As13 ) )
% 2.39/2.72 & ( Xa @ ( produc7507926704131184380et_nat @ H3 @ As24 ) ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % times_assn_raw.elims(2)
% 2.39/2.72 thf(fact_743_times__assn__raw_Oelims_I1_J,axiom,
% 2.39/2.72 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat,Y: $o] :
% 2.39/2.72 ( ( ( times_assn_raw @ X @ Xa @ Xb )
% 2.39/2.72 = Y )
% 2.39/2.72 => ~ ! [H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.39/2.72 ( ( Xb
% 2.39/2.72 = ( produc7507926704131184380et_nat @ H3 @ As ) )
% 2.39/2.72 => ( Y
% 2.39/2.72 = ( ~ ? [As1: set_nat,As22: set_nat] :
% 2.39/2.72 ( ( As
% 2.39/2.72 = ( sup_sup_set_nat @ As1 @ As22 ) )
% 2.39/2.72 & ( ( inf_inf_set_nat @ As1 @ As22 )
% 2.39/2.72 = bot_bot_set_nat )
% 2.39/2.72 & ( X @ ( produc7507926704131184380et_nat @ H3 @ As1 ) )
% 2.39/2.72 & ( Xa @ ( produc7507926704131184380et_nat @ H3 @ As22 ) ) ) ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % times_assn_raw.elims(1)
% 2.39/2.72 thf(fact_744_times__assn__raw_Osimps,axiom,
% 2.39/2.72 ! [P2: produc3658429121746597890et_nat > $o,Q2: produc3658429121746597890et_nat > $o,H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 2.39/2.72 ( ( times_assn_raw @ P2 @ Q2 @ ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 2.39/2.72 = ( ? [As1: set_nat,As22: set_nat] :
% 2.39/2.72 ( ( As2
% 2.39/2.72 = ( sup_sup_set_nat @ As1 @ As22 ) )
% 2.39/2.72 & ( ( inf_inf_set_nat @ As1 @ As22 )
% 2.39/2.72 = bot_bot_set_nat )
% 2.39/2.72 & ( P2 @ ( produc7507926704131184380et_nat @ H2 @ As1 ) )
% 2.39/2.72 & ( Q2 @ ( produc7507926704131184380et_nat @ H2 @ As22 ) ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % times_assn_raw.simps
% 2.39/2.72 thf(fact_745_disjointI,axiom,
% 2.39/2.72 ! [A: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o] :
% 2.39/2.72 ( ! [X3: produc3658429121746597890et_nat > $o] :
% 2.39/2.72 ( ( member6576561426505652726_nat_o @ X3 @ A )
% 2.39/2.72 => ~ ( member6576561426505652726_nat_o @ X3 @ B ) )
% 2.39/2.72 => ( ( inf_in1906310914598751387_nat_o @ A @ B )
% 2.39/2.72 = bot_bo7824918357723582233_nat_o ) ) ).
% 2.39/2.72
% 2.39/2.72 % disjointI
% 2.39/2.72 thf(fact_746_disjointI,axiom,
% 2.39/2.72 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ! [X3: product_prod_nat_nat] :
% 2.39/2.72 ( ( member8440522571783428010at_nat @ X3 @ A )
% 2.39/2.72 => ~ ( member8440522571783428010at_nat @ X3 @ B ) )
% 2.39/2.72 => ( ( inf_in2572325071724192079at_nat @ A @ B )
% 2.39/2.72 = bot_bo2099793752762293965at_nat ) ) ).
% 2.39/2.72
% 2.39/2.72 % disjointI
% 2.39/2.72 thf(fact_747_disjointI,axiom,
% 2.39/2.72 ! [A: set_nat,B: set_nat] :
% 2.39/2.72 ( ! [X3: nat] :
% 2.39/2.72 ( ( member_nat2 @ X3 @ A )
% 2.39/2.72 => ~ ( member_nat2 @ X3 @ B ) )
% 2.39/2.72 => ( ( inf_inf_set_nat @ A @ B )
% 2.39/2.72 = bot_bot_set_nat ) ) ).
% 2.39/2.72
% 2.39/2.72 % disjointI
% 2.39/2.72 thf(fact_748_disjointI,axiom,
% 2.39/2.72 ! [A: set_int,B: set_int] :
% 2.39/2.72 ( ! [X3: int] :
% 2.39/2.72 ( ( member_int2 @ X3 @ A )
% 2.39/2.72 => ~ ( member_int2 @ X3 @ B ) )
% 2.39/2.72 => ( ( inf_inf_set_int @ A @ B )
% 2.39/2.72 = bot_bot_set_int ) ) ).
% 2.39/2.72
% 2.39/2.72 % disjointI
% 2.39/2.72 thf(fact_749_boolean__algebra__class_Oboolean__algebra_Ocompl__unique,axiom,
% 2.39/2.72 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 2.39/2.72 = bot_bo2099793752762293965at_nat )
% 2.39/2.72 => ( ( ( sup_su6327502436637775413at_nat @ X @ Y )
% 2.39/2.72 = top_to4669805908274784177at_nat )
% 2.39/2.72 => ( ( uminus6524753893492686040at_nat @ X )
% 2.39/2.72 = Y ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra_class.boolean_algebra.compl_unique
% 2.39/2.72 thf(fact_750_boolean__algebra__class_Oboolean__algebra_Ocompl__unique,axiom,
% 2.39/2.72 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 2.39/2.72 ( ( ( inf_in3604695632404883862_int_o @ X @ Y )
% 2.39/2.72 = bot_bo8147686125503663512_int_o )
% 2.39/2.72 => ( ( ( sup_su8463660629351352368_int_o @ X @ Y )
% 2.39/2.72 = top_to1578927101902068148_int_o )
% 2.39/2.72 => ( ( uminus7117520113953359693_int_o @ X )
% 2.39/2.72 = Y ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra_class.boolean_algebra.compl_unique
% 2.39/2.72 thf(fact_751_boolean__algebra__class_Oboolean__algebra_Ocompl__unique,axiom,
% 2.39/2.72 ! [X: set_nat,Y: set_nat] :
% 2.39/2.72 ( ( ( inf_inf_set_nat @ X @ Y )
% 2.39/2.72 = bot_bot_set_nat )
% 2.39/2.72 => ( ( ( sup_sup_set_nat @ X @ Y )
% 2.39/2.72 = top_top_set_nat )
% 2.39/2.72 => ( ( uminus5710092332889474511et_nat @ X )
% 2.39/2.72 = Y ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra_class.boolean_algebra.compl_unique
% 2.39/2.72 thf(fact_752_boolean__algebra__class_Oboolean__algebra_Ocompl__unique,axiom,
% 2.39/2.72 ! [X: set_int,Y: set_int] :
% 2.39/2.72 ( ( ( inf_inf_set_int @ X @ Y )
% 2.39/2.72 = bot_bot_set_int )
% 2.39/2.72 => ( ( ( sup_sup_set_int @ X @ Y )
% 2.39/2.72 = top_top_set_int )
% 2.39/2.72 => ( ( uminus1532241313380277803et_int @ X )
% 2.39/2.72 = Y ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra_class.boolean_algebra.compl_unique
% 2.39/2.72 thf(fact_753_boolean__algebra__class_Oboolean__algebra_Ocompl__unique,axiom,
% 2.39/2.72 ! [X: set_Product_unit,Y: set_Product_unit] :
% 2.39/2.72 ( ( ( inf_in4660618365625256667t_unit @ X @ Y )
% 2.39/2.72 = bot_bo3957492148770167129t_unit )
% 2.39/2.72 => ( ( ( sup_su793286257634532545t_unit @ X @ Y )
% 2.39/2.72 = top_to1996260823553986621t_unit )
% 2.39/2.72 => ( ( uminus5944136376168626660t_unit @ X )
% 2.39/2.72 = Y ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra_class.boolean_algebra.compl_unique
% 2.39/2.72 thf(fact_754_boolean__algebra__class_Oboolean__algebra_Ocompl__unique,axiom,
% 2.39/2.72 ! [X: assn,Y: assn] :
% 2.39/2.72 ( ( ( inf_inf_assn @ X @ Y )
% 2.39/2.72 = bot_bot_assn )
% 2.39/2.72 => ( ( ( sup_sup_assn @ X @ Y )
% 2.39/2.72 = top_top_assn )
% 2.39/2.72 => ( ( uminus_uminus_assn @ X )
% 2.39/2.72 = Y ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra_class.boolean_algebra.compl_unique
% 2.39/2.72 thf(fact_755_properI,axiom,
% 2.39/2.72 ! [P2: produc3658429121746597890et_nat > $o] :
% 2.39/2.72 ( ! [As: set_nat,H3: heap_e7401611519738050253t_unit] :
% 2.39/2.72 ( ( P2 @ ( produc7507926704131184380et_nat @ H3 @ As ) )
% 2.39/2.72 => ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As ) ) )
% 2.39/2.72 => ( ! [As: set_nat,H3: heap_e7401611519738050253t_unit,H4: heap_e7401611519738050253t_unit] :
% 2.39/2.72 ( ( P2 @ ( produc7507926704131184380et_nat @ H3 @ As ) )
% 2.39/2.72 => ( ( relH @ As @ H3 @ H4 )
% 2.39/2.72 => ( ( in_range @ ( produc7507926704131184380et_nat @ H4 @ As ) )
% 2.39/2.72 => ( P2 @ ( produc7507926704131184380et_nat @ H4 @ As ) ) ) ) )
% 2.39/2.72 => ( proper @ P2 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % properI
% 2.39/2.72 thf(fact_756_neg__equal__iff__equal,axiom,
% 2.39/2.72 ! [A: int,B: int] :
% 2.39/2.72 ( ( ( uminus_uminus_int @ A )
% 2.39/2.72 = ( uminus_uminus_int @ B ) )
% 2.39/2.72 = ( A = B ) ) ).
% 2.39/2.72
% 2.39/2.72 % neg_equal_iff_equal
% 2.39/2.72 thf(fact_757_neg__equal__iff__equal,axiom,
% 2.39/2.72 ! [A: rat,B: rat] :
% 2.39/2.72 ( ( ( uminus_uminus_rat @ A )
% 2.39/2.72 = ( uminus_uminus_rat @ B ) )
% 2.39/2.72 = ( A = B ) ) ).
% 2.39/2.72
% 2.39/2.72 % neg_equal_iff_equal
% 2.39/2.72 thf(fact_758_neg__equal__iff__equal,axiom,
% 2.39/2.72 ! [A: code_integer,B: code_integer] :
% 2.39/2.72 ( ( ( uminus1351360451143612070nteger @ A )
% 2.39/2.72 = ( uminus1351360451143612070nteger @ B ) )
% 2.39/2.72 = ( A = B ) ) ).
% 2.39/2.72
% 2.39/2.72 % neg_equal_iff_equal
% 2.39/2.72 thf(fact_759_add_Oinverse__inverse,axiom,
% 2.39/2.72 ! [A: int] :
% 2.39/2.72 ( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
% 2.39/2.72 = A ) ).
% 2.39/2.72
% 2.39/2.72 % add.inverse_inverse
% 2.39/2.72 thf(fact_760_add_Oinverse__inverse,axiom,
% 2.39/2.72 ! [A: rat] :
% 2.39/2.72 ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ A ) )
% 2.39/2.72 = A ) ).
% 2.39/2.72
% 2.39/2.72 % add.inverse_inverse
% 2.39/2.72 thf(fact_761_add_Oinverse__inverse,axiom,
% 2.39/2.72 ! [A: code_integer] :
% 2.39/2.72 ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ A ) )
% 2.39/2.72 = A ) ).
% 2.39/2.72
% 2.39/2.72 % add.inverse_inverse
% 2.39/2.72 thf(fact_762_pure__assn__proper,axiom,
% 2.39/2.72 ! [B: $o] : ( proper @ ( pure_a825153325127701367it_nat @ B ) ) ).
% 2.39/2.72
% 2.39/2.72 % pure_assn_proper
% 2.39/2.72 thf(fact_763_Compl__disjoint,axiom,
% 2.39/2.72 ! [A3: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( inf_in2572325071724192079at_nat @ A3 @ ( uminus6524753893492686040at_nat @ A3 ) )
% 2.39/2.72 = bot_bo2099793752762293965at_nat ) ).
% 2.39/2.72
% 2.39/2.72 % Compl_disjoint
% 2.39/2.72 thf(fact_764_Compl__disjoint,axiom,
% 2.39/2.72 ! [A3: set_nat] :
% 2.39/2.72 ( ( inf_inf_set_nat @ A3 @ ( uminus5710092332889474511et_nat @ A3 ) )
% 2.39/2.72 = bot_bot_set_nat ) ).
% 2.39/2.72
% 2.39/2.72 % Compl_disjoint
% 2.39/2.72 thf(fact_765_Compl__disjoint,axiom,
% 2.39/2.72 ! [A3: set_int] :
% 2.39/2.72 ( ( inf_inf_set_int @ A3 @ ( uminus1532241313380277803et_int @ A3 ) )
% 2.39/2.72 = bot_bot_set_int ) ).
% 2.39/2.72
% 2.39/2.72 % Compl_disjoint
% 2.39/2.72 thf(fact_766_Compl__disjoint2,axiom,
% 2.39/2.72 ! [A3: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ A3 ) @ A3 )
% 2.39/2.72 = bot_bo2099793752762293965at_nat ) ).
% 2.39/2.72
% 2.39/2.72 % Compl_disjoint2
% 2.39/2.72 thf(fact_767_Compl__disjoint2,axiom,
% 2.39/2.72 ! [A3: set_nat] :
% 2.39/2.72 ( ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ A3 ) @ A3 )
% 2.39/2.72 = bot_bot_set_nat ) ).
% 2.39/2.72
% 2.39/2.72 % Compl_disjoint2
% 2.39/2.72 thf(fact_768_Compl__disjoint2,axiom,
% 2.39/2.72 ! [A3: set_int] :
% 2.39/2.72 ( ( inf_inf_set_int @ ( uminus1532241313380277803et_int @ A3 ) @ A3 )
% 2.39/2.72 = bot_bot_set_int ) ).
% 2.39/2.72
% 2.39/2.72 % Compl_disjoint2
% 2.39/2.72 thf(fact_769_mod__not__dist,axiom,
% 2.39/2.72 ! [P2: assn,H2: produc3658429121746597890et_nat] :
% 2.39/2.72 ( ( rep_assn @ ( uminus_uminus_assn @ P2 ) @ H2 )
% 2.39/2.72 = ( ( in_range @ H2 )
% 2.39/2.72 & ~ ( rep_assn @ P2 @ H2 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % mod_not_dist
% 2.39/2.72 thf(fact_770_bool__assn__proper_I1_J,axiom,
% 2.39/2.72 proper @ in_range ).
% 2.39/2.72
% 2.39/2.72 % bool_assn_proper(1)
% 2.39/2.72 thf(fact_771_times__assn__proper,axiom,
% 2.39/2.72 ! [P2: produc3658429121746597890et_nat > $o,Q2: produc3658429121746597890et_nat > $o] :
% 2.39/2.72 ( ( proper @ P2 )
% 2.39/2.72 => ( ( proper @ Q2 )
% 2.39/2.72 => ( proper @ ( times_assn_raw @ P2 @ Q2 ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % times_assn_proper
% 2.39/2.72 thf(fact_772_wand__proper,axiom,
% 2.39/2.72 ! [P2: produc3658429121746597890et_nat > $o,Q2: produc3658429121746597890et_nat > $o] : ( proper @ ( wand_raw @ P2 @ Q2 ) ) ).
% 2.39/2.72
% 2.39/2.72 % wand_proper
% 2.39/2.72 thf(fact_773_one__assn__proper,axiom,
% 2.39/2.72 proper @ one_assn_raw ).
% 2.39/2.72
% 2.39/2.72 % one_assn_proper
% 2.39/2.72 thf(fact_774_inf__compl__bot__left1,axiom,
% 2.39/2.72 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ X ) @ ( inf_in2572325071724192079at_nat @ X @ Y ) )
% 2.39/2.72 = bot_bo2099793752762293965at_nat ) ).
% 2.39/2.72
% 2.39/2.72 % inf_compl_bot_left1
% 2.39/2.72 thf(fact_775_inf__compl__bot__left1,axiom,
% 2.39/2.72 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 2.39/2.72 ( ( inf_in3604695632404883862_int_o @ ( uminus7117520113953359693_int_o @ X ) @ ( inf_in3604695632404883862_int_o @ X @ Y ) )
% 2.39/2.72 = bot_bo8147686125503663512_int_o ) ).
% 2.39/2.72
% 2.39/2.72 % inf_compl_bot_left1
% 2.39/2.72 thf(fact_776_inf__compl__bot__left1,axiom,
% 2.39/2.72 ! [X: set_nat,Y: set_nat] :
% 2.39/2.72 ( ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ ( inf_inf_set_nat @ X @ Y ) )
% 2.39/2.72 = bot_bot_set_nat ) ).
% 2.39/2.72
% 2.39/2.72 % inf_compl_bot_left1
% 2.39/2.72 thf(fact_777_inf__compl__bot__left1,axiom,
% 2.39/2.72 ! [X: set_int,Y: set_int] :
% 2.39/2.72 ( ( inf_inf_set_int @ ( uminus1532241313380277803et_int @ X ) @ ( inf_inf_set_int @ X @ Y ) )
% 2.39/2.72 = bot_bot_set_int ) ).
% 2.39/2.72
% 2.39/2.72 % inf_compl_bot_left1
% 2.39/2.72 thf(fact_778_inf__compl__bot__left1,axiom,
% 2.39/2.72 ! [X: assn,Y: assn] :
% 2.39/2.72 ( ( inf_inf_assn @ ( uminus_uminus_assn @ X ) @ ( inf_inf_assn @ X @ Y ) )
% 2.39/2.72 = bot_bot_assn ) ).
% 2.39/2.72
% 2.39/2.72 % inf_compl_bot_left1
% 2.39/2.72 thf(fact_779_inf__compl__bot__left2,axiom,
% 2.39/2.72 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( inf_in2572325071724192079at_nat @ X @ ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ X ) @ Y ) )
% 2.39/2.72 = bot_bo2099793752762293965at_nat ) ).
% 2.39/2.72
% 2.39/2.72 % inf_compl_bot_left2
% 2.39/2.72 thf(fact_780_inf__compl__bot__left2,axiom,
% 2.39/2.72 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 2.39/2.72 ( ( inf_in3604695632404883862_int_o @ X @ ( inf_in3604695632404883862_int_o @ ( uminus7117520113953359693_int_o @ X ) @ Y ) )
% 2.39/2.72 = bot_bo8147686125503663512_int_o ) ).
% 2.39/2.72
% 2.39/2.72 % inf_compl_bot_left2
% 2.39/2.72 thf(fact_781_inf__compl__bot__left2,axiom,
% 2.39/2.72 ! [X: set_nat,Y: set_nat] :
% 2.39/2.72 ( ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ Y ) )
% 2.39/2.72 = bot_bot_set_nat ) ).
% 2.39/2.72
% 2.39/2.72 % inf_compl_bot_left2
% 2.39/2.72 thf(fact_782_inf__compl__bot__left2,axiom,
% 2.39/2.72 ! [X: set_int,Y: set_int] :
% 2.39/2.72 ( ( inf_inf_set_int @ X @ ( inf_inf_set_int @ ( uminus1532241313380277803et_int @ X ) @ Y ) )
% 2.39/2.72 = bot_bot_set_int ) ).
% 2.39/2.72
% 2.39/2.72 % inf_compl_bot_left2
% 2.39/2.72 thf(fact_783_inf__compl__bot__left2,axiom,
% 2.39/2.72 ! [X: assn,Y: assn] :
% 2.39/2.72 ( ( inf_inf_assn @ X @ ( inf_inf_assn @ ( uminus_uminus_assn @ X ) @ Y ) )
% 2.39/2.72 = bot_bot_assn ) ).
% 2.39/2.72
% 2.39/2.72 % inf_compl_bot_left2
% 2.39/2.72 thf(fact_784_inf__compl__bot__right,axiom,
% 2.39/2.72 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( inf_in2572325071724192079at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ ( uminus6524753893492686040at_nat @ X ) ) )
% 2.39/2.72 = bot_bo2099793752762293965at_nat ) ).
% 2.39/2.72
% 2.39/2.72 % inf_compl_bot_right
% 2.39/2.72 thf(fact_785_inf__compl__bot__right,axiom,
% 2.39/2.72 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 2.39/2.72 ( ( inf_in3604695632404883862_int_o @ X @ ( inf_in3604695632404883862_int_o @ Y @ ( uminus7117520113953359693_int_o @ X ) ) )
% 2.39/2.72 = bot_bo8147686125503663512_int_o ) ).
% 2.39/2.72
% 2.39/2.72 % inf_compl_bot_right
% 2.39/2.72 thf(fact_786_inf__compl__bot__right,axiom,
% 2.39/2.72 ! [X: set_nat,Y: set_nat] :
% 2.39/2.72 ( ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ Y @ ( uminus5710092332889474511et_nat @ X ) ) )
% 2.39/2.72 = bot_bot_set_nat ) ).
% 2.39/2.72
% 2.39/2.72 % inf_compl_bot_right
% 2.39/2.72 thf(fact_787_inf__compl__bot__right,axiom,
% 2.39/2.72 ! [X: set_int,Y: set_int] :
% 2.39/2.72 ( ( inf_inf_set_int @ X @ ( inf_inf_set_int @ Y @ ( uminus1532241313380277803et_int @ X ) ) )
% 2.39/2.72 = bot_bot_set_int ) ).
% 2.39/2.72
% 2.39/2.72 % inf_compl_bot_right
% 2.39/2.72 thf(fact_788_inf__compl__bot__right,axiom,
% 2.39/2.72 ! [X: assn,Y: assn] :
% 2.39/2.72 ( ( inf_inf_assn @ X @ ( inf_inf_assn @ Y @ ( uminus_uminus_assn @ X ) ) )
% 2.39/2.72 = bot_bot_assn ) ).
% 2.39/2.72
% 2.39/2.72 % inf_compl_bot_right
% 2.39/2.72 thf(fact_789_boolean__algebra_Oconj__cancel__left,axiom,
% 2.39/2.72 ! [X: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ X ) @ X )
% 2.39/2.72 = bot_bo2099793752762293965at_nat ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.conj_cancel_left
% 2.39/2.72 thf(fact_790_boolean__algebra_Oconj__cancel__left,axiom,
% 2.39/2.72 ! [X: product_prod_int_int > $o] :
% 2.39/2.72 ( ( inf_in3604695632404883862_int_o @ ( uminus7117520113953359693_int_o @ X ) @ X )
% 2.39/2.72 = bot_bo8147686125503663512_int_o ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.conj_cancel_left
% 2.39/2.72 thf(fact_791_boolean__algebra_Oconj__cancel__left,axiom,
% 2.39/2.72 ! [X: set_nat] :
% 2.39/2.72 ( ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ X )
% 2.39/2.72 = bot_bot_set_nat ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.conj_cancel_left
% 2.39/2.72 thf(fact_792_boolean__algebra_Oconj__cancel__left,axiom,
% 2.39/2.72 ! [X: set_int] :
% 2.39/2.72 ( ( inf_inf_set_int @ ( uminus1532241313380277803et_int @ X ) @ X )
% 2.39/2.72 = bot_bot_set_int ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.conj_cancel_left
% 2.39/2.72 thf(fact_793_boolean__algebra_Oconj__cancel__left,axiom,
% 2.39/2.72 ! [X: assn] :
% 2.39/2.72 ( ( inf_inf_assn @ ( uminus_uminus_assn @ X ) @ X )
% 2.39/2.72 = bot_bot_assn ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.conj_cancel_left
% 2.39/2.72 thf(fact_794_boolean__algebra_Oconj__cancel__right,axiom,
% 2.39/2.72 ! [X: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( inf_in2572325071724192079at_nat @ X @ ( uminus6524753893492686040at_nat @ X ) )
% 2.39/2.72 = bot_bo2099793752762293965at_nat ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.conj_cancel_right
% 2.39/2.72 thf(fact_795_boolean__algebra_Oconj__cancel__right,axiom,
% 2.39/2.72 ! [X: product_prod_int_int > $o] :
% 2.39/2.72 ( ( inf_in3604695632404883862_int_o @ X @ ( uminus7117520113953359693_int_o @ X ) )
% 2.39/2.72 = bot_bo8147686125503663512_int_o ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.conj_cancel_right
% 2.39/2.72 thf(fact_796_boolean__algebra_Oconj__cancel__right,axiom,
% 2.39/2.72 ! [X: set_nat] :
% 2.39/2.72 ( ( inf_inf_set_nat @ X @ ( uminus5710092332889474511et_nat @ X ) )
% 2.39/2.72 = bot_bot_set_nat ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.conj_cancel_right
% 2.39/2.72 thf(fact_797_boolean__algebra_Oconj__cancel__right,axiom,
% 2.39/2.72 ! [X: set_int] :
% 2.39/2.72 ( ( inf_inf_set_int @ X @ ( uminus1532241313380277803et_int @ X ) )
% 2.39/2.72 = bot_bot_set_int ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.conj_cancel_right
% 2.39/2.72 thf(fact_798_boolean__algebra_Oconj__cancel__right,axiom,
% 2.39/2.72 ! [X: assn] :
% 2.39/2.72 ( ( inf_inf_assn @ X @ ( uminus_uminus_assn @ X ) )
% 2.39/2.72 = bot_bot_assn ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.conj_cancel_right
% 2.39/2.72 thf(fact_799_boolean__algebra_Ode__Morgan__conj,axiom,
% 2.39/2.72 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( uminus6524753893492686040at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) )
% 2.39/2.72 = ( sup_su6327502436637775413at_nat @ ( uminus6524753893492686040at_nat @ X ) @ ( uminus6524753893492686040at_nat @ Y ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.de_Morgan_conj
% 2.39/2.72 thf(fact_800_boolean__algebra_Ode__Morgan__conj,axiom,
% 2.39/2.72 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 2.39/2.72 ( ( uminus7117520113953359693_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) )
% 2.39/2.72 = ( sup_su8463660629351352368_int_o @ ( uminus7117520113953359693_int_o @ X ) @ ( uminus7117520113953359693_int_o @ Y ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.de_Morgan_conj
% 2.39/2.72 thf(fact_801_boolean__algebra_Ode__Morgan__conj,axiom,
% 2.39/2.72 ! [X: set_nat,Y: set_nat] :
% 2.39/2.72 ( ( uminus5710092332889474511et_nat @ ( inf_inf_set_nat @ X @ Y ) )
% 2.39/2.72 = ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ ( uminus5710092332889474511et_nat @ Y ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.de_Morgan_conj
% 2.39/2.72 thf(fact_802_boolean__algebra_Ode__Morgan__conj,axiom,
% 2.39/2.72 ! [X: assn,Y: assn] :
% 2.39/2.72 ( ( uminus_uminus_assn @ ( inf_inf_assn @ X @ Y ) )
% 2.39/2.72 = ( sup_sup_assn @ ( uminus_uminus_assn @ X ) @ ( uminus_uminus_assn @ Y ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.de_Morgan_conj
% 2.39/2.72 thf(fact_803_boolean__algebra_Ode__Morgan__disj,axiom,
% 2.39/2.72 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( uminus6524753893492686040at_nat @ ( sup_su6327502436637775413at_nat @ X @ Y ) )
% 2.39/2.72 = ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ X ) @ ( uminus6524753893492686040at_nat @ Y ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.de_Morgan_disj
% 2.39/2.72 thf(fact_804_boolean__algebra_Ode__Morgan__disj,axiom,
% 2.39/2.72 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 2.39/2.72 ( ( uminus7117520113953359693_int_o @ ( sup_su8463660629351352368_int_o @ X @ Y ) )
% 2.39/2.72 = ( inf_in3604695632404883862_int_o @ ( uminus7117520113953359693_int_o @ X ) @ ( uminus7117520113953359693_int_o @ Y ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.de_Morgan_disj
% 2.39/2.72 thf(fact_805_boolean__algebra_Ode__Morgan__disj,axiom,
% 2.39/2.72 ! [X: set_nat,Y: set_nat] :
% 2.39/2.72 ( ( uminus5710092332889474511et_nat @ ( sup_sup_set_nat @ X @ Y ) )
% 2.39/2.72 = ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ ( uminus5710092332889474511et_nat @ Y ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.de_Morgan_disj
% 2.39/2.72 thf(fact_806_boolean__algebra_Ode__Morgan__disj,axiom,
% 2.39/2.72 ! [X: assn,Y: assn] :
% 2.39/2.72 ( ( uminus_uminus_assn @ ( sup_sup_assn @ X @ Y ) )
% 2.39/2.72 = ( inf_inf_assn @ ( uminus_uminus_assn @ X ) @ ( uminus_uminus_assn @ Y ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.de_Morgan_disj
% 2.39/2.72 thf(fact_807_assn__aci_I8_J,axiom,
% 2.39/2.72 ! [X: assn,Y: assn] :
% 2.39/2.72 ( ( sup_sup_assn @ X @ ( sup_sup_assn @ X @ Y ) )
% 2.39/2.72 = ( sup_sup_assn @ X @ Y ) ) ).
% 2.39/2.72
% 2.39/2.72 % assn_aci(8)
% 2.39/2.72 thf(fact_808_assn__aci_I7_J,axiom,
% 2.39/2.72 ! [X: assn,Y: assn,Z: assn] :
% 2.39/2.72 ( ( sup_sup_assn @ X @ ( sup_sup_assn @ Y @ Z ) )
% 2.39/2.72 = ( sup_sup_assn @ Y @ ( sup_sup_assn @ X @ Z ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % assn_aci(7)
% 2.39/2.72 thf(fact_809_assn__aci_I5_J,axiom,
% 2.39/2.72 ( sup_sup_assn
% 2.39/2.72 = ( ^ [X2: assn,Y2: assn] : ( sup_sup_assn @ Y2 @ X2 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % assn_aci(5)
% 2.39/2.72 thf(fact_810_norm__assertion__simps_I32_J,axiom,
% 2.39/2.72 ! [X: assn] :
% 2.39/2.72 ( ( sup_sup_assn @ X @ X )
% 2.39/2.72 = X ) ).
% 2.39/2.72
% 2.39/2.72 % norm_assertion_simps(32)
% 2.39/2.72 thf(fact_811_norm__assertion__simps_I15_J,axiom,
% 2.39/2.72 ! [X: assn,Y: assn,Z: assn] :
% 2.39/2.72 ( ( sup_sup_assn @ ( sup_sup_assn @ X @ Y ) @ Z )
% 2.39/2.72 = ( sup_sup_assn @ X @ ( sup_sup_assn @ Y @ Z ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % norm_assertion_simps(15)
% 2.39/2.72 thf(fact_812_minus__equation__iff,axiom,
% 2.39/2.72 ! [A: int,B: int] :
% 2.39/2.72 ( ( ( uminus_uminus_int @ A )
% 2.39/2.72 = B )
% 2.39/2.72 = ( ( uminus_uminus_int @ B )
% 2.39/2.72 = A ) ) ).
% 2.39/2.72
% 2.39/2.72 % minus_equation_iff
% 2.39/2.72 thf(fact_813_minus__equation__iff,axiom,
% 2.39/2.72 ! [A: rat,B: rat] :
% 2.39/2.72 ( ( ( uminus_uminus_rat @ A )
% 2.39/2.72 = B )
% 2.39/2.72 = ( ( uminus_uminus_rat @ B )
% 2.39/2.72 = A ) ) ).
% 2.39/2.72
% 2.39/2.72 % minus_equation_iff
% 2.39/2.72 thf(fact_814_minus__equation__iff,axiom,
% 2.39/2.72 ! [A: code_integer,B: code_integer] :
% 2.39/2.72 ( ( ( uminus1351360451143612070nteger @ A )
% 2.39/2.72 = B )
% 2.39/2.72 = ( ( uminus1351360451143612070nteger @ B )
% 2.39/2.72 = A ) ) ).
% 2.39/2.72
% 2.39/2.72 % minus_equation_iff
% 2.39/2.72 thf(fact_815_equation__minus__iff,axiom,
% 2.39/2.72 ! [A: int,B: int] :
% 2.39/2.72 ( ( A
% 2.39/2.72 = ( uminus_uminus_int @ B ) )
% 2.39/2.72 = ( B
% 2.39/2.72 = ( uminus_uminus_int @ A ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % equation_minus_iff
% 2.39/2.72 thf(fact_816_equation__minus__iff,axiom,
% 2.39/2.72 ! [A: rat,B: rat] :
% 2.39/2.72 ( ( A
% 2.39/2.72 = ( uminus_uminus_rat @ B ) )
% 2.39/2.72 = ( B
% 2.39/2.72 = ( uminus_uminus_rat @ A ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % equation_minus_iff
% 2.39/2.72 thf(fact_817_equation__minus__iff,axiom,
% 2.39/2.72 ! [A: code_integer,B: code_integer] :
% 2.39/2.72 ( ( A
% 2.39/2.72 = ( uminus1351360451143612070nteger @ B ) )
% 2.39/2.72 = ( B
% 2.39/2.72 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % equation_minus_iff
% 2.39/2.72 thf(fact_818_Rep__assn__induct,axiom,
% 2.39/2.72 ! [Y: produc3658429121746597890et_nat > $o,P2: ( produc3658429121746597890et_nat > $o ) > $o] :
% 2.39/2.72 ( ( member6576561426505652726_nat_o @ Y @ ( collec939566748876313656_nat_o @ proper ) )
% 2.39/2.72 => ( ! [X3: assn] : ( P2 @ ( rep_assn @ X3 ) )
% 2.39/2.72 => ( P2 @ Y ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % Rep_assn_induct
% 2.39/2.72 thf(fact_819_Rep__assn__cases,axiom,
% 2.39/2.72 ! [Y: produc3658429121746597890et_nat > $o] :
% 2.39/2.72 ( ( member6576561426505652726_nat_o @ Y @ ( collec939566748876313656_nat_o @ proper ) )
% 2.39/2.72 => ~ ! [X3: assn] :
% 2.39/2.72 ( Y
% 2.39/2.72 != ( rep_assn @ X3 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % Rep_assn_cases
% 2.39/2.72 thf(fact_820_Rep__assn,axiom,
% 2.39/2.72 ! [X: assn] : ( member6576561426505652726_nat_o @ ( rep_assn @ X ) @ ( collec939566748876313656_nat_o @ proper ) ) ).
% 2.39/2.72
% 2.39/2.72 % Rep_assn
% 2.39/2.72 thf(fact_821_inf__cancel__left1,axiom,
% 2.39/2.72 ! [X: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ X @ A ) @ ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ X ) @ B ) )
% 2.39/2.72 = bot_bo2099793752762293965at_nat ) ).
% 2.39/2.72
% 2.39/2.72 % inf_cancel_left1
% 2.39/2.72 thf(fact_822_inf__cancel__left1,axiom,
% 2.39/2.72 ! [X: product_prod_int_int > $o,A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 2.39/2.72 ( ( inf_in3604695632404883862_int_o @ ( inf_in3604695632404883862_int_o @ X @ A ) @ ( inf_in3604695632404883862_int_o @ ( uminus7117520113953359693_int_o @ X ) @ B ) )
% 2.39/2.72 = bot_bo8147686125503663512_int_o ) ).
% 2.39/2.72
% 2.39/2.72 % inf_cancel_left1
% 2.39/2.72 thf(fact_823_inf__cancel__left1,axiom,
% 2.39/2.72 ! [X: set_nat,A: set_nat,B: set_nat] :
% 2.39/2.72 ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ X @ A ) @ ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ B ) )
% 2.39/2.72 = bot_bot_set_nat ) ).
% 2.39/2.72
% 2.39/2.72 % inf_cancel_left1
% 2.39/2.72 thf(fact_824_inf__cancel__left1,axiom,
% 2.39/2.72 ! [X: set_int,A: set_int,B: set_int] :
% 2.39/2.72 ( ( inf_inf_set_int @ ( inf_inf_set_int @ X @ A ) @ ( inf_inf_set_int @ ( uminus1532241313380277803et_int @ X ) @ B ) )
% 2.39/2.72 = bot_bot_set_int ) ).
% 2.39/2.72
% 2.39/2.72 % inf_cancel_left1
% 2.39/2.72 thf(fact_825_inf__cancel__left1,axiom,
% 2.39/2.72 ! [X: assn,A: assn,B: assn] :
% 2.39/2.72 ( ( inf_inf_assn @ ( inf_inf_assn @ X @ A ) @ ( inf_inf_assn @ ( uminus_uminus_assn @ X ) @ B ) )
% 2.39/2.72 = bot_bot_assn ) ).
% 2.39/2.72
% 2.39/2.72 % inf_cancel_left1
% 2.39/2.72 thf(fact_826_inf__cancel__left2,axiom,
% 2.39/2.72 ! [X: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ X ) @ A ) @ ( inf_in2572325071724192079at_nat @ X @ B ) )
% 2.39/2.72 = bot_bo2099793752762293965at_nat ) ).
% 2.39/2.72
% 2.39/2.72 % inf_cancel_left2
% 2.39/2.72 thf(fact_827_inf__cancel__left2,axiom,
% 2.39/2.72 ! [X: product_prod_int_int > $o,A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 2.39/2.72 ( ( inf_in3604695632404883862_int_o @ ( inf_in3604695632404883862_int_o @ ( uminus7117520113953359693_int_o @ X ) @ A ) @ ( inf_in3604695632404883862_int_o @ X @ B ) )
% 2.39/2.72 = bot_bo8147686125503663512_int_o ) ).
% 2.39/2.72
% 2.39/2.72 % inf_cancel_left2
% 2.39/2.72 thf(fact_828_inf__cancel__left2,axiom,
% 2.39/2.72 ! [X: set_nat,A: set_nat,B: set_nat] :
% 2.39/2.72 ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ A ) @ ( inf_inf_set_nat @ X @ B ) )
% 2.39/2.72 = bot_bot_set_nat ) ).
% 2.39/2.72
% 2.39/2.72 % inf_cancel_left2
% 2.39/2.72 thf(fact_829_inf__cancel__left2,axiom,
% 2.39/2.72 ! [X: set_int,A: set_int,B: set_int] :
% 2.39/2.72 ( ( inf_inf_set_int @ ( inf_inf_set_int @ ( uminus1532241313380277803et_int @ X ) @ A ) @ ( inf_inf_set_int @ X @ B ) )
% 2.39/2.72 = bot_bot_set_int ) ).
% 2.39/2.72
% 2.39/2.72 % inf_cancel_left2
% 2.39/2.72 thf(fact_830_inf__cancel__left2,axiom,
% 2.39/2.72 ! [X: assn,A: assn,B: assn] :
% 2.39/2.72 ( ( inf_inf_assn @ ( inf_inf_assn @ ( uminus_uminus_assn @ X ) @ A ) @ ( inf_inf_assn @ X @ B ) )
% 2.39/2.72 = bot_bot_assn ) ).
% 2.39/2.72
% 2.39/2.72 % inf_cancel_left2
% 2.39/2.72 thf(fact_831_Compl__Un,axiom,
% 2.39/2.72 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( uminus6524753893492686040at_nat @ ( sup_su6327502436637775413at_nat @ A3 @ B3 ) )
% 2.39/2.72 = ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ A3 ) @ ( uminus6524753893492686040at_nat @ B3 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % Compl_Un
% 2.39/2.72 thf(fact_832_Compl__Un,axiom,
% 2.39/2.72 ! [A3: set_nat,B3: set_nat] :
% 2.39/2.72 ( ( uminus5710092332889474511et_nat @ ( sup_sup_set_nat @ A3 @ B3 ) )
% 2.39/2.72 = ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ A3 ) @ ( uminus5710092332889474511et_nat @ B3 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % Compl_Un
% 2.39/2.72 thf(fact_833_Compl__Int,axiom,
% 2.39/2.72 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.72 ( ( uminus6524753893492686040at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) )
% 2.39/2.72 = ( sup_su6327502436637775413at_nat @ ( uminus6524753893492686040at_nat @ A3 ) @ ( uminus6524753893492686040at_nat @ B3 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % Compl_Int
% 2.39/2.72 thf(fact_834_Compl__Int,axiom,
% 2.39/2.72 ! [A3: set_nat,B3: set_nat] :
% 2.39/2.72 ( ( uminus5710092332889474511et_nat @ ( inf_inf_set_nat @ A3 @ B3 ) )
% 2.39/2.72 = ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ A3 ) @ ( uminus5710092332889474511et_nat @ B3 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % Compl_Int
% 2.39/2.72 thf(fact_835_properD1,axiom,
% 2.39/2.72 ! [P2: produc3658429121746597890et_nat > $o,H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 2.39/2.72 ( ( proper @ P2 )
% 2.39/2.72 => ( ( P2 @ ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 2.39/2.72 => ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As2 ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % properD1
% 2.39/2.72 thf(fact_836_proper__iff,axiom,
% 2.39/2.72 ! [P2: produc3658429121746597890et_nat > $o,As2: set_nat,H2: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit] :
% 2.39/2.72 ( ( proper @ P2 )
% 2.39/2.72 => ( ( relH @ As2 @ H2 @ H5 )
% 2.39/2.72 => ( ( in_range @ ( produc7507926704131184380et_nat @ H5 @ As2 ) )
% 2.39/2.72 => ( ( P2 @ ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 2.39/2.72 = ( P2 @ ( produc7507926704131184380et_nat @ H5 @ As2 ) ) ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % proper_iff
% 2.39/2.72 thf(fact_837_proper__def,axiom,
% 2.39/2.72 ( proper
% 2.39/2.72 = ( ^ [P: produc3658429121746597890et_nat > $o] :
% 2.39/2.72 ! [H: heap_e7401611519738050253t_unit,H7: heap_e7401611519738050253t_unit,As7: set_nat] :
% 2.39/2.72 ( ( ( P @ ( produc7507926704131184380et_nat @ H @ As7 ) )
% 2.39/2.72 => ( in_range @ ( produc7507926704131184380et_nat @ H @ As7 ) ) )
% 2.39/2.72 & ( ( ( P @ ( produc7507926704131184380et_nat @ H @ As7 ) )
% 2.39/2.72 & ( relH @ As7 @ H @ H7 )
% 2.39/2.72 & ( in_range @ ( produc7507926704131184380et_nat @ H7 @ As7 ) ) )
% 2.39/2.72 => ( P @ ( produc7507926704131184380et_nat @ H7 @ As7 ) ) ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % proper_def
% 2.39/2.72 thf(fact_838_properD2,axiom,
% 2.39/2.72 ! [P2: produc3658429121746597890et_nat > $o,H2: heap_e7401611519738050253t_unit,As2: set_nat,H5: heap_e7401611519738050253t_unit] :
% 2.39/2.72 ( ( proper @ P2 )
% 2.39/2.72 => ( ( P2 @ ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 2.39/2.72 => ( ( relH @ As2 @ H2 @ H5 )
% 2.39/2.72 => ( ( in_range @ ( produc7507926704131184380et_nat @ H5 @ As2 ) )
% 2.39/2.72 => ( P2 @ ( produc7507926704131184380et_nat @ H5 @ As2 ) ) ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % properD2
% 2.39/2.72 thf(fact_839_mult__minus1,axiom,
% 2.39/2.72 ! [Z: int] :
% 2.39/2.72 ( ( times_times_int @ ( uminus_uminus_int @ one_one_int ) @ Z )
% 2.39/2.72 = ( uminus_uminus_int @ Z ) ) ).
% 2.39/2.72
% 2.39/2.72 % mult_minus1
% 2.39/2.72 thf(fact_840_mult__minus1,axiom,
% 2.39/2.72 ! [Z: rat] :
% 2.39/2.72 ( ( times_times_rat @ ( uminus_uminus_rat @ one_one_rat ) @ Z )
% 2.39/2.72 = ( uminus_uminus_rat @ Z ) ) ).
% 2.39/2.72
% 2.39/2.72 % mult_minus1
% 2.39/2.72 thf(fact_841_mult__minus1,axiom,
% 2.39/2.72 ! [Z: code_integer] :
% 2.39/2.72 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ Z )
% 2.39/2.72 = ( uminus1351360451143612070nteger @ Z ) ) ).
% 2.39/2.72
% 2.39/2.72 % mult_minus1
% 2.39/2.72 thf(fact_842_mult__minus1__right,axiom,
% 2.39/2.72 ! [Z: int] :
% 2.39/2.72 ( ( times_times_int @ Z @ ( uminus_uminus_int @ one_one_int ) )
% 2.39/2.72 = ( uminus_uminus_int @ Z ) ) ).
% 2.39/2.72
% 2.39/2.72 % mult_minus1_right
% 2.39/2.72 thf(fact_843_mult__minus1__right,axiom,
% 2.39/2.72 ! [Z: rat] :
% 2.39/2.72 ( ( times_times_rat @ Z @ ( uminus_uminus_rat @ one_one_rat ) )
% 2.39/2.72 = ( uminus_uminus_rat @ Z ) ) ).
% 2.39/2.72
% 2.39/2.72 % mult_minus1_right
% 2.39/2.72 thf(fact_844_mult__minus1__right,axiom,
% 2.39/2.72 ! [Z: code_integer] :
% 2.39/2.72 ( ( times_3573771949741848930nteger @ Z @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 2.39/2.72 = ( uminus1351360451143612070nteger @ Z ) ) ).
% 2.39/2.72
% 2.39/2.72 % mult_minus1_right
% 2.39/2.72 thf(fact_845_mult__minus__left,axiom,
% 2.39/2.72 ! [A: int,B: int] :
% 2.39/2.72 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 2.39/2.72 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % mult_minus_left
% 2.39/2.72 thf(fact_846_mult__minus__left,axiom,
% 2.39/2.72 ! [A: rat,B: rat] :
% 2.39/2.72 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 2.39/2.72 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % mult_minus_left
% 2.39/2.72 thf(fact_847_mult__minus__left,axiom,
% 2.39/2.72 ! [A: code_integer,B: code_integer] :
% 2.39/2.72 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 2.39/2.72 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % mult_minus_left
% 2.39/2.72 thf(fact_848_minus__mult__minus,axiom,
% 2.39/2.72 ! [A: int,B: int] :
% 2.39/2.72 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 2.39/2.72 = ( times_times_int @ A @ B ) ) ).
% 2.39/2.72
% 2.39/2.72 % minus_mult_minus
% 2.39/2.72 thf(fact_849_minus__mult__minus,axiom,
% 2.39/2.72 ! [A: rat,B: rat] :
% 2.39/2.72 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 2.39/2.72 = ( times_times_rat @ A @ B ) ) ).
% 2.39/2.72
% 2.39/2.72 % minus_mult_minus
% 2.39/2.72 thf(fact_850_minus__mult__minus,axiom,
% 2.39/2.72 ! [A: code_integer,B: code_integer] :
% 2.39/2.72 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 2.39/2.72 = ( times_3573771949741848930nteger @ A @ B ) ) ).
% 2.39/2.72
% 2.39/2.72 % minus_mult_minus
% 2.39/2.72 thf(fact_851_mult__minus__right,axiom,
% 2.39/2.72 ! [A: int,B: int] :
% 2.39/2.72 ( ( times_times_int @ A @ ( uminus_uminus_int @ B ) )
% 2.39/2.72 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % mult_minus_right
% 2.39/2.72 thf(fact_852_mult__minus__right,axiom,
% 2.39/2.72 ! [A: rat,B: rat] :
% 2.39/2.72 ( ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) )
% 2.39/2.72 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % mult_minus_right
% 2.39/2.72 thf(fact_853_mult__minus__right,axiom,
% 2.39/2.72 ! [A: code_integer,B: code_integer] :
% 2.39/2.72 ( ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 2.39/2.72 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % mult_minus_right
% 2.39/2.72 thf(fact_854_square__eq__1__iff,axiom,
% 2.39/2.72 ! [X: int] :
% 2.39/2.72 ( ( ( times_times_int @ X @ X )
% 2.39/2.72 = one_one_int )
% 2.39/2.72 = ( ( X = one_one_int )
% 2.39/2.72 | ( X
% 2.39/2.72 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % square_eq_1_iff
% 2.39/2.72 thf(fact_855_square__eq__1__iff,axiom,
% 2.39/2.72 ! [X: rat] :
% 2.39/2.72 ( ( ( times_times_rat @ X @ X )
% 2.39/2.72 = one_one_rat )
% 2.39/2.72 = ( ( X = one_one_rat )
% 2.39/2.72 | ( X
% 2.39/2.72 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % square_eq_1_iff
% 2.39/2.72 thf(fact_856_square__eq__1__iff,axiom,
% 2.39/2.72 ! [X: code_integer] :
% 2.39/2.72 ( ( ( times_3573771949741848930nteger @ X @ X )
% 2.39/2.72 = one_one_Code_integer )
% 2.39/2.72 = ( ( X = one_one_Code_integer )
% 2.39/2.72 | ( X
% 2.39/2.72 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % square_eq_1_iff
% 2.39/2.72 thf(fact_857_one__neq__neg__one,axiom,
% 2.39/2.72 ( one_one_int
% 2.39/2.72 != ( uminus_uminus_int @ one_one_int ) ) ).
% 2.39/2.72
% 2.39/2.72 % one_neq_neg_one
% 2.39/2.72 thf(fact_858_one__neq__neg__one,axiom,
% 2.39/2.72 ( one_one_rat
% 2.39/2.72 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 2.39/2.72
% 2.39/2.72 % one_neq_neg_one
% 2.39/2.72 thf(fact_859_one__neq__neg__one,axiom,
% 2.39/2.72 ( one_one_Code_integer
% 2.39/2.72 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 2.39/2.72
% 2.39/2.72 % one_neq_neg_one
% 2.39/2.72 thf(fact_860_square__eq__iff,axiom,
% 2.39/2.72 ! [A: int,B: int] :
% 2.39/2.72 ( ( ( times_times_int @ A @ A )
% 2.39/2.72 = ( times_times_int @ B @ B ) )
% 2.39/2.72 = ( ( A = B )
% 2.39/2.72 | ( A
% 2.39/2.72 = ( uminus_uminus_int @ B ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % square_eq_iff
% 2.39/2.72 thf(fact_861_square__eq__iff,axiom,
% 2.39/2.72 ! [A: rat,B: rat] :
% 2.39/2.72 ( ( ( times_times_rat @ A @ A )
% 2.39/2.72 = ( times_times_rat @ B @ B ) )
% 2.39/2.72 = ( ( A = B )
% 2.39/2.72 | ( A
% 2.39/2.72 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % square_eq_iff
% 2.39/2.72 thf(fact_862_square__eq__iff,axiom,
% 2.39/2.72 ! [A: code_integer,B: code_integer] :
% 2.39/2.72 ( ( ( times_3573771949741848930nteger @ A @ A )
% 2.39/2.72 = ( times_3573771949741848930nteger @ B @ B ) )
% 2.39/2.72 = ( ( A = B )
% 2.39/2.72 | ( A
% 2.39/2.72 = ( uminus1351360451143612070nteger @ B ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % square_eq_iff
% 2.39/2.72 thf(fact_863_minus__mult__commute,axiom,
% 2.39/2.72 ! [A: int,B: int] :
% 2.39/2.72 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 2.39/2.72 = ( times_times_int @ A @ ( uminus_uminus_int @ B ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % minus_mult_commute
% 2.39/2.72 thf(fact_864_minus__mult__commute,axiom,
% 2.39/2.72 ! [A: rat,B: rat] :
% 2.39/2.72 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 2.39/2.72 = ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % minus_mult_commute
% 2.39/2.72 thf(fact_865_minus__mult__commute,axiom,
% 2.39/2.72 ! [A: code_integer,B: code_integer] :
% 2.39/2.72 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 2.39/2.72 = ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % minus_mult_commute
% 2.39/2.72 thf(fact_866_boolean__algebra_Oabstract__boolean__algebra__axioms,axiom,
% 2.39/2.72 boolea949959532490082519at_nat @ inf_in2572325071724192079at_nat @ sup_su6327502436637775413at_nat @ uminus6524753893492686040at_nat @ bot_bo2099793752762293965at_nat @ top_to4669805908274784177at_nat ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.abstract_boolean_algebra_axioms
% 2.39/2.72 thf(fact_867_boolean__algebra_Oabstract__boolean__algebra__axioms,axiom,
% 2.39/2.72 boolea1849928419393854478_int_o @ inf_in3604695632404883862_int_o @ sup_su8463660629351352368_int_o @ uminus7117520113953359693_int_o @ bot_bo8147686125503663512_int_o @ top_to1578927101902068148_int_o ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.abstract_boolean_algebra_axioms
% 2.39/2.72 thf(fact_868_boolean__algebra_Oabstract__boolean__algebra__axioms,axiom,
% 2.39/2.72 boolea778851993438741648et_nat @ inf_inf_set_nat @ sup_sup_set_nat @ uminus5710092332889474511et_nat @ bot_bot_set_nat @ top_top_set_nat ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.abstract_boolean_algebra_axioms
% 2.39/2.72 thf(fact_869_boolean__algebra_Oabstract__boolean__algebra__axioms,axiom,
% 2.39/2.72 boolea5824373010784320748et_int @ inf_inf_set_int @ sup_sup_set_int @ uminus1532241313380277803et_int @ bot_bot_set_int @ top_top_set_int ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.abstract_boolean_algebra_axioms
% 2.39/2.72 thf(fact_870_boolean__algebra_Oabstract__boolean__algebra__axioms,axiom,
% 2.39/2.72 boolea3191171876098928227t_unit @ inf_in4660618365625256667t_unit @ sup_su793286257634532545t_unit @ uminus5944136376168626660t_unit @ bot_bo3957492148770167129t_unit @ top_to1996260823553986621t_unit ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.abstract_boolean_algebra_axioms
% 2.39/2.72 thf(fact_871_boolean__algebra_Oabstract__boolean__algebra__axioms,axiom,
% 2.39/2.72 boolea5875918072483028530a_assn @ inf_inf_assn @ sup_sup_assn @ uminus_uminus_assn @ bot_bot_assn @ top_top_assn ).
% 2.39/2.72
% 2.39/2.72 % boolean_algebra.abstract_boolean_algebra_axioms
% 2.39/2.72 thf(fact_872_wand__assn__def,axiom,
% 2.39/2.72 ( wand_assn
% 2.39/2.72 = ( ^ [P: assn,Q: assn] : ( abs_assn @ ( wand_raw @ ( rep_assn @ P ) @ ( rep_assn @ Q ) ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % wand_assn_def
% 2.39/2.72 thf(fact_873_Rep__assn__inverse,axiom,
% 2.39/2.72 ! [X: assn] :
% 2.39/2.72 ( ( abs_assn @ ( rep_assn @ X ) )
% 2.39/2.72 = X ) ).
% 2.39/2.72
% 2.39/2.72 % Rep_assn_inverse
% 2.39/2.72 thf(fact_874_Abs__assn__eqI_I2_J,axiom,
% 2.39/2.72 ! [P2: produc3658429121746597890et_nat > $o,Pr: assn] :
% 2.39/2.72 ( ! [H3: produc3658429121746597890et_nat] :
% 2.39/2.72 ( ( P2 @ H3 )
% 2.39/2.72 = ( rep_assn @ Pr @ H3 ) )
% 2.39/2.72 => ( Pr
% 2.39/2.72 = ( abs_assn @ P2 ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % Abs_assn_eqI(2)
% 2.39/2.72 thf(fact_875_Abs__assn__eqI_I1_J,axiom,
% 2.39/2.72 ! [P2: produc3658429121746597890et_nat > $o,Pr: assn] :
% 2.39/2.72 ( ! [H3: produc3658429121746597890et_nat] :
% 2.39/2.72 ( ( P2 @ H3 )
% 2.39/2.72 = ( rep_assn @ Pr @ H3 ) )
% 2.39/2.72 => ( ( abs_assn @ P2 )
% 2.39/2.72 = Pr ) ) ).
% 2.39/2.72
% 2.39/2.72 % Abs_assn_eqI(1)
% 2.39/2.72 thf(fact_876_pure__assn__def,axiom,
% 2.39/2.72 ( pure_assn
% 2.39/2.72 = ( ^ [B2: $o] : ( abs_assn @ ( pure_a825153325127701367it_nat @ B2 ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % pure_assn_def
% 2.39/2.72 thf(fact_877_Abs__assn__cases,axiom,
% 2.39/2.72 ! [X: assn] :
% 2.39/2.72 ~ ! [Y3: produc3658429121746597890et_nat > $o] :
% 2.39/2.72 ( ( X
% 2.39/2.72 = ( abs_assn @ Y3 ) )
% 2.39/2.72 => ~ ( member6576561426505652726_nat_o @ Y3 @ ( collec939566748876313656_nat_o @ proper ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % Abs_assn_cases
% 2.39/2.72 thf(fact_878_Abs__assn__induct,axiom,
% 2.39/2.72 ! [P2: assn > $o,X: assn] :
% 2.39/2.72 ( ! [Y3: produc3658429121746597890et_nat > $o] :
% 2.39/2.72 ( ( member6576561426505652726_nat_o @ Y3 @ ( collec939566748876313656_nat_o @ proper ) )
% 2.39/2.72 => ( P2 @ ( abs_assn @ Y3 ) ) )
% 2.39/2.72 => ( P2 @ X ) ) ).
% 2.39/2.72
% 2.39/2.72 % Abs_assn_induct
% 2.39/2.72 thf(fact_879_Abs__assn__inject,axiom,
% 2.39/2.72 ! [X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat > $o] :
% 2.39/2.72 ( ( member6576561426505652726_nat_o @ X @ ( collec939566748876313656_nat_o @ proper ) )
% 2.39/2.72 => ( ( member6576561426505652726_nat_o @ Y @ ( collec939566748876313656_nat_o @ proper ) )
% 2.39/2.72 => ( ( ( abs_assn @ X )
% 2.39/2.72 = ( abs_assn @ Y ) )
% 2.39/2.72 = ( X = Y ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % Abs_assn_inject
% 2.39/2.72 thf(fact_880_Abs__assn__inverse,axiom,
% 2.39/2.72 ! [Y: produc3658429121746597890et_nat > $o] :
% 2.39/2.72 ( ( member6576561426505652726_nat_o @ Y @ ( collec939566748876313656_nat_o @ proper ) )
% 2.39/2.72 => ( ( rep_assn @ ( abs_assn @ Y ) )
% 2.39/2.72 = Y ) ) ).
% 2.39/2.72
% 2.39/2.72 % Abs_assn_inverse
% 2.39/2.72 thf(fact_881_top__assn__def,axiom,
% 2.39/2.72 ( top_top_assn
% 2.39/2.72 = ( abs_assn @ in_range ) ) ).
% 2.39/2.72
% 2.39/2.72 % top_assn_def
% 2.39/2.72 thf(fact_882_one__assn__def,axiom,
% 2.39/2.72 ( one_one_assn
% 2.39/2.72 = ( abs_assn @ one_assn_raw ) ) ).
% 2.39/2.72
% 2.39/2.72 % one_assn_def
% 2.39/2.72 thf(fact_883_times__assn__def,axiom,
% 2.39/2.72 ( times_times_assn
% 2.39/2.72 = ( ^ [P: assn,Q: assn] : ( abs_assn @ ( times_assn_raw @ ( rep_assn @ P ) @ ( rep_assn @ Q ) ) ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % times_assn_def
% 2.39/2.72 thf(fact_884_dbl__inc__simps_I4_J,axiom,
% 2.39/2.72 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ one_one_int ) )
% 2.39/2.72 = ( uminus_uminus_int @ one_one_int ) ) ).
% 2.39/2.72
% 2.39/2.72 % dbl_inc_simps(4)
% 2.39/2.72 thf(fact_885_dbl__inc__simps_I4_J,axiom,
% 2.39/2.72 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 2.39/2.72 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 2.39/2.72
% 2.39/2.72 % dbl_inc_simps(4)
% 2.39/2.72 thf(fact_886_dbl__inc__simps_I4_J,axiom,
% 2.39/2.72 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 2.39/2.72 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 2.39/2.72
% 2.39/2.72 % dbl_inc_simps(4)
% 2.39/2.72 thf(fact_887_list__collect__set__simps_I1_J,axiom,
% 2.39/2.72 ! [F2: produc6575502325842934193n_assn > set_nat] :
% 2.39/2.72 ( ( list_c6061723043370948915sn_nat @ F2 @ nil_Pr5671120429643327159n_assn )
% 2.39/2.72 = bot_bot_set_nat ) ).
% 2.39/2.72
% 2.39/2.72 % list_collect_set_simps(1)
% 2.39/2.72 thf(fact_888_list__collect__set__simps_I1_J,axiom,
% 2.39/2.72 ! [F2: int > set_nat] :
% 2.39/2.72 ( ( list_c3451693981498911948nt_nat @ F2 @ nil_int )
% 2.39/2.72 = bot_bot_set_nat ) ).
% 2.39/2.72
% 2.39/2.72 % list_collect_set_simps(1)
% 2.39/2.72 thf(fact_889_list__collect__set__simps_I1_J,axiom,
% 2.39/2.72 ! [F2: nat > set_nat] :
% 2.39/2.72 ( ( list_c2452340269597857392at_nat @ F2 @ nil_nat )
% 2.39/2.72 = bot_bot_set_nat ) ).
% 2.39/2.72
% 2.39/2.72 % list_collect_set_simps(1)
% 2.39/2.72 thf(fact_890_list__collect__set__simps_I1_J,axiom,
% 2.39/2.72 ! [F2: produc6575502325842934193n_assn > set_int] :
% 2.39/2.72 ( ( list_c6059232572861898639sn_int @ F2 @ nil_Pr5671120429643327159n_assn )
% 2.39/2.72 = bot_bot_set_int ) ).
% 2.39/2.72
% 2.39/2.72 % list_collect_set_simps(1)
% 2.39/2.72 thf(fact_891_list__collect__set__simps_I1_J,axiom,
% 2.39/2.72 ! [F2: int > set_int] :
% 2.39/2.72 ( ( list_c3449203510989861672nt_int @ F2 @ nil_int )
% 2.39/2.72 = bot_bot_set_int ) ).
% 2.39/2.72
% 2.39/2.72 % list_collect_set_simps(1)
% 2.39/2.72 thf(fact_892_list__collect__set__simps_I1_J,axiom,
% 2.39/2.72 ! [F2: nat > set_int] :
% 2.39/2.72 ( ( list_c2449849799088807116at_int @ F2 @ nil_nat )
% 2.39/2.72 = bot_bot_set_int ) ).
% 2.39/2.72
% 2.39/2.72 % list_collect_set_simps(1)
% 2.39/2.72 thf(fact_893_mod__pure,axiom,
% 2.39/2.72 ! [B: $o,H2: produc3658429121746597890et_nat] :
% 2.39/2.72 ( ( rep_assn @ ( pure_assn @ B ) @ H2 )
% 2.39/2.72 = ( ( ( produc8586169260539613262et_nat @ H2 )
% 2.39/2.72 = bot_bot_set_nat )
% 2.39/2.72 & B ) ) ).
% 2.39/2.72
% 2.39/2.72 % mod_pure
% 2.39/2.72 thf(fact_894_type__definition__assn,axiom,
% 2.39/2.72 type_d3909072315231072503_nat_o @ rep_assn @ abs_assn @ ( collec939566748876313656_nat_o @ proper ) ).
% 2.39/2.72
% 2.39/2.72 % type_definition_assn
% 2.39/2.72 thf(fact_895_dbl__dec__simps_I3_J,axiom,
% 2.39/2.72 ( ( neg_nu7757733837767384882nteger @ one_one_Code_integer )
% 2.39/2.72 = one_one_Code_integer ) ).
% 2.39/2.72
% 2.39/2.72 % dbl_dec_simps(3)
% 2.39/2.72 thf(fact_896_dbl__dec__simps_I3_J,axiom,
% 2.39/2.72 ( ( neg_nu3179335615603231917ec_rat @ one_one_rat )
% 2.39/2.72 = one_one_rat ) ).
% 2.39/2.72
% 2.39/2.72 % dbl_dec_simps(3)
% 2.39/2.72 thf(fact_897_dbl__dec__simps_I3_J,axiom,
% 2.39/2.72 ( ( neg_nu3811975205180677377ec_int @ one_one_int )
% 2.39/2.72 = one_one_int ) ).
% 2.39/2.72
% 2.39/2.72 % dbl_dec_simps(3)
% 2.39/2.72 thf(fact_898_sorted__list__of__set_Osorted__key__list__of__set__empty,axiom,
% 2.39/2.72 ( ( linord2612477271533052124et_int @ bot_bot_set_int )
% 2.39/2.72 = nil_int ) ).
% 2.39/2.72
% 2.39/2.72 % sorted_list_of_set.sorted_key_list_of_set_empty
% 2.39/2.72 thf(fact_899_sorted__list__of__set_Osorted__key__list__of__set__empty,axiom,
% 2.39/2.72 ( ( linord2614967742042102400et_nat @ bot_bot_set_nat )
% 2.39/2.72 = nil_nat ) ).
% 2.39/2.72
% 2.39/2.72 % sorted_list_of_set.sorted_key_list_of_set_empty
% 2.39/2.72 thf(fact_900_UNIV__coset,axiom,
% 2.39/2.72 ( top_to5722533637347664993n_assn
% 2.39/2.72 = ( coset_703488708621576356n_assn @ nil_Pr5671120429643327159n_assn ) ) ).
% 2.39/2.72
% 2.39/2.72 % UNIV_coset
% 2.39/2.72 thf(fact_901_UNIV__coset,axiom,
% 2.39/2.72 ( top_top_set_int
% 2.39/2.72 = ( coset_int @ nil_int ) ) ).
% 2.39/2.72
% 2.39/2.72 % UNIV_coset
% 2.39/2.72 thf(fact_902_UNIV__coset,axiom,
% 2.39/2.72 ( top_top_set_nat
% 2.39/2.72 = ( coset_nat @ nil_nat ) ) ).
% 2.39/2.72
% 2.39/2.72 % UNIV_coset
% 2.39/2.72 thf(fact_903_UNIV__coset,axiom,
% 2.39/2.72 ( top_to1996260823553986621t_unit
% 2.39/2.72 = ( coset_Product_unit @ nil_Product_unit ) ) ).
% 2.39/2.72
% 2.39/2.72 % UNIV_coset
% 2.39/2.72 thf(fact_904_mod__emp,axiom,
% 2.39/2.72 ! [H2: produc3658429121746597890et_nat] :
% 2.39/2.72 ( ( rep_assn @ one_one_assn @ H2 )
% 2.39/2.72 = ( ( produc8586169260539613262et_nat @ H2 )
% 2.39/2.72 = bot_bot_set_nat ) ) ).
% 2.39/2.72
% 2.39/2.72 % mod_emp
% 2.39/2.72 thf(fact_905_dbl__dec__simps_I2_J,axiom,
% 2.39/2.72 ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 2.39/2.72 = ( uminus_uminus_int @ one_one_int ) ) ).
% 2.39/2.72
% 2.39/2.72 % dbl_dec_simps(2)
% 2.39/2.72 thf(fact_906_dbl__dec__simps_I2_J,axiom,
% 2.39/2.72 ( ( neg_nu3179335615603231917ec_rat @ zero_zero_rat )
% 2.39/2.72 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 2.39/2.72
% 2.39/2.72 % dbl_dec_simps(2)
% 2.39/2.72 thf(fact_907_dbl__dec__simps_I2_J,axiom,
% 2.39/2.72 ( ( neg_nu7757733837767384882nteger @ zero_z3403309356797280102nteger )
% 2.39/2.72 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 2.39/2.72
% 2.39/2.72 % dbl_dec_simps(2)
% 2.39/2.72 thf(fact_908_sorted__list__of__set_Osorted__key__list__of__set__eq__Nil__iff,axiom,
% 2.39/2.72 ! [A3: set_int] :
% 2.39/2.72 ( ( finite_finite_int @ A3 )
% 2.39/2.72 => ( ( ( linord2612477271533052124et_int @ A3 )
% 2.39/2.72 = nil_int )
% 2.39/2.72 = ( A3 = bot_bot_set_int ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % sorted_list_of_set.sorted_key_list_of_set_eq_Nil_iff
% 2.39/2.72 thf(fact_909_sorted__list__of__set_Osorted__key__list__of__set__eq__Nil__iff,axiom,
% 2.39/2.72 ! [A3: set_nat] :
% 2.39/2.72 ( ( finite_finite_nat @ A3 )
% 2.39/2.72 => ( ( ( linord2614967742042102400et_nat @ A3 )
% 2.39/2.72 = nil_nat )
% 2.39/2.72 = ( A3 = bot_bot_set_nat ) ) ) ).
% 2.39/2.72
% 2.39/2.72 % sorted_list_of_set.sorted_key_list_of_set_eq_Nil_iff
% 2.39/2.72 thf(fact_910_list__collect__set__map__simps_I1_J,axiom,
% 2.39/2.72 ! [F2: nat > set_nat,X: nat > nat] :
% 2.39/2.72 ( ( list_c2452340269597857392at_nat @ F2 @ ( map_nat_nat @ X @ nil_nat ) )
% 2.39/2.72 = bot_bot_set_nat ) ).
% 2.39/2.72
% 2.39/2.72 % list_collect_set_map_simps(1)
% 2.39/2.72 thf(fact_911_list__collect__set__map__simps_I1_J,axiom,
% 2.39/2.72 ! [F2: assn > set_nat,X: produc6575502325842934193n_assn > assn] :
% 2.39/2.72 ( ( list_c1844713377658005960sn_nat @ F2 @ ( map_Pr8991440229025900053n_assn @ X @ nil_Pr5671120429643327159n_assn ) )
% 2.39/2.72 = bot_bot_set_nat ) ).
% 2.39/2.72
% 2.39/2.72 % list_collect_set_map_simps(1)
% 2.39/2.72 thf(fact_912_list__collect__set__map__simps_I1_J,axiom,
% 2.39/2.72 ! [F2: nat > set_int,X: nat > nat] :
% 2.39/2.72 ( ( list_c2449849799088807116at_int @ F2 @ ( map_nat_nat @ X @ nil_nat ) )
% 2.39/2.72 = bot_bot_set_int ) ).
% 2.39/2.72
% 2.39/2.72 % list_collect_set_map_simps(1)
% 2.39/2.72 thf(fact_913_list__collect__set__map__simps_I1_J,axiom,
% 2.39/2.72 ! [F2: assn > set_int,X: produc6575502325842934193n_assn > assn] :
% 2.39/2.72 ( ( list_c1842222907148955684sn_int @ F2 @ ( map_Pr8991440229025900053n_assn @ X @ nil_Pr5671120429643327159n_assn ) )
% 2.39/2.72 = bot_bot_set_int ) ).
% 2.39/2.72
% 2.39/2.72 % list_collect_set_map_simps(1)
% 2.39/2.72 thf(fact_914_nths__empty,axiom,
% 2.39/2.72 ! [Xs: list_P8527749157015355191n_assn] :
% 2.39/2.72 ( ( nths_P5537322223065504949n_assn @ Xs @ bot_bot_set_nat )
% 2.39/2.72 = nil_Pr5671120429643327159n_assn ) ).
% 2.39/2.72
% 2.39/2.72 % nths_empty
% 2.39/2.72 thf(fact_915_nths__empty,axiom,
% 2.39/2.72 ! [Xs: list_int] :
% 2.39/2.72 ( ( nths_int @ Xs @ bot_bot_set_nat )
% 2.39/2.72 = nil_int ) ).
% 2.39/2.72
% 2.39/2.72 % nths_empty
% 2.39/2.72 thf(fact_916_nths__empty,axiom,
% 2.39/2.72 ! [Xs: list_nat] :
% 2.39/2.72 ( ( nths_nat @ Xs @ bot_bot_set_nat )
% 2.39/2.72 = nil_nat ) ).
% 2.39/2.72
% 2.39/2.72 % nths_empty
% 2.39/2.72 thf(fact_917_dbl__inc__simps_I2_J,axiom,
% 2.39/2.72 ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 2.39/2.72 = one_one_int ) ).
% 2.39/2.72
% 2.39/2.72 % dbl_inc_simps(2)
% 2.39/2.72 thf(fact_918_dbl__inc__simps_I2_J,axiom,
% 2.39/2.73 ( ( neg_nu5219082963157363817nc_rat @ zero_zero_rat )
% 2.39/2.73 = one_one_rat ) ).
% 2.39/2.73
% 2.39/2.73 % dbl_inc_simps(2)
% 2.39/2.73 thf(fact_919_dbl__inc__simps_I2_J,axiom,
% 2.39/2.73 ( ( neg_nu5831290666863070958nteger @ zero_z3403309356797280102nteger )
% 2.39/2.73 = one_one_Code_integer ) ).
% 2.39/2.73
% 2.39/2.73 % dbl_inc_simps(2)
% 2.39/2.73 thf(fact_920_disjoint__eq__subset__Compl,axiom,
% 2.39/2.73 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.73 ( ( ( inf_in2572325071724192079at_nat @ A3 @ B3 )
% 2.39/2.73 = bot_bo2099793752762293965at_nat )
% 2.39/2.73 = ( ord_le3146513528884898305at_nat @ A3 @ ( uminus6524753893492686040at_nat @ B3 ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % disjoint_eq_subset_Compl
% 2.39/2.73 thf(fact_921_disjoint__eq__subset__Compl,axiom,
% 2.39/2.73 ! [A3: set_int,B3: set_int] :
% 2.39/2.73 ( ( ( inf_inf_set_int @ A3 @ B3 )
% 2.39/2.73 = bot_bot_set_int )
% 2.39/2.73 = ( ord_less_eq_set_int @ A3 @ ( uminus1532241313380277803et_int @ B3 ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % disjoint_eq_subset_Compl
% 2.39/2.73 thf(fact_922_disjoint__eq__subset__Compl,axiom,
% 2.39/2.73 ! [A3: set_nat,B3: set_nat] :
% 2.39/2.73 ( ( ( inf_inf_set_nat @ A3 @ B3 )
% 2.39/2.73 = bot_bot_set_nat )
% 2.39/2.73 = ( ord_less_eq_set_nat @ A3 @ ( uminus5710092332889474511et_nat @ B3 ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % disjoint_eq_subset_Compl
% 2.39/2.73 thf(fact_923_in__measures_I1_J,axiom,
% 2.39/2.73 ! [X: nat,Y: nat] :
% 2.39/2.73 ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( measures_nat @ nil_nat_nat ) ) ).
% 2.39/2.73
% 2.39/2.73 % in_measures(1)
% 2.39/2.73 thf(fact_924_in__measures_I1_J,axiom,
% 2.39/2.73 ! [X: int,Y: int] :
% 2.39/2.73 ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( measures_int @ nil_int_nat ) ) ).
% 2.39/2.73
% 2.39/2.73 % in_measures(1)
% 2.39/2.73 thf(fact_925_sup__neg__inf,axiom,
% 2.39/2.73 ! [P5: set_Pr1261947904930325089at_nat,Q4: set_Pr1261947904930325089at_nat,R2: set_Pr1261947904930325089at_nat] :
% 2.39/2.73 ( ( ord_le3146513528884898305at_nat @ P5 @ ( sup_su6327502436637775413at_nat @ Q4 @ R2 ) )
% 2.39/2.73 = ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ P5 @ ( uminus6524753893492686040at_nat @ Q4 ) ) @ R2 ) ) ).
% 2.39/2.73
% 2.39/2.73 % sup_neg_inf
% 2.39/2.73 thf(fact_926_sup__neg__inf,axiom,
% 2.39/2.73 ! [P5: product_prod_int_int > $o,Q4: product_prod_int_int > $o,R2: product_prod_int_int > $o] :
% 2.39/2.73 ( ( ord_le8369615600986905444_int_o @ P5 @ ( sup_su8463660629351352368_int_o @ Q4 @ R2 ) )
% 2.39/2.73 = ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ P5 @ ( uminus7117520113953359693_int_o @ Q4 ) ) @ R2 ) ) ).
% 2.39/2.73
% 2.39/2.73 % sup_neg_inf
% 2.39/2.73 thf(fact_927_sup__neg__inf,axiom,
% 2.39/2.73 ! [P5: assn,Q4: assn,R2: assn] :
% 2.39/2.73 ( ( ord_less_eq_assn @ P5 @ ( sup_sup_assn @ Q4 @ R2 ) )
% 2.39/2.73 = ( ord_less_eq_assn @ ( inf_inf_assn @ P5 @ ( uminus_uminus_assn @ Q4 ) ) @ R2 ) ) ).
% 2.39/2.73
% 2.39/2.73 % sup_neg_inf
% 2.39/2.73 thf(fact_928_sup__neg__inf,axiom,
% 2.39/2.73 ! [P5: set_nat,Q4: set_nat,R2: set_nat] :
% 2.39/2.73 ( ( ord_less_eq_set_nat @ P5 @ ( sup_sup_set_nat @ Q4 @ R2 ) )
% 2.39/2.73 = ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ P5 @ ( uminus5710092332889474511et_nat @ Q4 ) ) @ R2 ) ) ).
% 2.39/2.73
% 2.39/2.73 % sup_neg_inf
% 2.39/2.73 thf(fact_929_shunt2,axiom,
% 2.39/2.73 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 2.39/2.73 ( ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ ( uminus6524753893492686040at_nat @ Y ) ) @ Z )
% 2.39/2.73 = ( ord_le3146513528884898305at_nat @ X @ ( sup_su6327502436637775413at_nat @ Y @ Z ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % shunt2
% 2.39/2.73 thf(fact_930_shunt2,axiom,
% 2.39/2.73 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 2.39/2.73 ( ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ X @ ( uminus7117520113953359693_int_o @ Y ) ) @ Z )
% 2.39/2.73 = ( ord_le8369615600986905444_int_o @ X @ ( sup_su8463660629351352368_int_o @ Y @ Z ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % shunt2
% 2.39/2.73 thf(fact_931_shunt2,axiom,
% 2.39/2.73 ! [X: assn,Y: assn,Z: assn] :
% 2.39/2.73 ( ( ord_less_eq_assn @ ( inf_inf_assn @ X @ ( uminus_uminus_assn @ Y ) ) @ Z )
% 2.39/2.73 = ( ord_less_eq_assn @ X @ ( sup_sup_assn @ Y @ Z ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % shunt2
% 2.39/2.73 thf(fact_932_shunt2,axiom,
% 2.39/2.73 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 2.39/2.73 ( ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ ( uminus5710092332889474511et_nat @ Y ) ) @ Z )
% 2.39/2.73 = ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % shunt2
% 2.39/2.73 thf(fact_933_shunt1,axiom,
% 2.39/2.73 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 2.39/2.73 ( ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ Z )
% 2.39/2.73 = ( ord_le3146513528884898305at_nat @ X @ ( sup_su6327502436637775413at_nat @ ( uminus6524753893492686040at_nat @ Y ) @ Z ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % shunt1
% 2.39/2.73 thf(fact_934_shunt1,axiom,
% 2.39/2.73 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 2.39/2.73 ( ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ Z )
% 2.39/2.73 = ( ord_le8369615600986905444_int_o @ X @ ( sup_su8463660629351352368_int_o @ ( uminus7117520113953359693_int_o @ Y ) @ Z ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % shunt1
% 2.39/2.73 thf(fact_935_shunt1,axiom,
% 2.39/2.73 ! [X: assn,Y: assn,Z: assn] :
% 2.39/2.73 ( ( ord_less_eq_assn @ ( inf_inf_assn @ X @ Y ) @ Z )
% 2.39/2.73 = ( ord_less_eq_assn @ X @ ( sup_sup_assn @ ( uminus_uminus_assn @ Y ) @ Z ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % shunt1
% 2.39/2.73 thf(fact_936_shunt1,axiom,
% 2.39/2.73 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 2.39/2.73 ( ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ Z )
% 2.39/2.73 = ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ Y ) @ Z ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % shunt1
% 2.39/2.73 thf(fact_937_relH__def,axiom,
% 2.39/2.73 ( relH
% 2.39/2.73 = ( ^ [As7: set_nat,H: heap_e7401611519738050253t_unit,H7: heap_e7401611519738050253t_unit] :
% 2.39/2.73 ( ( in_range @ ( produc7507926704131184380et_nat @ H @ As7 ) )
% 2.39/2.73 & ( in_range @ ( produc7507926704131184380et_nat @ H7 @ As7 ) )
% 2.39/2.73 & ! [T2: typerep,X2: nat] :
% 2.39/2.73 ( ( member_nat2 @ X2 @ As7 )
% 2.39/2.73 => ( ( ( refs_Product_unit @ H @ T2 @ X2 )
% 2.39/2.73 = ( refs_Product_unit @ H7 @ T2 @ X2 ) )
% 2.39/2.73 & ( ( arrays_Product_unit @ H @ T2 @ X2 )
% 2.39/2.73 = ( arrays_Product_unit @ H7 @ T2 @ X2 ) ) ) ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % relH_def
% 2.39/2.73 thf(fact_938_le__zero__eq,axiom,
% 2.39/2.73 ! [N: nat] :
% 2.39/2.73 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 2.39/2.73 = ( N = zero_zero_nat ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_zero_eq
% 2.39/2.73 thf(fact_939_mult__cancel__right,axiom,
% 2.39/2.73 ! [A: rat,C: rat,B: rat] :
% 2.39/2.73 ( ( ( times_times_rat @ A @ C )
% 2.39/2.73 = ( times_times_rat @ B @ C ) )
% 2.39/2.73 = ( ( C = zero_zero_rat )
% 2.39/2.73 | ( A = B ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_cancel_right
% 2.39/2.73 thf(fact_940_mult__cancel__right,axiom,
% 2.39/2.73 ! [A: nat,C: nat,B: nat] :
% 2.39/2.73 ( ( ( times_times_nat @ A @ C )
% 2.39/2.73 = ( times_times_nat @ B @ C ) )
% 2.39/2.73 = ( ( C = zero_zero_nat )
% 2.39/2.73 | ( A = B ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_cancel_right
% 2.39/2.73 thf(fact_941_mult__cancel__right,axiom,
% 2.39/2.73 ! [A: int,C: int,B: int] :
% 2.39/2.73 ( ( ( times_times_int @ A @ C )
% 2.39/2.73 = ( times_times_int @ B @ C ) )
% 2.39/2.73 = ( ( C = zero_zero_int )
% 2.39/2.73 | ( A = B ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_cancel_right
% 2.39/2.73 thf(fact_942_mult__cancel__right,axiom,
% 2.39/2.73 ! [A: code_integer,C: code_integer,B: code_integer] :
% 2.39/2.73 ( ( ( times_3573771949741848930nteger @ A @ C )
% 2.39/2.73 = ( times_3573771949741848930nteger @ B @ C ) )
% 2.39/2.73 = ( ( C = zero_z3403309356797280102nteger )
% 2.39/2.73 | ( A = B ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_cancel_right
% 2.39/2.73 thf(fact_943_mult__cancel__right,axiom,
% 2.39/2.73 ! [A: code_natural,C: code_natural,B: code_natural] :
% 2.39/2.73 ( ( ( times_2397367101498566445atural @ A @ C )
% 2.39/2.73 = ( times_2397367101498566445atural @ B @ C ) )
% 2.39/2.73 = ( ( C = zero_z2226904508553997617atural )
% 2.39/2.73 | ( A = B ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_cancel_right
% 2.39/2.73 thf(fact_944_mult__cancel__left,axiom,
% 2.39/2.73 ! [C: rat,A: rat,B: rat] :
% 2.39/2.73 ( ( ( times_times_rat @ C @ A )
% 2.39/2.73 = ( times_times_rat @ C @ B ) )
% 2.39/2.73 = ( ( C = zero_zero_rat )
% 2.39/2.73 | ( A = B ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_cancel_left
% 2.39/2.73 thf(fact_945_mult__cancel__left,axiom,
% 2.39/2.73 ! [C: nat,A: nat,B: nat] :
% 2.39/2.73 ( ( ( times_times_nat @ C @ A )
% 2.39/2.73 = ( times_times_nat @ C @ B ) )
% 2.39/2.73 = ( ( C = zero_zero_nat )
% 2.39/2.73 | ( A = B ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_cancel_left
% 2.39/2.73 thf(fact_946_mult__cancel__left,axiom,
% 2.39/2.73 ! [C: int,A: int,B: int] :
% 2.39/2.73 ( ( ( times_times_int @ C @ A )
% 2.39/2.73 = ( times_times_int @ C @ B ) )
% 2.39/2.73 = ( ( C = zero_zero_int )
% 2.39/2.73 | ( A = B ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_cancel_left
% 2.39/2.73 thf(fact_947_mult__cancel__left,axiom,
% 2.39/2.73 ! [C: code_integer,A: code_integer,B: code_integer] :
% 2.39/2.73 ( ( ( times_3573771949741848930nteger @ C @ A )
% 2.39/2.73 = ( times_3573771949741848930nteger @ C @ B ) )
% 2.39/2.73 = ( ( C = zero_z3403309356797280102nteger )
% 2.39/2.73 | ( A = B ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_cancel_left
% 2.39/2.73 thf(fact_948_mult__cancel__left,axiom,
% 2.39/2.73 ! [C: code_natural,A: code_natural,B: code_natural] :
% 2.39/2.73 ( ( ( times_2397367101498566445atural @ C @ A )
% 2.39/2.73 = ( times_2397367101498566445atural @ C @ B ) )
% 2.39/2.73 = ( ( C = zero_z2226904508553997617atural )
% 2.39/2.73 | ( A = B ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_cancel_left
% 2.39/2.73 thf(fact_949_mult__eq__0__iff,axiom,
% 2.39/2.73 ! [A: rat,B: rat] :
% 2.39/2.73 ( ( ( times_times_rat @ A @ B )
% 2.39/2.73 = zero_zero_rat )
% 2.39/2.73 = ( ( A = zero_zero_rat )
% 2.39/2.73 | ( B = zero_zero_rat ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_eq_0_iff
% 2.39/2.73 thf(fact_950_mult__eq__0__iff,axiom,
% 2.39/2.73 ! [A: nat,B: nat] :
% 2.39/2.73 ( ( ( times_times_nat @ A @ B )
% 2.39/2.73 = zero_zero_nat )
% 2.39/2.73 = ( ( A = zero_zero_nat )
% 2.39/2.73 | ( B = zero_zero_nat ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_eq_0_iff
% 2.39/2.73 thf(fact_951_mult__eq__0__iff,axiom,
% 2.39/2.73 ! [A: int,B: int] :
% 2.39/2.73 ( ( ( times_times_int @ A @ B )
% 2.39/2.73 = zero_zero_int )
% 2.39/2.73 = ( ( A = zero_zero_int )
% 2.39/2.73 | ( B = zero_zero_int ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_eq_0_iff
% 2.39/2.73 thf(fact_952_mult__eq__0__iff,axiom,
% 2.39/2.73 ! [A: code_integer,B: code_integer] :
% 2.39/2.73 ( ( ( times_3573771949741848930nteger @ A @ B )
% 2.39/2.73 = zero_z3403309356797280102nteger )
% 2.39/2.73 = ( ( A = zero_z3403309356797280102nteger )
% 2.39/2.73 | ( B = zero_z3403309356797280102nteger ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_eq_0_iff
% 2.39/2.73 thf(fact_953_mult__eq__0__iff,axiom,
% 2.39/2.73 ! [A: code_natural,B: code_natural] :
% 2.39/2.73 ( ( ( times_2397367101498566445atural @ A @ B )
% 2.39/2.73 = zero_z2226904508553997617atural )
% 2.39/2.73 = ( ( A = zero_z2226904508553997617atural )
% 2.39/2.73 | ( B = zero_z2226904508553997617atural ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_eq_0_iff
% 2.39/2.73 thf(fact_954_mult__zero__right,axiom,
% 2.39/2.73 ! [A: rat] :
% 2.39/2.73 ( ( times_times_rat @ A @ zero_zero_rat )
% 2.39/2.73 = zero_zero_rat ) ).
% 2.39/2.73
% 2.39/2.73 % mult_zero_right
% 2.39/2.73 thf(fact_955_mult__zero__right,axiom,
% 2.39/2.73 ! [A: nat] :
% 2.39/2.73 ( ( times_times_nat @ A @ zero_zero_nat )
% 2.39/2.73 = zero_zero_nat ) ).
% 2.39/2.73
% 2.39/2.73 % mult_zero_right
% 2.39/2.73 thf(fact_956_mult__zero__right,axiom,
% 2.39/2.73 ! [A: int] :
% 2.39/2.73 ( ( times_times_int @ A @ zero_zero_int )
% 2.39/2.73 = zero_zero_int ) ).
% 2.39/2.73
% 2.39/2.73 % mult_zero_right
% 2.39/2.73 thf(fact_957_mult__zero__right,axiom,
% 2.39/2.73 ! [A: code_integer] :
% 2.39/2.73 ( ( times_3573771949741848930nteger @ A @ zero_z3403309356797280102nteger )
% 2.39/2.73 = zero_z3403309356797280102nteger ) ).
% 2.39/2.73
% 2.39/2.73 % mult_zero_right
% 2.39/2.73 thf(fact_958_mult__zero__right,axiom,
% 2.39/2.73 ! [A: code_natural] :
% 2.39/2.73 ( ( times_2397367101498566445atural @ A @ zero_z2226904508553997617atural )
% 2.39/2.73 = zero_z2226904508553997617atural ) ).
% 2.39/2.73
% 2.39/2.73 % mult_zero_right
% 2.39/2.73 thf(fact_959_mult__zero__left,axiom,
% 2.39/2.73 ! [A: rat] :
% 2.39/2.73 ( ( times_times_rat @ zero_zero_rat @ A )
% 2.39/2.73 = zero_zero_rat ) ).
% 2.39/2.73
% 2.39/2.73 % mult_zero_left
% 2.39/2.73 thf(fact_960_mult__zero__left,axiom,
% 2.39/2.73 ! [A: nat] :
% 2.39/2.73 ( ( times_times_nat @ zero_zero_nat @ A )
% 2.39/2.73 = zero_zero_nat ) ).
% 2.39/2.73
% 2.39/2.73 % mult_zero_left
% 2.39/2.73 thf(fact_961_mult__zero__left,axiom,
% 2.39/2.73 ! [A: int] :
% 2.39/2.73 ( ( times_times_int @ zero_zero_int @ A )
% 2.39/2.73 = zero_zero_int ) ).
% 2.39/2.73
% 2.39/2.73 % mult_zero_left
% 2.39/2.73 thf(fact_962_mult__zero__left,axiom,
% 2.39/2.73 ! [A: code_integer] :
% 2.39/2.73 ( ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.73 = zero_z3403309356797280102nteger ) ).
% 2.39/2.73
% 2.39/2.73 % mult_zero_left
% 2.39/2.73 thf(fact_963_mult__zero__left,axiom,
% 2.39/2.73 ! [A: code_natural] :
% 2.39/2.73 ( ( times_2397367101498566445atural @ zero_z2226904508553997617atural @ A )
% 2.39/2.73 = zero_z2226904508553997617atural ) ).
% 2.39/2.73
% 2.39/2.73 % mult_zero_left
% 2.39/2.73 thf(fact_964_neg__le__iff__le,axiom,
% 2.39/2.73 ! [B: code_integer,A: code_integer] :
% 2.39/2.73 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 2.39/2.73 = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 2.39/2.73
% 2.39/2.73 % neg_le_iff_le
% 2.39/2.73 thf(fact_965_neg__le__iff__le,axiom,
% 2.39/2.73 ! [B: rat,A: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 2.39/2.73 = ( ord_less_eq_rat @ A @ B ) ) ).
% 2.39/2.73
% 2.39/2.73 % neg_le_iff_le
% 2.39/2.73 thf(fact_966_neg__le__iff__le,axiom,
% 2.39/2.73 ! [B: int,A: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 2.39/2.73 = ( ord_less_eq_int @ A @ B ) ) ).
% 2.39/2.73
% 2.39/2.73 % neg_le_iff_le
% 2.39/2.73 thf(fact_967_add_Oinverse__neutral,axiom,
% 2.39/2.73 ( ( uminus_uminus_int @ zero_zero_int )
% 2.39/2.73 = zero_zero_int ) ).
% 2.39/2.73
% 2.39/2.73 % add.inverse_neutral
% 2.39/2.73 thf(fact_968_add_Oinverse__neutral,axiom,
% 2.39/2.73 ( ( uminus_uminus_rat @ zero_zero_rat )
% 2.39/2.73 = zero_zero_rat ) ).
% 2.39/2.73
% 2.39/2.73 % add.inverse_neutral
% 2.39/2.73 thf(fact_969_add_Oinverse__neutral,axiom,
% 2.39/2.73 ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 2.39/2.73 = zero_z3403309356797280102nteger ) ).
% 2.39/2.73
% 2.39/2.73 % add.inverse_neutral
% 2.39/2.73 thf(fact_970_neg__0__equal__iff__equal,axiom,
% 2.39/2.73 ! [A: int] :
% 2.39/2.73 ( ( zero_zero_int
% 2.39/2.73 = ( uminus_uminus_int @ A ) )
% 2.39/2.73 = ( zero_zero_int = A ) ) ).
% 2.39/2.73
% 2.39/2.73 % neg_0_equal_iff_equal
% 2.39/2.73 thf(fact_971_neg__0__equal__iff__equal,axiom,
% 2.39/2.73 ! [A: rat] :
% 2.39/2.73 ( ( zero_zero_rat
% 2.39/2.73 = ( uminus_uminus_rat @ A ) )
% 2.39/2.73 = ( zero_zero_rat = A ) ) ).
% 2.39/2.73
% 2.39/2.73 % neg_0_equal_iff_equal
% 2.39/2.73 thf(fact_972_neg__0__equal__iff__equal,axiom,
% 2.39/2.73 ! [A: code_integer] :
% 2.39/2.73 ( ( zero_z3403309356797280102nteger
% 2.39/2.73 = ( uminus1351360451143612070nteger @ A ) )
% 2.39/2.73 = ( zero_z3403309356797280102nteger = A ) ) ).
% 2.39/2.73
% 2.39/2.73 % neg_0_equal_iff_equal
% 2.39/2.73 thf(fact_973_neg__equal__0__iff__equal,axiom,
% 2.39/2.73 ! [A: int] :
% 2.39/2.73 ( ( ( uminus_uminus_int @ A )
% 2.39/2.73 = zero_zero_int )
% 2.39/2.73 = ( A = zero_zero_int ) ) ).
% 2.39/2.73
% 2.39/2.73 % neg_equal_0_iff_equal
% 2.39/2.73 thf(fact_974_neg__equal__0__iff__equal,axiom,
% 2.39/2.73 ! [A: rat] :
% 2.39/2.73 ( ( ( uminus_uminus_rat @ A )
% 2.39/2.73 = zero_zero_rat )
% 2.39/2.73 = ( A = zero_zero_rat ) ) ).
% 2.39/2.73
% 2.39/2.73 % neg_equal_0_iff_equal
% 2.39/2.73 thf(fact_975_neg__equal__0__iff__equal,axiom,
% 2.39/2.73 ! [A: code_integer] :
% 2.39/2.73 ( ( ( uminus1351360451143612070nteger @ A )
% 2.39/2.73 = zero_z3403309356797280102nteger )
% 2.39/2.73 = ( A = zero_z3403309356797280102nteger ) ) ).
% 2.39/2.73
% 2.39/2.73 % neg_equal_0_iff_equal
% 2.39/2.73 thf(fact_976_equal__neg__zero,axiom,
% 2.39/2.73 ! [A: int] :
% 2.39/2.73 ( ( A
% 2.39/2.73 = ( uminus_uminus_int @ A ) )
% 2.39/2.73 = ( A = zero_zero_int ) ) ).
% 2.39/2.73
% 2.39/2.73 % equal_neg_zero
% 2.39/2.73 thf(fact_977_equal__neg__zero,axiom,
% 2.39/2.73 ! [A: rat] :
% 2.39/2.73 ( ( A
% 2.39/2.73 = ( uminus_uminus_rat @ A ) )
% 2.39/2.73 = ( A = zero_zero_rat ) ) ).
% 2.39/2.73
% 2.39/2.73 % equal_neg_zero
% 2.39/2.73 thf(fact_978_equal__neg__zero,axiom,
% 2.39/2.73 ! [A: code_integer] :
% 2.39/2.73 ( ( A
% 2.39/2.73 = ( uminus1351360451143612070nteger @ A ) )
% 2.39/2.73 = ( A = zero_z3403309356797280102nteger ) ) ).
% 2.39/2.73
% 2.39/2.73 % equal_neg_zero
% 2.39/2.73 thf(fact_979_neg__equal__zero,axiom,
% 2.39/2.73 ! [A: int] :
% 2.39/2.73 ( ( ( uminus_uminus_int @ A )
% 2.39/2.73 = A )
% 2.39/2.73 = ( A = zero_zero_int ) ) ).
% 2.39/2.73
% 2.39/2.73 % neg_equal_zero
% 2.39/2.73 thf(fact_980_neg__equal__zero,axiom,
% 2.39/2.73 ! [A: rat] :
% 2.39/2.73 ( ( ( uminus_uminus_rat @ A )
% 2.39/2.73 = A )
% 2.39/2.73 = ( A = zero_zero_rat ) ) ).
% 2.39/2.73
% 2.39/2.73 % neg_equal_zero
% 2.39/2.73 thf(fact_981_neg__equal__zero,axiom,
% 2.39/2.73 ! [A: code_integer] :
% 2.39/2.73 ( ( ( uminus1351360451143612070nteger @ A )
% 2.39/2.73 = A )
% 2.39/2.73 = ( A = zero_z3403309356797280102nteger ) ) ).
% 2.39/2.73
% 2.39/2.73 % neg_equal_zero
% 2.39/2.73 thf(fact_982_inf_Obounded__iff,axiom,
% 2.39/2.73 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat] :
% 2.39/2.73 ( ( ord_le3146513528884898305at_nat @ A @ ( inf_in2572325071724192079at_nat @ B @ C ) )
% 2.39/2.73 = ( ( ord_le3146513528884898305at_nat @ A @ B )
% 2.39/2.73 & ( ord_le3146513528884898305at_nat @ A @ C ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.bounded_iff
% 2.39/2.73 thf(fact_983_inf_Obounded__iff,axiom,
% 2.39/2.73 ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o,C: product_prod_int_int > $o] :
% 2.39/2.73 ( ( ord_le8369615600986905444_int_o @ A @ ( inf_in3604695632404883862_int_o @ B @ C ) )
% 2.39/2.73 = ( ( ord_le8369615600986905444_int_o @ A @ B )
% 2.39/2.73 & ( ord_le8369615600986905444_int_o @ A @ C ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.bounded_iff
% 2.39/2.73 thf(fact_984_inf_Obounded__iff,axiom,
% 2.39/2.73 ! [A: assn,B: assn,C: assn] :
% 2.39/2.73 ( ( ord_less_eq_assn @ A @ ( inf_inf_assn @ B @ C ) )
% 2.39/2.73 = ( ( ord_less_eq_assn @ A @ B )
% 2.39/2.73 & ( ord_less_eq_assn @ A @ C ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.bounded_iff
% 2.39/2.73 thf(fact_985_inf_Obounded__iff,axiom,
% 2.39/2.73 ! [A: set_nat,B: set_nat,C: set_nat] :
% 2.39/2.73 ( ( ord_less_eq_set_nat @ A @ ( inf_inf_set_nat @ B @ C ) )
% 2.39/2.73 = ( ( ord_less_eq_set_nat @ A @ B )
% 2.39/2.73 & ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.bounded_iff
% 2.39/2.73 thf(fact_986_inf_Obounded__iff,axiom,
% 2.39/2.73 ! [A: rat,B: rat,C: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ A @ ( inf_inf_rat @ B @ C ) )
% 2.39/2.73 = ( ( ord_less_eq_rat @ A @ B )
% 2.39/2.73 & ( ord_less_eq_rat @ A @ C ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.bounded_iff
% 2.39/2.73 thf(fact_987_inf_Obounded__iff,axiom,
% 2.39/2.73 ! [A: nat,B: nat,C: nat] :
% 2.39/2.73 ( ( ord_less_eq_nat @ A @ ( inf_inf_nat @ B @ C ) )
% 2.39/2.73 = ( ( ord_less_eq_nat @ A @ B )
% 2.39/2.73 & ( ord_less_eq_nat @ A @ C ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.bounded_iff
% 2.39/2.73 thf(fact_988_inf_Obounded__iff,axiom,
% 2.39/2.73 ! [A: int,B: int,C: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ A @ ( inf_inf_int @ B @ C ) )
% 2.39/2.73 = ( ( ord_less_eq_int @ A @ B )
% 2.39/2.73 & ( ord_less_eq_int @ A @ C ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.bounded_iff
% 2.39/2.73 thf(fact_989_le__inf__iff,axiom,
% 2.39/2.73 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 2.39/2.73 ( ( ord_le3146513528884898305at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) )
% 2.39/2.73 = ( ( ord_le3146513528884898305at_nat @ X @ Y )
% 2.39/2.73 & ( ord_le3146513528884898305at_nat @ X @ Z ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_inf_iff
% 2.39/2.73 thf(fact_990_le__inf__iff,axiom,
% 2.39/2.73 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 2.39/2.73 ( ( ord_le8369615600986905444_int_o @ X @ ( inf_in3604695632404883862_int_o @ Y @ Z ) )
% 2.39/2.73 = ( ( ord_le8369615600986905444_int_o @ X @ Y )
% 2.39/2.73 & ( ord_le8369615600986905444_int_o @ X @ Z ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_inf_iff
% 2.39/2.73 thf(fact_991_le__inf__iff,axiom,
% 2.39/2.73 ! [X: assn,Y: assn,Z: assn] :
% 2.39/2.73 ( ( ord_less_eq_assn @ X @ ( inf_inf_assn @ Y @ Z ) )
% 2.39/2.73 = ( ( ord_less_eq_assn @ X @ Y )
% 2.39/2.73 & ( ord_less_eq_assn @ X @ Z ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_inf_iff
% 2.39/2.73 thf(fact_992_le__inf__iff,axiom,
% 2.39/2.73 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 2.39/2.73 ( ( ord_less_eq_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) )
% 2.39/2.73 = ( ( ord_less_eq_set_nat @ X @ Y )
% 2.39/2.73 & ( ord_less_eq_set_nat @ X @ Z ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_inf_iff
% 2.39/2.73 thf(fact_993_le__inf__iff,axiom,
% 2.39/2.73 ! [X: rat,Y: rat,Z: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ X @ ( inf_inf_rat @ Y @ Z ) )
% 2.39/2.73 = ( ( ord_less_eq_rat @ X @ Y )
% 2.39/2.73 & ( ord_less_eq_rat @ X @ Z ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_inf_iff
% 2.39/2.73 thf(fact_994_le__inf__iff,axiom,
% 2.39/2.73 ! [X: nat,Y: nat,Z: nat] :
% 2.39/2.73 ( ( ord_less_eq_nat @ X @ ( inf_inf_nat @ Y @ Z ) )
% 2.39/2.73 = ( ( ord_less_eq_nat @ X @ Y )
% 2.39/2.73 & ( ord_less_eq_nat @ X @ Z ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_inf_iff
% 2.39/2.73 thf(fact_995_le__inf__iff,axiom,
% 2.39/2.73 ! [X: int,Y: int,Z: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ X @ ( inf_inf_int @ Y @ Z ) )
% 2.39/2.73 = ( ( ord_less_eq_int @ X @ Y )
% 2.39/2.73 & ( ord_less_eq_int @ X @ Z ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_inf_iff
% 2.39/2.73 thf(fact_996_le__sup__iff,axiom,
% 2.39/2.73 ! [X: assn,Y: assn,Z: assn] :
% 2.39/2.73 ( ( ord_less_eq_assn @ ( sup_sup_assn @ X @ Y ) @ Z )
% 2.39/2.73 = ( ( ord_less_eq_assn @ X @ Z )
% 2.39/2.73 & ( ord_less_eq_assn @ Y @ Z ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_sup_iff
% 2.39/2.73 thf(fact_997_le__sup__iff,axiom,
% 2.39/2.73 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 2.39/2.73 ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ Z )
% 2.39/2.73 = ( ( ord_less_eq_set_nat @ X @ Z )
% 2.39/2.73 & ( ord_less_eq_set_nat @ Y @ Z ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_sup_iff
% 2.39/2.73 thf(fact_998_le__sup__iff,axiom,
% 2.39/2.73 ! [X: rat,Y: rat,Z: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ ( sup_sup_rat @ X @ Y ) @ Z )
% 2.39/2.73 = ( ( ord_less_eq_rat @ X @ Z )
% 2.39/2.73 & ( ord_less_eq_rat @ Y @ Z ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_sup_iff
% 2.39/2.73 thf(fact_999_le__sup__iff,axiom,
% 2.39/2.73 ! [X: nat,Y: nat,Z: nat] :
% 2.39/2.73 ( ( ord_less_eq_nat @ ( sup_sup_nat @ X @ Y ) @ Z )
% 2.39/2.73 = ( ( ord_less_eq_nat @ X @ Z )
% 2.39/2.73 & ( ord_less_eq_nat @ Y @ Z ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_sup_iff
% 2.39/2.73 thf(fact_1000_le__sup__iff,axiom,
% 2.39/2.73 ! [X: int,Y: int,Z: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ ( sup_sup_int @ X @ Y ) @ Z )
% 2.39/2.73 = ( ( ord_less_eq_int @ X @ Z )
% 2.39/2.73 & ( ord_less_eq_int @ Y @ Z ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_sup_iff
% 2.39/2.73 thf(fact_1001_sup_Obounded__iff,axiom,
% 2.39/2.73 ! [B: assn,C: assn,A: assn] :
% 2.39/2.73 ( ( ord_less_eq_assn @ ( sup_sup_assn @ B @ C ) @ A )
% 2.39/2.73 = ( ( ord_less_eq_assn @ B @ A )
% 2.39/2.73 & ( ord_less_eq_assn @ C @ A ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % sup.bounded_iff
% 2.39/2.73 thf(fact_1002_sup_Obounded__iff,axiom,
% 2.39/2.73 ! [B: set_nat,C: set_nat,A: set_nat] :
% 2.39/2.73 ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ B @ C ) @ A )
% 2.39/2.73 = ( ( ord_less_eq_set_nat @ B @ A )
% 2.39/2.73 & ( ord_less_eq_set_nat @ C @ A ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % sup.bounded_iff
% 2.39/2.73 thf(fact_1003_sup_Obounded__iff,axiom,
% 2.39/2.73 ! [B: rat,C: rat,A: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ ( sup_sup_rat @ B @ C ) @ A )
% 2.39/2.73 = ( ( ord_less_eq_rat @ B @ A )
% 2.39/2.73 & ( ord_less_eq_rat @ C @ A ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % sup.bounded_iff
% 2.39/2.73 thf(fact_1004_sup_Obounded__iff,axiom,
% 2.39/2.73 ! [B: nat,C: nat,A: nat] :
% 2.39/2.73 ( ( ord_less_eq_nat @ ( sup_sup_nat @ B @ C ) @ A )
% 2.39/2.73 = ( ( ord_less_eq_nat @ B @ A )
% 2.39/2.73 & ( ord_less_eq_nat @ C @ A ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % sup.bounded_iff
% 2.39/2.73 thf(fact_1005_sup_Obounded__iff,axiom,
% 2.39/2.73 ! [B: int,C: int,A: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ ( sup_sup_int @ B @ C ) @ A )
% 2.39/2.73 = ( ( ord_less_eq_int @ B @ A )
% 2.39/2.73 & ( ord_less_eq_int @ C @ A ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % sup.bounded_iff
% 2.39/2.73 thf(fact_1006_map__is__Nil__conv,axiom,
% 2.39/2.73 ! [F2: produc6575502325842934193n_assn > produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn] :
% 2.39/2.73 ( ( ( map_Pr7925354932063753860n_assn @ F2 @ Xs )
% 2.39/2.73 = nil_Pr5671120429643327159n_assn )
% 2.39/2.73 = ( Xs = nil_Pr5671120429643327159n_assn ) ) ).
% 2.39/2.73
% 2.39/2.73 % map_is_Nil_conv
% 2.39/2.73 thf(fact_1007_map__is__Nil__conv,axiom,
% 2.39/2.73 ! [F2: int > produc6575502325842934193n_assn,Xs: list_int] :
% 2.39/2.73 ( ( ( map_in4427992030928829247n_assn @ F2 @ Xs )
% 2.39/2.73 = nil_Pr5671120429643327159n_assn )
% 2.39/2.73 = ( Xs = nil_int ) ) ).
% 2.39/2.73
% 2.39/2.73 % map_is_Nil_conv
% 2.39/2.73 thf(fact_1008_map__is__Nil__conv,axiom,
% 2.39/2.73 ! [F2: nat > produc6575502325842934193n_assn,Xs: list_nat] :
% 2.39/2.73 ( ( ( map_na2667955367175718043n_assn @ F2 @ Xs )
% 2.39/2.73 = nil_Pr5671120429643327159n_assn )
% 2.39/2.73 = ( Xs = nil_nat ) ) ).
% 2.39/2.73
% 2.39/2.73 % map_is_Nil_conv
% 2.39/2.73 thf(fact_1009_map__is__Nil__conv,axiom,
% 2.39/2.73 ! [F2: produc6575502325842934193n_assn > int,Xs: list_P8527749157015355191n_assn] :
% 2.39/2.73 ( ( ( map_Pr7568062423562401049sn_int @ F2 @ Xs )
% 2.39/2.73 = nil_int )
% 2.39/2.73 = ( Xs = nil_Pr5671120429643327159n_assn ) ) ).
% 2.39/2.73
% 2.39/2.73 % map_is_Nil_conv
% 2.39/2.73 thf(fact_1010_map__is__Nil__conv,axiom,
% 2.39/2.73 ! [F2: int > int,Xs: list_int] :
% 2.39/2.73 ( ( ( map_int_int @ F2 @ Xs )
% 2.39/2.73 = nil_int )
% 2.39/2.73 = ( Xs = nil_int ) ) ).
% 2.39/2.73
% 2.39/2.73 % map_is_Nil_conv
% 2.39/2.73 thf(fact_1011_map__is__Nil__conv,axiom,
% 2.39/2.73 ! [F2: nat > int,Xs: list_nat] :
% 2.39/2.73 ( ( ( map_nat_int @ F2 @ Xs )
% 2.39/2.73 = nil_int )
% 2.39/2.73 = ( Xs = nil_nat ) ) ).
% 2.39/2.73
% 2.39/2.73 % map_is_Nil_conv
% 2.39/2.73 thf(fact_1012_map__is__Nil__conv,axiom,
% 2.39/2.73 ! [F2: produc6575502325842934193n_assn > nat,Xs: list_P8527749157015355191n_assn] :
% 2.39/2.73 ( ( ( map_Pr7570552894071451325sn_nat @ F2 @ Xs )
% 2.39/2.73 = nil_nat )
% 2.39/2.73 = ( Xs = nil_Pr5671120429643327159n_assn ) ) ).
% 2.39/2.73
% 2.39/2.73 % map_is_Nil_conv
% 2.39/2.73 thf(fact_1013_map__is__Nil__conv,axiom,
% 2.39/2.73 ! [F2: int > nat,Xs: list_int] :
% 2.39/2.73 ( ( ( map_int_nat @ F2 @ Xs )
% 2.39/2.73 = nil_nat )
% 2.39/2.73 = ( Xs = nil_int ) ) ).
% 2.39/2.73
% 2.39/2.73 % map_is_Nil_conv
% 2.39/2.73 thf(fact_1014_map__is__Nil__conv,axiom,
% 2.39/2.73 ! [F2: nat > nat,Xs: list_nat] :
% 2.39/2.73 ( ( ( map_nat_nat @ F2 @ Xs )
% 2.39/2.73 = nil_nat )
% 2.39/2.73 = ( Xs = nil_nat ) ) ).
% 2.39/2.73
% 2.39/2.73 % map_is_Nil_conv
% 2.39/2.73 thf(fact_1015_map__is__Nil__conv,axiom,
% 2.39/2.73 ! [F2: produc6575502325842934193n_assn > assn,Xs: list_P8527749157015355191n_assn] :
% 2.39/2.73 ( ( ( map_Pr8991440229025900053n_assn @ F2 @ Xs )
% 2.39/2.73 = nil_assn )
% 2.39/2.73 = ( Xs = nil_Pr5671120429643327159n_assn ) ) ).
% 2.39/2.73
% 2.39/2.73 % map_is_Nil_conv
% 2.39/2.73 thf(fact_1016_Nil__is__map__conv,axiom,
% 2.39/2.73 ! [F2: produc6575502325842934193n_assn > produc6575502325842934193n_assn,Xs: list_P8527749157015355191n_assn] :
% 2.39/2.73 ( ( nil_Pr5671120429643327159n_assn
% 2.39/2.73 = ( map_Pr7925354932063753860n_assn @ F2 @ Xs ) )
% 2.39/2.73 = ( Xs = nil_Pr5671120429643327159n_assn ) ) ).
% 2.39/2.73
% 2.39/2.73 % Nil_is_map_conv
% 2.39/2.73 thf(fact_1017_Nil__is__map__conv,axiom,
% 2.39/2.73 ! [F2: int > produc6575502325842934193n_assn,Xs: list_int] :
% 2.39/2.73 ( ( nil_Pr5671120429643327159n_assn
% 2.39/2.73 = ( map_in4427992030928829247n_assn @ F2 @ Xs ) )
% 2.39/2.73 = ( Xs = nil_int ) ) ).
% 2.39/2.73
% 2.39/2.73 % Nil_is_map_conv
% 2.39/2.73 thf(fact_1018_Nil__is__map__conv,axiom,
% 2.39/2.73 ! [F2: nat > produc6575502325842934193n_assn,Xs: list_nat] :
% 2.39/2.73 ( ( nil_Pr5671120429643327159n_assn
% 2.39/2.73 = ( map_na2667955367175718043n_assn @ F2 @ Xs ) )
% 2.39/2.73 = ( Xs = nil_nat ) ) ).
% 2.39/2.73
% 2.39/2.73 % Nil_is_map_conv
% 2.39/2.73 thf(fact_1019_Nil__is__map__conv,axiom,
% 2.39/2.73 ! [F2: produc6575502325842934193n_assn > int,Xs: list_P8527749157015355191n_assn] :
% 2.39/2.73 ( ( nil_int
% 2.39/2.73 = ( map_Pr7568062423562401049sn_int @ F2 @ Xs ) )
% 2.39/2.73 = ( Xs = nil_Pr5671120429643327159n_assn ) ) ).
% 2.39/2.73
% 2.39/2.73 % Nil_is_map_conv
% 2.39/2.73 thf(fact_1020_Nil__is__map__conv,axiom,
% 2.39/2.73 ! [F2: int > int,Xs: list_int] :
% 2.39/2.73 ( ( nil_int
% 2.39/2.73 = ( map_int_int @ F2 @ Xs ) )
% 2.39/2.73 = ( Xs = nil_int ) ) ).
% 2.39/2.73
% 2.39/2.73 % Nil_is_map_conv
% 2.39/2.73 thf(fact_1021_Nil__is__map__conv,axiom,
% 2.39/2.73 ! [F2: nat > int,Xs: list_nat] :
% 2.39/2.73 ( ( nil_int
% 2.39/2.73 = ( map_nat_int @ F2 @ Xs ) )
% 2.39/2.73 = ( Xs = nil_nat ) ) ).
% 2.39/2.73
% 2.39/2.73 % Nil_is_map_conv
% 2.39/2.73 thf(fact_1022_Nil__is__map__conv,axiom,
% 2.39/2.73 ! [F2: produc6575502325842934193n_assn > nat,Xs: list_P8527749157015355191n_assn] :
% 2.39/2.73 ( ( nil_nat
% 2.39/2.73 = ( map_Pr7570552894071451325sn_nat @ F2 @ Xs ) )
% 2.39/2.73 = ( Xs = nil_Pr5671120429643327159n_assn ) ) ).
% 2.39/2.73
% 2.39/2.73 % Nil_is_map_conv
% 2.39/2.73 thf(fact_1023_Nil__is__map__conv,axiom,
% 2.39/2.73 ! [F2: int > nat,Xs: list_int] :
% 2.39/2.73 ( ( nil_nat
% 2.39/2.73 = ( map_int_nat @ F2 @ Xs ) )
% 2.39/2.73 = ( Xs = nil_int ) ) ).
% 2.39/2.73
% 2.39/2.73 % Nil_is_map_conv
% 2.39/2.73 thf(fact_1024_Nil__is__map__conv,axiom,
% 2.39/2.73 ! [F2: nat > nat,Xs: list_nat] :
% 2.39/2.73 ( ( nil_nat
% 2.39/2.73 = ( map_nat_nat @ F2 @ Xs ) )
% 2.39/2.73 = ( Xs = nil_nat ) ) ).
% 2.39/2.73
% 2.39/2.73 % Nil_is_map_conv
% 2.39/2.73 thf(fact_1025_Nil__is__map__conv,axiom,
% 2.39/2.73 ! [F2: produc6575502325842934193n_assn > assn,Xs: list_P8527749157015355191n_assn] :
% 2.39/2.73 ( ( nil_assn
% 2.39/2.73 = ( map_Pr8991440229025900053n_assn @ F2 @ Xs ) )
% 2.39/2.73 = ( Xs = nil_Pr5671120429643327159n_assn ) ) ).
% 2.39/2.73
% 2.39/2.73 % Nil_is_map_conv
% 2.39/2.73 thf(fact_1026_list_Omap__disc__iff,axiom,
% 2.39/2.73 ! [F2: produc6575502325842934193n_assn > produc6575502325842934193n_assn,A: list_P8527749157015355191n_assn] :
% 2.39/2.73 ( ( ( map_Pr7925354932063753860n_assn @ F2 @ A )
% 2.39/2.73 = nil_Pr5671120429643327159n_assn )
% 2.39/2.73 = ( A = nil_Pr5671120429643327159n_assn ) ) ).
% 2.39/2.73
% 2.39/2.73 % list.map_disc_iff
% 2.39/2.73 thf(fact_1027_list_Omap__disc__iff,axiom,
% 2.39/2.73 ! [F2: int > produc6575502325842934193n_assn,A: list_int] :
% 2.39/2.73 ( ( ( map_in4427992030928829247n_assn @ F2 @ A )
% 2.39/2.73 = nil_Pr5671120429643327159n_assn )
% 2.39/2.73 = ( A = nil_int ) ) ).
% 2.39/2.73
% 2.39/2.73 % list.map_disc_iff
% 2.39/2.73 thf(fact_1028_list_Omap__disc__iff,axiom,
% 2.39/2.73 ! [F2: nat > produc6575502325842934193n_assn,A: list_nat] :
% 2.39/2.73 ( ( ( map_na2667955367175718043n_assn @ F2 @ A )
% 2.39/2.73 = nil_Pr5671120429643327159n_assn )
% 2.39/2.73 = ( A = nil_nat ) ) ).
% 2.39/2.73
% 2.39/2.73 % list.map_disc_iff
% 2.39/2.73 thf(fact_1029_list_Omap__disc__iff,axiom,
% 2.39/2.73 ! [F2: produc6575502325842934193n_assn > int,A: list_P8527749157015355191n_assn] :
% 2.39/2.73 ( ( ( map_Pr7568062423562401049sn_int @ F2 @ A )
% 2.39/2.73 = nil_int )
% 2.39/2.73 = ( A = nil_Pr5671120429643327159n_assn ) ) ).
% 2.39/2.73
% 2.39/2.73 % list.map_disc_iff
% 2.39/2.73 thf(fact_1030_list_Omap__disc__iff,axiom,
% 2.39/2.73 ! [F2: int > int,A: list_int] :
% 2.39/2.73 ( ( ( map_int_int @ F2 @ A )
% 2.39/2.73 = nil_int )
% 2.39/2.73 = ( A = nil_int ) ) ).
% 2.39/2.73
% 2.39/2.73 % list.map_disc_iff
% 2.39/2.73 thf(fact_1031_list_Omap__disc__iff,axiom,
% 2.39/2.73 ! [F2: nat > int,A: list_nat] :
% 2.39/2.73 ( ( ( map_nat_int @ F2 @ A )
% 2.39/2.73 = nil_int )
% 2.39/2.73 = ( A = nil_nat ) ) ).
% 2.39/2.73
% 2.39/2.73 % list.map_disc_iff
% 2.39/2.73 thf(fact_1032_list_Omap__disc__iff,axiom,
% 2.39/2.73 ! [F2: produc6575502325842934193n_assn > nat,A: list_P8527749157015355191n_assn] :
% 2.39/2.73 ( ( ( map_Pr7570552894071451325sn_nat @ F2 @ A )
% 2.39/2.73 = nil_nat )
% 2.39/2.73 = ( A = nil_Pr5671120429643327159n_assn ) ) ).
% 2.39/2.73
% 2.39/2.73 % list.map_disc_iff
% 2.39/2.73 thf(fact_1033_list_Omap__disc__iff,axiom,
% 2.39/2.73 ! [F2: int > nat,A: list_int] :
% 2.39/2.73 ( ( ( map_int_nat @ F2 @ A )
% 2.39/2.73 = nil_nat )
% 2.39/2.73 = ( A = nil_int ) ) ).
% 2.39/2.73
% 2.39/2.73 % list.map_disc_iff
% 2.39/2.73 thf(fact_1034_list_Omap__disc__iff,axiom,
% 2.39/2.73 ! [F2: nat > nat,A: list_nat] :
% 2.39/2.73 ( ( ( map_nat_nat @ F2 @ A )
% 2.39/2.73 = nil_nat )
% 2.39/2.73 = ( A = nil_nat ) ) ).
% 2.39/2.73
% 2.39/2.73 % list.map_disc_iff
% 2.39/2.73 thf(fact_1035_list_Omap__disc__iff,axiom,
% 2.39/2.73 ! [F2: produc6575502325842934193n_assn > assn,A: list_P8527749157015355191n_assn] :
% 2.39/2.73 ( ( ( map_Pr8991440229025900053n_assn @ F2 @ A )
% 2.39/2.73 = nil_assn )
% 2.39/2.73 = ( A = nil_Pr5671120429643327159n_assn ) ) ).
% 2.39/2.73
% 2.39/2.73 % list.map_disc_iff
% 2.39/2.73 thf(fact_1036_Int__subset__iff,axiom,
% 2.39/2.73 ! [C2: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.73 ( ( ord_le3146513528884898305at_nat @ C2 @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) )
% 2.39/2.73 = ( ( ord_le3146513528884898305at_nat @ C2 @ A3 )
% 2.39/2.73 & ( ord_le3146513528884898305at_nat @ C2 @ B3 ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % Int_subset_iff
% 2.39/2.73 thf(fact_1037_Int__subset__iff,axiom,
% 2.39/2.73 ! [C2: set_nat,A3: set_nat,B3: set_nat] :
% 2.39/2.73 ( ( ord_less_eq_set_nat @ C2 @ ( inf_inf_set_nat @ A3 @ B3 ) )
% 2.39/2.73 = ( ( ord_less_eq_set_nat @ C2 @ A3 )
% 2.39/2.73 & ( ord_less_eq_set_nat @ C2 @ B3 ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % Int_subset_iff
% 2.39/2.73 thf(fact_1038_nths__nil,axiom,
% 2.39/2.73 ! [A3: set_nat] :
% 2.39/2.73 ( ( nths_P5537322223065504949n_assn @ nil_Pr5671120429643327159n_assn @ A3 )
% 2.39/2.73 = nil_Pr5671120429643327159n_assn ) ).
% 2.39/2.73
% 2.39/2.73 % nths_nil
% 2.39/2.73 thf(fact_1039_nths__nil,axiom,
% 2.39/2.73 ! [A3: set_nat] :
% 2.39/2.73 ( ( nths_int @ nil_int @ A3 )
% 2.39/2.73 = nil_int ) ).
% 2.39/2.73
% 2.39/2.73 % nths_nil
% 2.39/2.73 thf(fact_1040_nths__nil,axiom,
% 2.39/2.73 ! [A3: set_nat] :
% 2.39/2.73 ( ( nths_nat @ nil_nat @ A3 )
% 2.39/2.73 = nil_nat ) ).
% 2.39/2.73
% 2.39/2.73 % nths_nil
% 2.39/2.73 thf(fact_1041_neg__0__le__iff__le,axiom,
% 2.39/2.73 ! [A: code_integer] :
% 2.39/2.73 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 2.39/2.73 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 2.39/2.73
% 2.39/2.73 % neg_0_le_iff_le
% 2.39/2.73 thf(fact_1042_neg__0__le__iff__le,axiom,
% 2.39/2.73 ! [A: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 2.39/2.73 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 2.39/2.73
% 2.39/2.73 % neg_0_le_iff_le
% 2.39/2.73 thf(fact_1043_neg__0__le__iff__le,axiom,
% 2.39/2.73 ! [A: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 2.39/2.73 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 2.39/2.73
% 2.39/2.73 % neg_0_le_iff_le
% 2.39/2.73 thf(fact_1044_neg__le__0__iff__le,axiom,
% 2.39/2.73 ! [A: code_integer] :
% 2.39/2.73 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 2.39/2.73 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 2.39/2.73
% 2.39/2.73 % neg_le_0_iff_le
% 2.39/2.73 thf(fact_1045_neg__le__0__iff__le,axiom,
% 2.39/2.73 ! [A: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 2.39/2.73 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 2.39/2.73
% 2.39/2.73 % neg_le_0_iff_le
% 2.39/2.73 thf(fact_1046_neg__le__0__iff__le,axiom,
% 2.39/2.73 ! [A: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 2.39/2.73 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 2.39/2.73
% 2.39/2.73 % neg_le_0_iff_le
% 2.39/2.73 thf(fact_1047_less__eq__neg__nonpos,axiom,
% 2.39/2.73 ! [A: code_integer] :
% 2.39/2.73 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 2.39/2.73 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 2.39/2.73
% 2.39/2.73 % less_eq_neg_nonpos
% 2.39/2.73 thf(fact_1048_less__eq__neg__nonpos,axiom,
% 2.39/2.73 ! [A: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ A ) )
% 2.39/2.73 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 2.39/2.73
% 2.39/2.73 % less_eq_neg_nonpos
% 2.39/2.73 thf(fact_1049_less__eq__neg__nonpos,axiom,
% 2.39/2.73 ! [A: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 2.39/2.73 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 2.39/2.73
% 2.39/2.73 % less_eq_neg_nonpos
% 2.39/2.73 thf(fact_1050_neg__less__eq__nonneg,axiom,
% 2.39/2.73 ! [A: code_integer] :
% 2.39/2.73 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 2.39/2.73 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 2.39/2.73
% 2.39/2.73 % neg_less_eq_nonneg
% 2.39/2.73 thf(fact_1051_neg__less__eq__nonneg,axiom,
% 2.39/2.73 ! [A: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ A )
% 2.39/2.73 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 2.39/2.73
% 2.39/2.73 % neg_less_eq_nonneg
% 2.39/2.73 thf(fact_1052_neg__less__eq__nonneg,axiom,
% 2.39/2.73 ! [A: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 2.39/2.73 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 2.39/2.73
% 2.39/2.73 % neg_less_eq_nonneg
% 2.39/2.73 thf(fact_1053_mult__cancel__right2,axiom,
% 2.39/2.73 ! [A: rat,C: rat] :
% 2.39/2.73 ( ( ( times_times_rat @ A @ C )
% 2.39/2.73 = C )
% 2.39/2.73 = ( ( C = zero_zero_rat )
% 2.39/2.73 | ( A = one_one_rat ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_cancel_right2
% 2.39/2.73 thf(fact_1054_mult__cancel__right2,axiom,
% 2.39/2.73 ! [A: int,C: int] :
% 2.39/2.73 ( ( ( times_times_int @ A @ C )
% 2.39/2.73 = C )
% 2.39/2.73 = ( ( C = zero_zero_int )
% 2.39/2.73 | ( A = one_one_int ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_cancel_right2
% 2.39/2.73 thf(fact_1055_mult__cancel__right2,axiom,
% 2.39/2.73 ! [A: code_integer,C: code_integer] :
% 2.39/2.73 ( ( ( times_3573771949741848930nteger @ A @ C )
% 2.39/2.73 = C )
% 2.39/2.73 = ( ( C = zero_z3403309356797280102nteger )
% 2.39/2.73 | ( A = one_one_Code_integer ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_cancel_right2
% 2.39/2.73 thf(fact_1056_mult__cancel__right1,axiom,
% 2.39/2.73 ! [C: rat,B: rat] :
% 2.39/2.73 ( ( C
% 2.39/2.73 = ( times_times_rat @ B @ C ) )
% 2.39/2.73 = ( ( C = zero_zero_rat )
% 2.39/2.73 | ( B = one_one_rat ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_cancel_right1
% 2.39/2.73 thf(fact_1057_mult__cancel__right1,axiom,
% 2.39/2.73 ! [C: int,B: int] :
% 2.39/2.73 ( ( C
% 2.39/2.73 = ( times_times_int @ B @ C ) )
% 2.39/2.73 = ( ( C = zero_zero_int )
% 2.39/2.73 | ( B = one_one_int ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_cancel_right1
% 2.39/2.73 thf(fact_1058_mult__cancel__right1,axiom,
% 2.39/2.73 ! [C: code_integer,B: code_integer] :
% 2.39/2.73 ( ( C
% 2.39/2.73 = ( times_3573771949741848930nteger @ B @ C ) )
% 2.39/2.73 = ( ( C = zero_z3403309356797280102nteger )
% 2.39/2.73 | ( B = one_one_Code_integer ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_cancel_right1
% 2.39/2.73 thf(fact_1059_mult__cancel__left2,axiom,
% 2.39/2.73 ! [C: rat,A: rat] :
% 2.39/2.73 ( ( ( times_times_rat @ C @ A )
% 2.39/2.73 = C )
% 2.39/2.73 = ( ( C = zero_zero_rat )
% 2.39/2.73 | ( A = one_one_rat ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_cancel_left2
% 2.39/2.73 thf(fact_1060_mult__cancel__left2,axiom,
% 2.39/2.73 ! [C: int,A: int] :
% 2.39/2.73 ( ( ( times_times_int @ C @ A )
% 2.39/2.73 = C )
% 2.39/2.73 = ( ( C = zero_zero_int )
% 2.39/2.73 | ( A = one_one_int ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_cancel_left2
% 2.39/2.73 thf(fact_1061_mult__cancel__left2,axiom,
% 2.39/2.73 ! [C: code_integer,A: code_integer] :
% 2.39/2.73 ( ( ( times_3573771949741848930nteger @ C @ A )
% 2.39/2.73 = C )
% 2.39/2.73 = ( ( C = zero_z3403309356797280102nteger )
% 2.39/2.73 | ( A = one_one_Code_integer ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_cancel_left2
% 2.39/2.73 thf(fact_1062_mult__cancel__left1,axiom,
% 2.39/2.73 ! [C: rat,B: rat] :
% 2.39/2.73 ( ( C
% 2.39/2.73 = ( times_times_rat @ C @ B ) )
% 2.39/2.73 = ( ( C = zero_zero_rat )
% 2.39/2.73 | ( B = one_one_rat ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_cancel_left1
% 2.39/2.73 thf(fact_1063_mult__cancel__left1,axiom,
% 2.39/2.73 ! [C: int,B: int] :
% 2.39/2.73 ( ( C
% 2.39/2.73 = ( times_times_int @ C @ B ) )
% 2.39/2.73 = ( ( C = zero_zero_int )
% 2.39/2.73 | ( B = one_one_int ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_cancel_left1
% 2.39/2.73 thf(fact_1064_mult__cancel__left1,axiom,
% 2.39/2.73 ! [C: code_integer,B: code_integer] :
% 2.39/2.73 ( ( C
% 2.39/2.73 = ( times_3573771949741848930nteger @ C @ B ) )
% 2.39/2.73 = ( ( C = zero_z3403309356797280102nteger )
% 2.39/2.73 | ( B = one_one_Code_integer ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_cancel_left1
% 2.39/2.73 thf(fact_1065_sorted__list__of__set_Ofold__insort__key_Oinfinite,axiom,
% 2.39/2.73 ! [A3: set_int] :
% 2.39/2.73 ( ~ ( finite_finite_int @ A3 )
% 2.39/2.73 => ( ( linord2612477271533052124et_int @ A3 )
% 2.39/2.73 = nil_int ) ) ).
% 2.39/2.73
% 2.39/2.73 % sorted_list_of_set.fold_insort_key.infinite
% 2.39/2.73 thf(fact_1066_sorted__list__of__set_Ofold__insort__key_Oinfinite,axiom,
% 2.39/2.73 ! [A3: set_nat] :
% 2.39/2.73 ( ~ ( finite_finite_nat @ A3 )
% 2.39/2.73 => ( ( linord2614967742042102400et_nat @ A3 )
% 2.39/2.73 = nil_nat ) ) ).
% 2.39/2.73
% 2.39/2.73 % sorted_list_of_set.fold_insort_key.infinite
% 2.39/2.73 thf(fact_1067_zero__le,axiom,
% 2.39/2.73 ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% 2.39/2.73
% 2.39/2.73 % zero_le
% 2.39/2.73 thf(fact_1068_nths__map,axiom,
% 2.39/2.73 ! [F2: nat > nat,Xs: list_nat,I: set_nat] :
% 2.39/2.73 ( ( nths_nat @ ( map_nat_nat @ F2 @ Xs ) @ I )
% 2.39/2.73 = ( map_nat_nat @ F2 @ ( nths_nat @ Xs @ I ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % nths_map
% 2.39/2.73 thf(fact_1069_nths__map,axiom,
% 2.39/2.73 ! [F2: produc6575502325842934193n_assn > assn,Xs: list_P8527749157015355191n_assn,I: set_nat] :
% 2.39/2.73 ( ( nths_assn @ ( map_Pr8991440229025900053n_assn @ F2 @ Xs ) @ I )
% 2.39/2.73 = ( map_Pr8991440229025900053n_assn @ F2 @ ( nths_P5537322223065504949n_assn @ Xs @ I ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % nths_map
% 2.39/2.73 thf(fact_1070_zero__reorient,axiom,
% 2.39/2.73 ! [X: nat] :
% 2.39/2.73 ( ( zero_zero_nat = X )
% 2.39/2.73 = ( X = zero_zero_nat ) ) ).
% 2.39/2.73
% 2.39/2.73 % zero_reorient
% 2.39/2.73 thf(fact_1071_zero__reorient,axiom,
% 2.39/2.73 ! [X: int] :
% 2.39/2.73 ( ( zero_zero_int = X )
% 2.39/2.73 = ( X = zero_zero_int ) ) ).
% 2.39/2.73
% 2.39/2.73 % zero_reorient
% 2.39/2.73 thf(fact_1072_zero__reorient,axiom,
% 2.39/2.73 ! [X: rat] :
% 2.39/2.73 ( ( zero_zero_rat = X )
% 2.39/2.73 = ( X = zero_zero_rat ) ) ).
% 2.39/2.73
% 2.39/2.73 % zero_reorient
% 2.39/2.73 thf(fact_1073_zero__reorient,axiom,
% 2.39/2.73 ! [X: code_integer] :
% 2.39/2.73 ( ( zero_z3403309356797280102nteger = X )
% 2.39/2.73 = ( X = zero_z3403309356797280102nteger ) ) ).
% 2.39/2.73
% 2.39/2.73 % zero_reorient
% 2.39/2.73 thf(fact_1074_zero__reorient,axiom,
% 2.39/2.73 ! [X: code_natural] :
% 2.39/2.73 ( ( zero_z2226904508553997617atural = X )
% 2.39/2.73 = ( X = zero_z2226904508553997617atural ) ) ).
% 2.39/2.73
% 2.39/2.73 % zero_reorient
% 2.39/2.73 thf(fact_1075_times__assn__raw_Ocases,axiom,
% 2.39/2.73 ! [X: produc2732055786443039994et_nat] :
% 2.39/2.73 ~ ! [P4: produc3658429121746597890et_nat > $o,Q5: produc3658429121746597890et_nat > $o,H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.39/2.73 ( X
% 2.39/2.73 != ( produc2245416461498447860et_nat @ P4 @ ( produc5001842942810119800et_nat @ Q5 @ ( produc7507926704131184380et_nat @ H3 @ As ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % times_assn_raw.cases
% 2.39/2.73 thf(fact_1076_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 2.39/2.73 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.73 ( ( ord_le3102999989581377725nteger @ A @ B )
% 2.39/2.73 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 2.39/2.73 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % ordered_comm_semiring_class.comm_mult_left_mono
% 2.39/2.73 thf(fact_1077_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 2.39/2.73 ! [A: code_natural,B: code_natural,C: code_natural] :
% 2.39/2.73 ( ( ord_le1926595141338095240atural @ A @ B )
% 2.39/2.73 => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ C )
% 2.39/2.73 => ( ord_le1926595141338095240atural @ ( times_2397367101498566445atural @ C @ A ) @ ( times_2397367101498566445atural @ C @ B ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % ordered_comm_semiring_class.comm_mult_left_mono
% 2.39/2.73 thf(fact_1078_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 2.39/2.73 ! [A: rat,B: rat,C: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ A @ B )
% 2.39/2.73 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 2.39/2.73 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % ordered_comm_semiring_class.comm_mult_left_mono
% 2.39/2.73 thf(fact_1079_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 2.39/2.73 ! [A: nat,B: nat,C: nat] :
% 2.39/2.73 ( ( ord_less_eq_nat @ A @ B )
% 2.39/2.73 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 2.39/2.73 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % ordered_comm_semiring_class.comm_mult_left_mono
% 2.39/2.73 thf(fact_1080_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 2.39/2.73 ! [A: int,B: int,C: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ A @ B )
% 2.39/2.73 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 2.39/2.73 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % ordered_comm_semiring_class.comm_mult_left_mono
% 2.39/2.73 thf(fact_1081_zero__le__mult__iff,axiom,
% 2.39/2.73 ! [A: code_integer,B: code_integer] :
% 2.39/2.73 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) )
% 2.39/2.73 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.73 & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) )
% 2.39/2.73 | ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 2.39/2.73 & ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % zero_le_mult_iff
% 2.39/2.73 thf(fact_1082_zero__le__mult__iff,axiom,
% 2.39/2.73 ! [A: rat,B: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 2.39/2.73 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 2.39/2.73 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 2.39/2.73 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 2.39/2.73 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % zero_le_mult_iff
% 2.39/2.73 thf(fact_1083_zero__le__mult__iff,axiom,
% 2.39/2.73 ! [A: int,B: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 2.39/2.73 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 2.39/2.73 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 2.39/2.73 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 2.39/2.73 & ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % zero_le_mult_iff
% 2.39/2.73 thf(fact_1084_mult__nonneg__nonpos2,axiom,
% 2.39/2.73 ! [A: code_integer,B: code_integer] :
% 2.39/2.73 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.73 => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 2.39/2.73 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ B @ A ) @ zero_z3403309356797280102nteger ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_nonneg_nonpos2
% 2.39/2.73 thf(fact_1085_mult__nonneg__nonpos2,axiom,
% 2.39/2.73 ! [A: code_natural,B: code_natural] :
% 2.39/2.73 ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 2.39/2.73 => ( ( ord_le1926595141338095240atural @ B @ zero_z2226904508553997617atural )
% 2.39/2.73 => ( ord_le1926595141338095240atural @ ( times_2397367101498566445atural @ B @ A ) @ zero_z2226904508553997617atural ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_nonneg_nonpos2
% 2.39/2.73 thf(fact_1086_mult__nonneg__nonpos2,axiom,
% 2.39/2.73 ! [A: rat,B: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 2.39/2.73 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 2.39/2.73 => ( ord_less_eq_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_nonneg_nonpos2
% 2.39/2.73 thf(fact_1087_mult__nonneg__nonpos2,axiom,
% 2.39/2.73 ! [A: nat,B: nat] :
% 2.39/2.73 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 2.39/2.73 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 2.39/2.73 => ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_nonneg_nonpos2
% 2.39/2.73 thf(fact_1088_mult__nonneg__nonpos2,axiom,
% 2.39/2.73 ! [A: int,B: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 2.39/2.73 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 2.39/2.73 => ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_nonneg_nonpos2
% 2.39/2.73 thf(fact_1089_mult__nonpos__nonneg,axiom,
% 2.39/2.73 ! [A: code_integer,B: code_integer] :
% 2.39/2.73 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 2.39/2.73 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 2.39/2.73 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_nonpos_nonneg
% 2.39/2.73 thf(fact_1090_mult__nonpos__nonneg,axiom,
% 2.39/2.73 ! [A: code_natural,B: code_natural] :
% 2.39/2.73 ( ( ord_le1926595141338095240atural @ A @ zero_z2226904508553997617atural )
% 2.39/2.73 => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ B )
% 2.39/2.73 => ( ord_le1926595141338095240atural @ ( times_2397367101498566445atural @ A @ B ) @ zero_z2226904508553997617atural ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_nonpos_nonneg
% 2.39/2.73 thf(fact_1091_mult__nonpos__nonneg,axiom,
% 2.39/2.73 ! [A: rat,B: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 2.39/2.73 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 2.39/2.73 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_nonpos_nonneg
% 2.39/2.73 thf(fact_1092_mult__nonpos__nonneg,axiom,
% 2.39/2.73 ! [A: nat,B: nat] :
% 2.39/2.73 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 2.39/2.73 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 2.39/2.73 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_nonpos_nonneg
% 2.39/2.73 thf(fact_1093_mult__nonpos__nonneg,axiom,
% 2.39/2.73 ! [A: int,B: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 2.39/2.73 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 2.39/2.73 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_nonpos_nonneg
% 2.39/2.73 thf(fact_1094_mult__nonneg__nonpos,axiom,
% 2.39/2.73 ! [A: code_integer,B: code_integer] :
% 2.39/2.73 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.73 => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 2.39/2.73 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_nonneg_nonpos
% 2.39/2.73 thf(fact_1095_mult__nonneg__nonpos,axiom,
% 2.39/2.73 ! [A: code_natural,B: code_natural] :
% 2.39/2.73 ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 2.39/2.73 => ( ( ord_le1926595141338095240atural @ B @ zero_z2226904508553997617atural )
% 2.39/2.73 => ( ord_le1926595141338095240atural @ ( times_2397367101498566445atural @ A @ B ) @ zero_z2226904508553997617atural ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_nonneg_nonpos
% 2.39/2.73 thf(fact_1096_mult__nonneg__nonpos,axiom,
% 2.39/2.73 ! [A: rat,B: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 2.39/2.73 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 2.39/2.73 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_nonneg_nonpos
% 2.39/2.73 thf(fact_1097_mult__nonneg__nonpos,axiom,
% 2.39/2.73 ! [A: nat,B: nat] :
% 2.39/2.73 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 2.39/2.73 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 2.39/2.73 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_nonneg_nonpos
% 2.39/2.73 thf(fact_1098_mult__nonneg__nonpos,axiom,
% 2.39/2.73 ! [A: int,B: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 2.39/2.73 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 2.39/2.73 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_nonneg_nonpos
% 2.39/2.73 thf(fact_1099_mult__nonneg__nonneg,axiom,
% 2.39/2.73 ! [A: code_integer,B: code_integer] :
% 2.39/2.73 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.73 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 2.39/2.73 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_nonneg_nonneg
% 2.39/2.73 thf(fact_1100_mult__nonneg__nonneg,axiom,
% 2.39/2.73 ! [A: code_natural,B: code_natural] :
% 2.39/2.73 ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 2.39/2.73 => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ B )
% 2.39/2.73 => ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ ( times_2397367101498566445atural @ A @ B ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_nonneg_nonneg
% 2.39/2.73 thf(fact_1101_mult__nonneg__nonneg,axiom,
% 2.39/2.73 ! [A: rat,B: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 2.39/2.73 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 2.39/2.73 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_nonneg_nonneg
% 2.39/2.73 thf(fact_1102_mult__nonneg__nonneg,axiom,
% 2.39/2.73 ! [A: nat,B: nat] :
% 2.39/2.73 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 2.39/2.73 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 2.39/2.73 => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_nonneg_nonneg
% 2.39/2.73 thf(fact_1103_mult__nonneg__nonneg,axiom,
% 2.39/2.73 ! [A: int,B: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 2.39/2.73 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 2.39/2.73 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_nonneg_nonneg
% 2.39/2.73 thf(fact_1104_split__mult__neg__le,axiom,
% 2.39/2.73 ! [A: code_integer,B: code_integer] :
% 2.39/2.73 ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.73 & ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) )
% 2.39/2.73 | ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 2.39/2.73 & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) ) )
% 2.39/2.73 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ).
% 2.39/2.73
% 2.39/2.73 % split_mult_neg_le
% 2.39/2.73 thf(fact_1105_split__mult__neg__le,axiom,
% 2.39/2.73 ! [A: code_natural,B: code_natural] :
% 2.39/2.73 ( ( ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 2.39/2.73 & ( ord_le1926595141338095240atural @ B @ zero_z2226904508553997617atural ) )
% 2.39/2.73 | ( ( ord_le1926595141338095240atural @ A @ zero_z2226904508553997617atural )
% 2.39/2.73 & ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ B ) ) )
% 2.39/2.73 => ( ord_le1926595141338095240atural @ ( times_2397367101498566445atural @ A @ B ) @ zero_z2226904508553997617atural ) ) ).
% 2.39/2.73
% 2.39/2.73 % split_mult_neg_le
% 2.39/2.73 thf(fact_1106_split__mult__neg__le,axiom,
% 2.39/2.73 ! [A: rat,B: rat] :
% 2.39/2.73 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 2.39/2.73 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 2.39/2.73 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 2.39/2.73 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) )
% 2.39/2.73 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ).
% 2.39/2.73
% 2.39/2.73 % split_mult_neg_le
% 2.39/2.73 thf(fact_1107_split__mult__neg__le,axiom,
% 2.39/2.73 ! [A: nat,B: nat] :
% 2.39/2.73 ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 2.39/2.73 & ( ord_less_eq_nat @ B @ zero_zero_nat ) )
% 2.39/2.73 | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 2.39/2.73 & ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
% 2.39/2.73 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ).
% 2.39/2.73
% 2.39/2.73 % split_mult_neg_le
% 2.39/2.73 thf(fact_1108_split__mult__neg__le,axiom,
% 2.39/2.73 ! [A: int,B: int] :
% 2.39/2.73 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 2.39/2.73 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 2.39/2.73 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 2.39/2.73 & ( ord_less_eq_int @ zero_zero_int @ B ) ) )
% 2.39/2.73 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ).
% 2.39/2.73
% 2.39/2.73 % split_mult_neg_le
% 2.39/2.73 thf(fact_1109_mult__le__0__iff,axiom,
% 2.39/2.73 ! [A: code_integer,B: code_integer] :
% 2.39/2.73 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger )
% 2.39/2.73 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.73 & ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) )
% 2.39/2.73 | ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 2.39/2.73 & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_le_0_iff
% 2.39/2.73 thf(fact_1110_mult__le__0__iff,axiom,
% 2.39/2.73 ! [A: rat,B: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 2.39/2.73 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 2.39/2.73 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 2.39/2.73 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 2.39/2.73 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_le_0_iff
% 2.39/2.73 thf(fact_1111_mult__le__0__iff,axiom,
% 2.39/2.73 ! [A: int,B: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 2.39/2.73 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 2.39/2.73 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 2.39/2.73 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 2.39/2.73 & ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_le_0_iff
% 2.39/2.73 thf(fact_1112_mult__right__mono,axiom,
% 2.39/2.73 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.73 ( ( ord_le3102999989581377725nteger @ A @ B )
% 2.39/2.73 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 2.39/2.73 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_right_mono
% 2.39/2.73 thf(fact_1113_mult__right__mono,axiom,
% 2.39/2.73 ! [A: code_natural,B: code_natural,C: code_natural] :
% 2.39/2.73 ( ( ord_le1926595141338095240atural @ A @ B )
% 2.39/2.73 => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ C )
% 2.39/2.73 => ( ord_le1926595141338095240atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ C ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_right_mono
% 2.39/2.73 thf(fact_1114_mult__right__mono,axiom,
% 2.39/2.73 ! [A: rat,B: rat,C: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ A @ B )
% 2.39/2.73 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 2.39/2.73 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_right_mono
% 2.39/2.73 thf(fact_1115_mult__right__mono,axiom,
% 2.39/2.73 ! [A: nat,B: nat,C: nat] :
% 2.39/2.73 ( ( ord_less_eq_nat @ A @ B )
% 2.39/2.73 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 2.39/2.73 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_right_mono
% 2.39/2.73 thf(fact_1116_mult__right__mono,axiom,
% 2.39/2.73 ! [A: int,B: int,C: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ A @ B )
% 2.39/2.73 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 2.39/2.73 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_right_mono
% 2.39/2.73 thf(fact_1117_mult__right__mono__neg,axiom,
% 2.39/2.73 ! [B: code_integer,A: code_integer,C: code_integer] :
% 2.39/2.73 ( ( ord_le3102999989581377725nteger @ B @ A )
% 2.39/2.73 => ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 2.39/2.73 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_right_mono_neg
% 2.39/2.73 thf(fact_1118_mult__right__mono__neg,axiom,
% 2.39/2.73 ! [B: rat,A: rat,C: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ B @ A )
% 2.39/2.73 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 2.39/2.73 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_right_mono_neg
% 2.39/2.73 thf(fact_1119_mult__right__mono__neg,axiom,
% 2.39/2.73 ! [B: int,A: int,C: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ B @ A )
% 2.39/2.73 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 2.39/2.73 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_right_mono_neg
% 2.39/2.73 thf(fact_1120_mult__left__mono,axiom,
% 2.39/2.73 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.73 ( ( ord_le3102999989581377725nteger @ A @ B )
% 2.39/2.73 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 2.39/2.73 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_left_mono
% 2.39/2.73 thf(fact_1121_mult__left__mono,axiom,
% 2.39/2.73 ! [A: code_natural,B: code_natural,C: code_natural] :
% 2.39/2.73 ( ( ord_le1926595141338095240atural @ A @ B )
% 2.39/2.73 => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ C )
% 2.39/2.73 => ( ord_le1926595141338095240atural @ ( times_2397367101498566445atural @ C @ A ) @ ( times_2397367101498566445atural @ C @ B ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_left_mono
% 2.39/2.73 thf(fact_1122_mult__left__mono,axiom,
% 2.39/2.73 ! [A: rat,B: rat,C: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ A @ B )
% 2.39/2.73 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 2.39/2.73 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_left_mono
% 2.39/2.73 thf(fact_1123_mult__left__mono,axiom,
% 2.39/2.73 ! [A: nat,B: nat,C: nat] :
% 2.39/2.73 ( ( ord_less_eq_nat @ A @ B )
% 2.39/2.73 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 2.39/2.73 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_left_mono
% 2.39/2.73 thf(fact_1124_mult__left__mono,axiom,
% 2.39/2.73 ! [A: int,B: int,C: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ A @ B )
% 2.39/2.73 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 2.39/2.73 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_left_mono
% 2.39/2.73 thf(fact_1125_mult__nonpos__nonpos,axiom,
% 2.39/2.73 ! [A: code_integer,B: code_integer] :
% 2.39/2.73 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 2.39/2.73 => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 2.39/2.73 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_nonpos_nonpos
% 2.39/2.73 thf(fact_1126_mult__nonpos__nonpos,axiom,
% 2.39/2.73 ! [A: rat,B: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 2.39/2.73 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 2.39/2.73 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_nonpos_nonpos
% 2.39/2.73 thf(fact_1127_mult__nonpos__nonpos,axiom,
% 2.39/2.73 ! [A: int,B: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 2.39/2.73 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 2.39/2.73 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_nonpos_nonpos
% 2.39/2.73 thf(fact_1128_mult__left__mono__neg,axiom,
% 2.39/2.73 ! [B: code_integer,A: code_integer,C: code_integer] :
% 2.39/2.73 ( ( ord_le3102999989581377725nteger @ B @ A )
% 2.39/2.73 => ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 2.39/2.73 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_left_mono_neg
% 2.39/2.73 thf(fact_1129_mult__left__mono__neg,axiom,
% 2.39/2.73 ! [B: rat,A: rat,C: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ B @ A )
% 2.39/2.73 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 2.39/2.73 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_left_mono_neg
% 2.39/2.73 thf(fact_1130_mult__left__mono__neg,axiom,
% 2.39/2.73 ! [B: int,A: int,C: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ B @ A )
% 2.39/2.73 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 2.39/2.73 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_left_mono_neg
% 2.39/2.73 thf(fact_1131_split__mult__pos__le,axiom,
% 2.39/2.73 ! [A: code_integer,B: code_integer] :
% 2.39/2.73 ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.73 & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) )
% 2.39/2.73 | ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 2.39/2.73 & ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 2.39/2.73 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % split_mult_pos_le
% 2.39/2.73 thf(fact_1132_split__mult__pos__le,axiom,
% 2.39/2.73 ! [A: rat,B: rat] :
% 2.39/2.73 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 2.39/2.73 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 2.39/2.73 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 2.39/2.73 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 2.39/2.73 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % split_mult_pos_le
% 2.39/2.73 thf(fact_1133_split__mult__pos__le,axiom,
% 2.39/2.73 ! [A: int,B: int] :
% 2.39/2.73 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 2.39/2.73 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 2.39/2.73 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 2.39/2.73 & ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 2.39/2.73 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % split_mult_pos_le
% 2.39/2.73 thf(fact_1134_zero__le__square,axiom,
% 2.39/2.73 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ A ) ) ).
% 2.39/2.73
% 2.39/2.73 % zero_le_square
% 2.39/2.73 thf(fact_1135_zero__le__square,axiom,
% 2.39/2.73 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ A ) ) ).
% 2.39/2.73
% 2.39/2.73 % zero_le_square
% 2.39/2.73 thf(fact_1136_zero__le__square,axiom,
% 2.39/2.73 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).
% 2.39/2.73
% 2.39/2.73 % zero_le_square
% 2.39/2.73 thf(fact_1137_mult__mono_H,axiom,
% 2.39/2.73 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 2.39/2.73 ( ( ord_le3102999989581377725nteger @ A @ B )
% 2.39/2.73 => ( ( ord_le3102999989581377725nteger @ C @ D2 )
% 2.39/2.73 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.73 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 2.39/2.73 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_mono'
% 2.39/2.73 thf(fact_1138_mult__mono_H,axiom,
% 2.39/2.73 ! [A: code_natural,B: code_natural,C: code_natural,D2: code_natural] :
% 2.39/2.73 ( ( ord_le1926595141338095240atural @ A @ B )
% 2.39/2.73 => ( ( ord_le1926595141338095240atural @ C @ D2 )
% 2.39/2.73 => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 2.39/2.73 => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ C )
% 2.39/2.73 => ( ord_le1926595141338095240atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ D2 ) ) ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_mono'
% 2.39/2.73 thf(fact_1139_mult__mono_H,axiom,
% 2.39/2.73 ! [A: rat,B: rat,C: rat,D2: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ A @ B )
% 2.39/2.73 => ( ( ord_less_eq_rat @ C @ D2 )
% 2.39/2.73 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 2.39/2.73 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 2.39/2.73 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_mono'
% 2.39/2.73 thf(fact_1140_mult__mono_H,axiom,
% 2.39/2.73 ! [A: nat,B: nat,C: nat,D2: nat] :
% 2.39/2.73 ( ( ord_less_eq_nat @ A @ B )
% 2.39/2.73 => ( ( ord_less_eq_nat @ C @ D2 )
% 2.39/2.73 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 2.39/2.73 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 2.39/2.73 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_mono'
% 2.39/2.73 thf(fact_1141_mult__mono_H,axiom,
% 2.39/2.73 ! [A: int,B: int,C: int,D2: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ A @ B )
% 2.39/2.73 => ( ( ord_less_eq_int @ C @ D2 )
% 2.39/2.73 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 2.39/2.73 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 2.39/2.73 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_mono'
% 2.39/2.73 thf(fact_1142_mult__mono,axiom,
% 2.39/2.73 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 2.39/2.73 ( ( ord_le3102999989581377725nteger @ A @ B )
% 2.39/2.73 => ( ( ord_le3102999989581377725nteger @ C @ D2 )
% 2.39/2.73 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 2.39/2.73 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 2.39/2.73 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_mono
% 2.39/2.73 thf(fact_1143_mult__mono,axiom,
% 2.39/2.73 ! [A: code_natural,B: code_natural,C: code_natural,D2: code_natural] :
% 2.39/2.73 ( ( ord_le1926595141338095240atural @ A @ B )
% 2.39/2.73 => ( ( ord_le1926595141338095240atural @ C @ D2 )
% 2.39/2.73 => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ B )
% 2.39/2.73 => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ C )
% 2.39/2.73 => ( ord_le1926595141338095240atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ D2 ) ) ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_mono
% 2.39/2.73 thf(fact_1144_mult__mono,axiom,
% 2.39/2.73 ! [A: rat,B: rat,C: rat,D2: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ A @ B )
% 2.39/2.73 => ( ( ord_less_eq_rat @ C @ D2 )
% 2.39/2.73 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 2.39/2.73 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 2.39/2.73 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_mono
% 2.39/2.73 thf(fact_1145_mult__mono,axiom,
% 2.39/2.73 ! [A: nat,B: nat,C: nat,D2: nat] :
% 2.39/2.73 ( ( ord_less_eq_nat @ A @ B )
% 2.39/2.73 => ( ( ord_less_eq_nat @ C @ D2 )
% 2.39/2.73 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 2.39/2.73 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 2.39/2.73 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_mono
% 2.39/2.73 thf(fact_1146_mult__mono,axiom,
% 2.39/2.73 ! [A: int,B: int,C: int,D2: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ A @ B )
% 2.39/2.73 => ( ( ord_less_eq_int @ C @ D2 )
% 2.39/2.73 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 2.39/2.73 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 2.39/2.73 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_mono
% 2.39/2.73 thf(fact_1147_not__one__le__zero,axiom,
% 2.39/2.73 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ).
% 2.39/2.73
% 2.39/2.73 % not_one_le_zero
% 2.39/2.73 thf(fact_1148_not__one__le__zero,axiom,
% 2.39/2.73 ~ ( ord_le1926595141338095240atural @ one_one_Code_natural @ zero_z2226904508553997617atural ) ).
% 2.39/2.73
% 2.39/2.73 % not_one_le_zero
% 2.39/2.73 thf(fact_1149_not__one__le__zero,axiom,
% 2.39/2.73 ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 2.39/2.73
% 2.39/2.73 % not_one_le_zero
% 2.39/2.73 thf(fact_1150_not__one__le__zero,axiom,
% 2.39/2.73 ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 2.39/2.73
% 2.39/2.73 % not_one_le_zero
% 2.39/2.73 thf(fact_1151_not__one__le__zero,axiom,
% 2.39/2.73 ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 2.39/2.73
% 2.39/2.73 % not_one_le_zero
% 2.39/2.73 thf(fact_1152_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 2.39/2.73 ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 2.39/2.73
% 2.39/2.73 % linordered_nonzero_semiring_class.zero_le_one
% 2.39/2.73 thf(fact_1153_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 2.39/2.73 ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ one_one_Code_natural ).
% 2.39/2.73
% 2.39/2.73 % linordered_nonzero_semiring_class.zero_le_one
% 2.39/2.73 thf(fact_1154_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 2.39/2.73 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 2.39/2.73
% 2.39/2.73 % linordered_nonzero_semiring_class.zero_le_one
% 2.39/2.73 thf(fact_1155_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 2.39/2.73 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 2.39/2.73
% 2.39/2.73 % linordered_nonzero_semiring_class.zero_le_one
% 2.39/2.73 thf(fact_1156_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 2.39/2.73 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 2.39/2.73
% 2.39/2.73 % linordered_nonzero_semiring_class.zero_le_one
% 2.39/2.73 thf(fact_1157_zero__less__one__class_Ozero__le__one,axiom,
% 2.39/2.73 ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 2.39/2.73
% 2.39/2.73 % zero_less_one_class.zero_le_one
% 2.39/2.73 thf(fact_1158_zero__less__one__class_Ozero__le__one,axiom,
% 2.39/2.73 ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ one_one_Code_natural ).
% 2.39/2.73
% 2.39/2.73 % zero_less_one_class.zero_le_one
% 2.39/2.73 thf(fact_1159_zero__less__one__class_Ozero__le__one,axiom,
% 2.39/2.73 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 2.39/2.73
% 2.39/2.73 % zero_less_one_class.zero_le_one
% 2.39/2.73 thf(fact_1160_zero__less__one__class_Ozero__le__one,axiom,
% 2.39/2.73 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 2.39/2.73
% 2.39/2.73 % zero_less_one_class.zero_le_one
% 2.39/2.73 thf(fact_1161_zero__less__one__class_Ozero__le__one,axiom,
% 2.39/2.73 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 2.39/2.73
% 2.39/2.73 % zero_less_one_class.zero_le_one
% 2.39/2.73 thf(fact_1162_mult__left__le,axiom,
% 2.39/2.73 ! [C: code_integer,A: code_integer] :
% 2.39/2.73 ( ( ord_le3102999989581377725nteger @ C @ one_one_Code_integer )
% 2.39/2.73 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.73 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ A ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_left_le
% 2.39/2.73 thf(fact_1163_mult__left__le,axiom,
% 2.39/2.73 ! [C: code_natural,A: code_natural] :
% 2.39/2.73 ( ( ord_le1926595141338095240atural @ C @ one_one_Code_natural )
% 2.39/2.73 => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 2.39/2.73 => ( ord_le1926595141338095240atural @ ( times_2397367101498566445atural @ A @ C ) @ A ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_left_le
% 2.39/2.73 thf(fact_1164_mult__left__le,axiom,
% 2.39/2.73 ! [C: rat,A: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ C @ one_one_rat )
% 2.39/2.73 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 2.39/2.73 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ A ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_left_le
% 2.39/2.73 thf(fact_1165_mult__left__le,axiom,
% 2.39/2.73 ! [C: nat,A: nat] :
% 2.39/2.73 ( ( ord_less_eq_nat @ C @ one_one_nat )
% 2.39/2.73 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 2.39/2.73 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ A ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_left_le
% 2.39/2.73 thf(fact_1166_mult__left__le,axiom,
% 2.39/2.73 ! [C: int,A: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ C @ one_one_int )
% 2.39/2.73 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 2.39/2.73 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ A ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_left_le
% 2.39/2.73 thf(fact_1167_mult__le__one,axiom,
% 2.39/2.73 ! [A: code_integer,B: code_integer] :
% 2.39/2.73 ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 2.39/2.73 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 2.39/2.73 => ( ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer )
% 2.39/2.73 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_le_one
% 2.39/2.73 thf(fact_1168_mult__le__one,axiom,
% 2.39/2.73 ! [A: code_natural,B: code_natural] :
% 2.39/2.73 ( ( ord_le1926595141338095240atural @ A @ one_one_Code_natural )
% 2.39/2.73 => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ B )
% 2.39/2.73 => ( ( ord_le1926595141338095240atural @ B @ one_one_Code_natural )
% 2.39/2.73 => ( ord_le1926595141338095240atural @ ( times_2397367101498566445atural @ A @ B ) @ one_one_Code_natural ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_le_one
% 2.39/2.73 thf(fact_1169_mult__le__one,axiom,
% 2.39/2.73 ! [A: rat,B: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ A @ one_one_rat )
% 2.39/2.73 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 2.39/2.73 => ( ( ord_less_eq_rat @ B @ one_one_rat )
% 2.39/2.73 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ one_one_rat ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_le_one
% 2.39/2.73 thf(fact_1170_mult__le__one,axiom,
% 2.39/2.73 ! [A: nat,B: nat] :
% 2.39/2.73 ( ( ord_less_eq_nat @ A @ one_one_nat )
% 2.39/2.73 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 2.39/2.73 => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 2.39/2.73 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_le_one
% 2.39/2.73 thf(fact_1171_mult__le__one,axiom,
% 2.39/2.73 ! [A: int,B: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ A @ one_one_int )
% 2.39/2.73 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 2.39/2.73 => ( ( ord_less_eq_int @ B @ one_one_int )
% 2.39/2.73 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_le_one
% 2.39/2.73 thf(fact_1172_mult__right__le__one__le,axiom,
% 2.39/2.73 ! [X: code_integer,Y: code_integer] :
% 2.39/2.73 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 2.39/2.73 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 2.39/2.73 => ( ( ord_le3102999989581377725nteger @ Y @ one_one_Code_integer )
% 2.39/2.73 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ X @ Y ) @ X ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_right_le_one_le
% 2.39/2.73 thf(fact_1173_mult__right__le__one__le,axiom,
% 2.39/2.73 ! [X: rat,Y: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 2.39/2.73 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 2.39/2.73 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 2.39/2.73 => ( ord_less_eq_rat @ ( times_times_rat @ X @ Y ) @ X ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_right_le_one_le
% 2.39/2.73 thf(fact_1174_mult__right__le__one__le,axiom,
% 2.39/2.73 ! [X: int,Y: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 2.39/2.73 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 2.39/2.73 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 2.39/2.73 => ( ord_less_eq_int @ ( times_times_int @ X @ Y ) @ X ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_right_le_one_le
% 2.39/2.73 thf(fact_1175_mult__left__le__one__le,axiom,
% 2.39/2.73 ! [X: code_integer,Y: code_integer] :
% 2.39/2.73 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 2.39/2.73 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 2.39/2.73 => ( ( ord_le3102999989581377725nteger @ Y @ one_one_Code_integer )
% 2.39/2.73 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ Y @ X ) @ X ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_left_le_one_le
% 2.39/2.73 thf(fact_1176_mult__left__le__one__le,axiom,
% 2.39/2.73 ! [X: rat,Y: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 2.39/2.73 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 2.39/2.73 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 2.39/2.73 => ( ord_less_eq_rat @ ( times_times_rat @ Y @ X ) @ X ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_left_le_one_le
% 2.39/2.73 thf(fact_1177_mult__left__le__one__le,axiom,
% 2.39/2.73 ! [X: int,Y: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 2.39/2.73 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 2.39/2.73 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 2.39/2.73 => ( ord_less_eq_int @ ( times_times_int @ Y @ X ) @ X ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % mult_left_le_one_le
% 2.39/2.73 thf(fact_1178_le__minus__one__simps_I1_J,axiom,
% 2.39/2.73 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 2.39/2.73
% 2.39/2.73 % le_minus_one_simps(1)
% 2.39/2.73 thf(fact_1179_le__minus__one__simps_I1_J,axiom,
% 2.39/2.73 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 2.39/2.73
% 2.39/2.73 % le_minus_one_simps(1)
% 2.39/2.73 thf(fact_1180_le__minus__one__simps_I1_J,axiom,
% 2.39/2.73 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 2.39/2.73
% 2.39/2.73 % le_minus_one_simps(1)
% 2.39/2.73 thf(fact_1181_le__minus__one__simps_I3_J,axiom,
% 2.39/2.73 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_minus_one_simps(3)
% 2.39/2.73 thf(fact_1182_le__minus__one__simps_I3_J,axiom,
% 2.39/2.73 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_minus_one_simps(3)
% 2.39/2.73 thf(fact_1183_le__minus__one__simps_I3_J,axiom,
% 2.39/2.73 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_minus_one_simps(3)
% 2.39/2.73 thf(fact_1184_list_Osimps_I8_J,axiom,
% 2.39/2.73 ! [F2: produc6575502325842934193n_assn > produc6575502325842934193n_assn] :
% 2.39/2.73 ( ( map_Pr7925354932063753860n_assn @ F2 @ nil_Pr5671120429643327159n_assn )
% 2.39/2.73 = nil_Pr5671120429643327159n_assn ) ).
% 2.39/2.73
% 2.39/2.73 % list.simps(8)
% 2.39/2.73 thf(fact_1185_list_Osimps_I8_J,axiom,
% 2.39/2.73 ! [F2: produc6575502325842934193n_assn > int] :
% 2.39/2.73 ( ( map_Pr7568062423562401049sn_int @ F2 @ nil_Pr5671120429643327159n_assn )
% 2.39/2.73 = nil_int ) ).
% 2.39/2.73
% 2.39/2.73 % list.simps(8)
% 2.39/2.73 thf(fact_1186_list_Osimps_I8_J,axiom,
% 2.39/2.73 ! [F2: produc6575502325842934193n_assn > nat] :
% 2.39/2.73 ( ( map_Pr7570552894071451325sn_nat @ F2 @ nil_Pr5671120429643327159n_assn )
% 2.39/2.73 = nil_nat ) ).
% 2.39/2.73
% 2.39/2.73 % list.simps(8)
% 2.39/2.73 thf(fact_1187_list_Osimps_I8_J,axiom,
% 2.39/2.73 ! [F2: int > produc6575502325842934193n_assn] :
% 2.39/2.73 ( ( map_in4427992030928829247n_assn @ F2 @ nil_int )
% 2.39/2.73 = nil_Pr5671120429643327159n_assn ) ).
% 2.39/2.73
% 2.39/2.73 % list.simps(8)
% 2.39/2.73 thf(fact_1188_list_Osimps_I8_J,axiom,
% 2.39/2.73 ! [F2: int > int] :
% 2.39/2.73 ( ( map_int_int @ F2 @ nil_int )
% 2.39/2.73 = nil_int ) ).
% 2.39/2.73
% 2.39/2.73 % list.simps(8)
% 2.39/2.73 thf(fact_1189_list_Osimps_I8_J,axiom,
% 2.39/2.73 ! [F2: int > nat] :
% 2.39/2.73 ( ( map_int_nat @ F2 @ nil_int )
% 2.39/2.73 = nil_nat ) ).
% 2.39/2.73
% 2.39/2.73 % list.simps(8)
% 2.39/2.73 thf(fact_1190_list_Osimps_I8_J,axiom,
% 2.39/2.73 ! [F2: nat > produc6575502325842934193n_assn] :
% 2.39/2.73 ( ( map_na2667955367175718043n_assn @ F2 @ nil_nat )
% 2.39/2.73 = nil_Pr5671120429643327159n_assn ) ).
% 2.39/2.73
% 2.39/2.73 % list.simps(8)
% 2.39/2.73 thf(fact_1191_list_Osimps_I8_J,axiom,
% 2.39/2.73 ! [F2: nat > int] :
% 2.39/2.73 ( ( map_nat_int @ F2 @ nil_nat )
% 2.39/2.73 = nil_int ) ).
% 2.39/2.73
% 2.39/2.73 % list.simps(8)
% 2.39/2.73 thf(fact_1192_list_Osimps_I8_J,axiom,
% 2.39/2.73 ! [F2: nat > nat] :
% 2.39/2.73 ( ( map_nat_nat @ F2 @ nil_nat )
% 2.39/2.73 = nil_nat ) ).
% 2.39/2.73
% 2.39/2.73 % list.simps(8)
% 2.39/2.73 thf(fact_1193_list_Osimps_I8_J,axiom,
% 2.39/2.73 ! [F2: produc6575502325842934193n_assn > assn] :
% 2.39/2.73 ( ( map_Pr8991440229025900053n_assn @ F2 @ nil_Pr5671120429643327159n_assn )
% 2.39/2.73 = nil_assn ) ).
% 2.39/2.73
% 2.39/2.73 % list.simps(8)
% 2.39/2.73 thf(fact_1194_le__numeral__extra_I4_J,axiom,
% 2.39/2.73 ord_le3102999989581377725nteger @ one_one_Code_integer @ one_one_Code_integer ).
% 2.39/2.73
% 2.39/2.73 % le_numeral_extra(4)
% 2.39/2.73 thf(fact_1195_le__numeral__extra_I4_J,axiom,
% 2.39/2.73 ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 2.39/2.73
% 2.39/2.73 % le_numeral_extra(4)
% 2.39/2.73 thf(fact_1196_le__numeral__extra_I4_J,axiom,
% 2.39/2.73 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 2.39/2.73
% 2.39/2.73 % le_numeral_extra(4)
% 2.39/2.73 thf(fact_1197_le__numeral__extra_I4_J,axiom,
% 2.39/2.73 ord_less_eq_int @ one_one_int @ one_one_int ).
% 2.39/2.73
% 2.39/2.73 % le_numeral_extra(4)
% 2.39/2.73 thf(fact_1198_pure__assn__raw_Ocases,axiom,
% 2.39/2.73 ! [X: produc6197004810343482825et_nat] :
% 2.39/2.73 ~ ! [B5: $o,H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.39/2.73 ( X
% 2.39/2.73 != ( produc3762353314782720579et_nat @ B5 @ ( produc7507926704131184380et_nat @ H3 @ As ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % pure_assn_raw.cases
% 2.39/2.73 thf(fact_1199_le__minus__iff,axiom,
% 2.39/2.73 ! [A: code_integer,B: code_integer] :
% 2.39/2.73 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 2.39/2.73 = ( ord_le3102999989581377725nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_minus_iff
% 2.39/2.73 thf(fact_1200_le__minus__iff,axiom,
% 2.39/2.73 ! [A: rat,B: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ B ) )
% 2.39/2.73 = ( ord_less_eq_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_minus_iff
% 2.39/2.73 thf(fact_1201_le__minus__iff,axiom,
% 2.39/2.73 ! [A: int,B: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 2.39/2.73 = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_minus_iff
% 2.39/2.73 thf(fact_1202_minus__le__iff,axiom,
% 2.39/2.73 ! [A: code_integer,B: code_integer] :
% 2.39/2.73 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 2.39/2.73 = ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 2.39/2.73
% 2.39/2.73 % minus_le_iff
% 2.39/2.73 thf(fact_1203_minus__le__iff,axiom,
% 2.39/2.73 ! [A: rat,B: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 2.39/2.73 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 2.39/2.73
% 2.39/2.73 % minus_le_iff
% 2.39/2.73 thf(fact_1204_minus__le__iff,axiom,
% 2.39/2.73 ! [A: int,B: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 2.39/2.73 = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 2.39/2.73
% 2.39/2.73 % minus_le_iff
% 2.39/2.73 thf(fact_1205_le__imp__neg__le,axiom,
% 2.39/2.73 ! [A: code_integer,B: code_integer] :
% 2.39/2.73 ( ( ord_le3102999989581377725nteger @ A @ B )
% 2.39/2.73 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_imp_neg_le
% 2.39/2.73 thf(fact_1206_le__imp__neg__le,axiom,
% 2.39/2.73 ! [A: rat,B: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ A @ B )
% 2.39/2.73 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_imp_neg_le
% 2.39/2.73 thf(fact_1207_le__imp__neg__le,axiom,
% 2.39/2.73 ! [A: int,B: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ A @ B )
% 2.39/2.73 => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_imp_neg_le
% 2.39/2.73 thf(fact_1208_inf_OcoboundedI2,axiom,
% 2.39/2.73 ! [B: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 2.39/2.73 ( ( ord_le3146513528884898305at_nat @ B @ C )
% 2.39/2.73 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ C ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.coboundedI2
% 2.39/2.73 thf(fact_1209_inf_OcoboundedI2,axiom,
% 2.39/2.73 ! [B: product_prod_int_int > $o,C: product_prod_int_int > $o,A: product_prod_int_int > $o] :
% 2.39/2.73 ( ( ord_le8369615600986905444_int_o @ B @ C )
% 2.39/2.73 => ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ C ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.coboundedI2
% 2.39/2.73 thf(fact_1210_inf_OcoboundedI2,axiom,
% 2.39/2.73 ! [B: assn,C: assn,A: assn] :
% 2.39/2.73 ( ( ord_less_eq_assn @ B @ C )
% 2.39/2.73 => ( ord_less_eq_assn @ ( inf_inf_assn @ A @ B ) @ C ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.coboundedI2
% 2.39/2.73 thf(fact_1211_inf_OcoboundedI2,axiom,
% 2.39/2.73 ! [B: set_nat,C: set_nat,A: set_nat] :
% 2.39/2.73 ( ( ord_less_eq_set_nat @ B @ C )
% 2.39/2.73 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ C ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.coboundedI2
% 2.39/2.73 thf(fact_1212_inf_OcoboundedI2,axiom,
% 2.39/2.73 ! [B: rat,C: rat,A: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ B @ C )
% 2.39/2.73 => ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ C ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.coboundedI2
% 2.39/2.73 thf(fact_1213_inf_OcoboundedI2,axiom,
% 2.39/2.73 ! [B: nat,C: nat,A: nat] :
% 2.39/2.73 ( ( ord_less_eq_nat @ B @ C )
% 2.39/2.73 => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ C ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.coboundedI2
% 2.39/2.73 thf(fact_1214_inf_OcoboundedI2,axiom,
% 2.39/2.73 ! [B: int,C: int,A: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ B @ C )
% 2.39/2.73 => ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ C ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.coboundedI2
% 2.39/2.73 thf(fact_1215_inf_OcoboundedI1,axiom,
% 2.39/2.73 ! [A: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.39/2.73 ( ( ord_le3146513528884898305at_nat @ A @ C )
% 2.39/2.73 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ C ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.coboundedI1
% 2.39/2.73 thf(fact_1216_inf_OcoboundedI1,axiom,
% 2.39/2.73 ! [A: product_prod_int_int > $o,C: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 2.39/2.73 ( ( ord_le8369615600986905444_int_o @ A @ C )
% 2.39/2.73 => ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ C ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.coboundedI1
% 2.39/2.73 thf(fact_1217_inf_OcoboundedI1,axiom,
% 2.39/2.73 ! [A: assn,C: assn,B: assn] :
% 2.39/2.73 ( ( ord_less_eq_assn @ A @ C )
% 2.39/2.73 => ( ord_less_eq_assn @ ( inf_inf_assn @ A @ B ) @ C ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.coboundedI1
% 2.39/2.73 thf(fact_1218_inf_OcoboundedI1,axiom,
% 2.39/2.73 ! [A: set_nat,C: set_nat,B: set_nat] :
% 2.39/2.73 ( ( ord_less_eq_set_nat @ A @ C )
% 2.39/2.73 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ C ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.coboundedI1
% 2.39/2.73 thf(fact_1219_inf_OcoboundedI1,axiom,
% 2.39/2.73 ! [A: rat,C: rat,B: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ A @ C )
% 2.39/2.73 => ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ C ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.coboundedI1
% 2.39/2.73 thf(fact_1220_inf_OcoboundedI1,axiom,
% 2.39/2.73 ! [A: nat,C: nat,B: nat] :
% 2.39/2.73 ( ( ord_less_eq_nat @ A @ C )
% 2.39/2.73 => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ C ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.coboundedI1
% 2.39/2.73 thf(fact_1221_inf_OcoboundedI1,axiom,
% 2.39/2.73 ! [A: int,C: int,B: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ A @ C )
% 2.39/2.73 => ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ C ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.coboundedI1
% 2.39/2.73 thf(fact_1222_inf_Oabsorb__iff2,axiom,
% 2.39/2.73 ( ord_le3146513528884898305at_nat
% 2.39/2.73 = ( ^ [B2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
% 2.39/2.73 ( ( inf_in2572325071724192079at_nat @ A2 @ B2 )
% 2.39/2.73 = B2 ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.absorb_iff2
% 2.39/2.73 thf(fact_1223_inf_Oabsorb__iff2,axiom,
% 2.39/2.73 ( ord_le8369615600986905444_int_o
% 2.39/2.73 = ( ^ [B2: product_prod_int_int > $o,A2: product_prod_int_int > $o] :
% 2.39/2.73 ( ( inf_in3604695632404883862_int_o @ A2 @ B2 )
% 2.39/2.73 = B2 ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.absorb_iff2
% 2.39/2.73 thf(fact_1224_inf_Oabsorb__iff2,axiom,
% 2.39/2.73 ( ord_less_eq_assn
% 2.39/2.73 = ( ^ [B2: assn,A2: assn] :
% 2.39/2.73 ( ( inf_inf_assn @ A2 @ B2 )
% 2.39/2.73 = B2 ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.absorb_iff2
% 2.39/2.73 thf(fact_1225_inf_Oabsorb__iff2,axiom,
% 2.39/2.73 ( ord_less_eq_set_nat
% 2.39/2.73 = ( ^ [B2: set_nat,A2: set_nat] :
% 2.39/2.73 ( ( inf_inf_set_nat @ A2 @ B2 )
% 2.39/2.73 = B2 ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.absorb_iff2
% 2.39/2.73 thf(fact_1226_inf_Oabsorb__iff2,axiom,
% 2.39/2.73 ( ord_less_eq_rat
% 2.39/2.73 = ( ^ [B2: rat,A2: rat] :
% 2.39/2.73 ( ( inf_inf_rat @ A2 @ B2 )
% 2.39/2.73 = B2 ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.absorb_iff2
% 2.39/2.73 thf(fact_1227_inf_Oabsorb__iff2,axiom,
% 2.39/2.73 ( ord_less_eq_nat
% 2.39/2.73 = ( ^ [B2: nat,A2: nat] :
% 2.39/2.73 ( ( inf_inf_nat @ A2 @ B2 )
% 2.39/2.73 = B2 ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.absorb_iff2
% 2.39/2.73 thf(fact_1228_inf_Oabsorb__iff2,axiom,
% 2.39/2.73 ( ord_less_eq_int
% 2.39/2.73 = ( ^ [B2: int,A2: int] :
% 2.39/2.73 ( ( inf_inf_int @ A2 @ B2 )
% 2.39/2.73 = B2 ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.absorb_iff2
% 2.39/2.73 thf(fact_1229_inf_Oabsorb__iff1,axiom,
% 2.39/2.73 ( ord_le3146513528884898305at_nat
% 2.39/2.73 = ( ^ [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 2.39/2.73 ( ( inf_in2572325071724192079at_nat @ A2 @ B2 )
% 2.39/2.73 = A2 ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.absorb_iff1
% 2.39/2.73 thf(fact_1230_inf_Oabsorb__iff1,axiom,
% 2.39/2.73 ( ord_le8369615600986905444_int_o
% 2.39/2.73 = ( ^ [A2: product_prod_int_int > $o,B2: product_prod_int_int > $o] :
% 2.39/2.73 ( ( inf_in3604695632404883862_int_o @ A2 @ B2 )
% 2.39/2.73 = A2 ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.absorb_iff1
% 2.39/2.73 thf(fact_1231_inf_Oabsorb__iff1,axiom,
% 2.39/2.73 ( ord_less_eq_assn
% 2.39/2.73 = ( ^ [A2: assn,B2: assn] :
% 2.39/2.73 ( ( inf_inf_assn @ A2 @ B2 )
% 2.39/2.73 = A2 ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.absorb_iff1
% 2.39/2.73 thf(fact_1232_inf_Oabsorb__iff1,axiom,
% 2.39/2.73 ( ord_less_eq_set_nat
% 2.39/2.73 = ( ^ [A2: set_nat,B2: set_nat] :
% 2.39/2.73 ( ( inf_inf_set_nat @ A2 @ B2 )
% 2.39/2.73 = A2 ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.absorb_iff1
% 2.39/2.73 thf(fact_1233_inf_Oabsorb__iff1,axiom,
% 2.39/2.73 ( ord_less_eq_rat
% 2.39/2.73 = ( ^ [A2: rat,B2: rat] :
% 2.39/2.73 ( ( inf_inf_rat @ A2 @ B2 )
% 2.39/2.73 = A2 ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.absorb_iff1
% 2.39/2.73 thf(fact_1234_inf_Oabsorb__iff1,axiom,
% 2.39/2.73 ( ord_less_eq_nat
% 2.39/2.73 = ( ^ [A2: nat,B2: nat] :
% 2.39/2.73 ( ( inf_inf_nat @ A2 @ B2 )
% 2.39/2.73 = A2 ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.absorb_iff1
% 2.39/2.73 thf(fact_1235_inf_Oabsorb__iff1,axiom,
% 2.39/2.73 ( ord_less_eq_int
% 2.39/2.73 = ( ^ [A2: int,B2: int] :
% 2.39/2.73 ( ( inf_inf_int @ A2 @ B2 )
% 2.39/2.73 = A2 ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.absorb_iff1
% 2.39/2.73 thf(fact_1236_inf_Ocobounded2,axiom,
% 2.39/2.73 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ B ) ).
% 2.39/2.73
% 2.39/2.73 % inf.cobounded2
% 2.39/2.73 thf(fact_1237_inf_Ocobounded2,axiom,
% 2.39/2.73 ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o] : ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ B ) ).
% 2.39/2.73
% 2.39/2.73 % inf.cobounded2
% 2.39/2.73 thf(fact_1238_inf_Ocobounded2,axiom,
% 2.39/2.73 ! [A: assn,B: assn] : ( ord_less_eq_assn @ ( inf_inf_assn @ A @ B ) @ B ) ).
% 2.39/2.73
% 2.39/2.73 % inf.cobounded2
% 2.39/2.73 thf(fact_1239_inf_Ocobounded2,axiom,
% 2.39/2.73 ! [A: set_nat,B: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ B ) ).
% 2.39/2.73
% 2.39/2.73 % inf.cobounded2
% 2.39/2.73 thf(fact_1240_inf_Ocobounded2,axiom,
% 2.39/2.73 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ B ) ).
% 2.39/2.73
% 2.39/2.73 % inf.cobounded2
% 2.39/2.73 thf(fact_1241_inf_Ocobounded2,axiom,
% 2.39/2.73 ! [A: nat,B: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ B ) ).
% 2.39/2.73
% 2.39/2.73 % inf.cobounded2
% 2.39/2.73 thf(fact_1242_inf_Ocobounded2,axiom,
% 2.39/2.73 ! [A: int,B: int] : ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ B ) ).
% 2.39/2.73
% 2.39/2.73 % inf.cobounded2
% 2.39/2.73 thf(fact_1243_inf_Ocobounded1,axiom,
% 2.39/2.73 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ A ) ).
% 2.39/2.73
% 2.39/2.73 % inf.cobounded1
% 2.39/2.73 thf(fact_1244_inf_Ocobounded1,axiom,
% 2.39/2.73 ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o] : ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ A ) ).
% 2.39/2.73
% 2.39/2.73 % inf.cobounded1
% 2.39/2.73 thf(fact_1245_inf_Ocobounded1,axiom,
% 2.39/2.73 ! [A: assn,B: assn] : ( ord_less_eq_assn @ ( inf_inf_assn @ A @ B ) @ A ) ).
% 2.39/2.73
% 2.39/2.73 % inf.cobounded1
% 2.39/2.73 thf(fact_1246_inf_Ocobounded1,axiom,
% 2.39/2.73 ! [A: set_nat,B: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ A ) ).
% 2.39/2.73
% 2.39/2.73 % inf.cobounded1
% 2.39/2.73 thf(fact_1247_inf_Ocobounded1,axiom,
% 2.39/2.73 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ A ) ).
% 2.39/2.73
% 2.39/2.73 % inf.cobounded1
% 2.39/2.73 thf(fact_1248_inf_Ocobounded1,axiom,
% 2.39/2.73 ! [A: nat,B: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ A ) ).
% 2.39/2.73
% 2.39/2.73 % inf.cobounded1
% 2.39/2.73 thf(fact_1249_inf_Ocobounded1,axiom,
% 2.39/2.73 ! [A: int,B: int] : ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ A ) ).
% 2.39/2.73
% 2.39/2.73 % inf.cobounded1
% 2.39/2.73 thf(fact_1250_inf_Oorder__iff,axiom,
% 2.39/2.73 ( ord_le3146513528884898305at_nat
% 2.39/2.73 = ( ^ [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 2.39/2.73 ( A2
% 2.39/2.73 = ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.order_iff
% 2.39/2.73 thf(fact_1251_inf_Oorder__iff,axiom,
% 2.39/2.73 ( ord_le8369615600986905444_int_o
% 2.39/2.73 = ( ^ [A2: product_prod_int_int > $o,B2: product_prod_int_int > $o] :
% 2.39/2.73 ( A2
% 2.39/2.73 = ( inf_in3604695632404883862_int_o @ A2 @ B2 ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.order_iff
% 2.39/2.73 thf(fact_1252_inf_Oorder__iff,axiom,
% 2.39/2.73 ( ord_less_eq_assn
% 2.39/2.73 = ( ^ [A2: assn,B2: assn] :
% 2.39/2.73 ( A2
% 2.39/2.73 = ( inf_inf_assn @ A2 @ B2 ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.order_iff
% 2.39/2.73 thf(fact_1253_inf_Oorder__iff,axiom,
% 2.39/2.73 ( ord_less_eq_set_nat
% 2.39/2.73 = ( ^ [A2: set_nat,B2: set_nat] :
% 2.39/2.73 ( A2
% 2.39/2.73 = ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.order_iff
% 2.39/2.73 thf(fact_1254_inf_Oorder__iff,axiom,
% 2.39/2.73 ( ord_less_eq_rat
% 2.39/2.73 = ( ^ [A2: rat,B2: rat] :
% 2.39/2.73 ( A2
% 2.39/2.73 = ( inf_inf_rat @ A2 @ B2 ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.order_iff
% 2.39/2.73 thf(fact_1255_inf_Oorder__iff,axiom,
% 2.39/2.73 ( ord_less_eq_nat
% 2.39/2.73 = ( ^ [A2: nat,B2: nat] :
% 2.39/2.73 ( A2
% 2.39/2.73 = ( inf_inf_nat @ A2 @ B2 ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.order_iff
% 2.39/2.73 thf(fact_1256_inf_Oorder__iff,axiom,
% 2.39/2.73 ( ord_less_eq_int
% 2.39/2.73 = ( ^ [A2: int,B2: int] :
% 2.39/2.73 ( A2
% 2.39/2.73 = ( inf_inf_int @ A2 @ B2 ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.order_iff
% 2.39/2.73 thf(fact_1257_inf__greatest,axiom,
% 2.39/2.73 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 2.39/2.73 ( ( ord_le3146513528884898305at_nat @ X @ Y )
% 2.39/2.73 => ( ( ord_le3146513528884898305at_nat @ X @ Z )
% 2.39/2.73 => ( ord_le3146513528884898305at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf_greatest
% 2.39/2.73 thf(fact_1258_inf__greatest,axiom,
% 2.39/2.73 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 2.39/2.73 ( ( ord_le8369615600986905444_int_o @ X @ Y )
% 2.39/2.73 => ( ( ord_le8369615600986905444_int_o @ X @ Z )
% 2.39/2.73 => ( ord_le8369615600986905444_int_o @ X @ ( inf_in3604695632404883862_int_o @ Y @ Z ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf_greatest
% 2.39/2.73 thf(fact_1259_inf__greatest,axiom,
% 2.39/2.73 ! [X: assn,Y: assn,Z: assn] :
% 2.39/2.73 ( ( ord_less_eq_assn @ X @ Y )
% 2.39/2.73 => ( ( ord_less_eq_assn @ X @ Z )
% 2.39/2.73 => ( ord_less_eq_assn @ X @ ( inf_inf_assn @ Y @ Z ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf_greatest
% 2.39/2.73 thf(fact_1260_inf__greatest,axiom,
% 2.39/2.73 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 2.39/2.73 ( ( ord_less_eq_set_nat @ X @ Y )
% 2.39/2.73 => ( ( ord_less_eq_set_nat @ X @ Z )
% 2.39/2.73 => ( ord_less_eq_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf_greatest
% 2.39/2.73 thf(fact_1261_inf__greatest,axiom,
% 2.39/2.73 ! [X: rat,Y: rat,Z: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ X @ Y )
% 2.39/2.73 => ( ( ord_less_eq_rat @ X @ Z )
% 2.39/2.73 => ( ord_less_eq_rat @ X @ ( inf_inf_rat @ Y @ Z ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf_greatest
% 2.39/2.73 thf(fact_1262_inf__greatest,axiom,
% 2.39/2.73 ! [X: nat,Y: nat,Z: nat] :
% 2.39/2.73 ( ( ord_less_eq_nat @ X @ Y )
% 2.39/2.73 => ( ( ord_less_eq_nat @ X @ Z )
% 2.39/2.73 => ( ord_less_eq_nat @ X @ ( inf_inf_nat @ Y @ Z ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf_greatest
% 2.39/2.73 thf(fact_1263_inf__greatest,axiom,
% 2.39/2.73 ! [X: int,Y: int,Z: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ X @ Y )
% 2.39/2.73 => ( ( ord_less_eq_int @ X @ Z )
% 2.39/2.73 => ( ord_less_eq_int @ X @ ( inf_inf_int @ Y @ Z ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf_greatest
% 2.39/2.73 thf(fact_1264_inf_OboundedI,axiom,
% 2.39/2.73 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat] :
% 2.39/2.73 ( ( ord_le3146513528884898305at_nat @ A @ B )
% 2.39/2.73 => ( ( ord_le3146513528884898305at_nat @ A @ C )
% 2.39/2.73 => ( ord_le3146513528884898305at_nat @ A @ ( inf_in2572325071724192079at_nat @ B @ C ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.boundedI
% 2.39/2.73 thf(fact_1265_inf_OboundedI,axiom,
% 2.39/2.73 ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o,C: product_prod_int_int > $o] :
% 2.39/2.73 ( ( ord_le8369615600986905444_int_o @ A @ B )
% 2.39/2.73 => ( ( ord_le8369615600986905444_int_o @ A @ C )
% 2.39/2.73 => ( ord_le8369615600986905444_int_o @ A @ ( inf_in3604695632404883862_int_o @ B @ C ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.boundedI
% 2.39/2.73 thf(fact_1266_inf_OboundedI,axiom,
% 2.39/2.73 ! [A: assn,B: assn,C: assn] :
% 2.39/2.73 ( ( ord_less_eq_assn @ A @ B )
% 2.39/2.73 => ( ( ord_less_eq_assn @ A @ C )
% 2.39/2.73 => ( ord_less_eq_assn @ A @ ( inf_inf_assn @ B @ C ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.boundedI
% 2.39/2.73 thf(fact_1267_inf_OboundedI,axiom,
% 2.39/2.73 ! [A: set_nat,B: set_nat,C: set_nat] :
% 2.39/2.73 ( ( ord_less_eq_set_nat @ A @ B )
% 2.39/2.73 => ( ( ord_less_eq_set_nat @ A @ C )
% 2.39/2.73 => ( ord_less_eq_set_nat @ A @ ( inf_inf_set_nat @ B @ C ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.boundedI
% 2.39/2.73 thf(fact_1268_inf_OboundedI,axiom,
% 2.39/2.73 ! [A: rat,B: rat,C: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ A @ B )
% 2.39/2.73 => ( ( ord_less_eq_rat @ A @ C )
% 2.39/2.73 => ( ord_less_eq_rat @ A @ ( inf_inf_rat @ B @ C ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.boundedI
% 2.39/2.73 thf(fact_1269_inf_OboundedI,axiom,
% 2.39/2.73 ! [A: nat,B: nat,C: nat] :
% 2.39/2.73 ( ( ord_less_eq_nat @ A @ B )
% 2.39/2.73 => ( ( ord_less_eq_nat @ A @ C )
% 2.39/2.73 => ( ord_less_eq_nat @ A @ ( inf_inf_nat @ B @ C ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.boundedI
% 2.39/2.73 thf(fact_1270_inf_OboundedI,axiom,
% 2.39/2.73 ! [A: int,B: int,C: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ A @ B )
% 2.39/2.73 => ( ( ord_less_eq_int @ A @ C )
% 2.39/2.73 => ( ord_less_eq_int @ A @ ( inf_inf_int @ B @ C ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.boundedI
% 2.39/2.73 thf(fact_1271_inf_OboundedE,axiom,
% 2.39/2.73 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat] :
% 2.39/2.73 ( ( ord_le3146513528884898305at_nat @ A @ ( inf_in2572325071724192079at_nat @ B @ C ) )
% 2.39/2.73 => ~ ( ( ord_le3146513528884898305at_nat @ A @ B )
% 2.39/2.73 => ~ ( ord_le3146513528884898305at_nat @ A @ C ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.boundedE
% 2.39/2.73 thf(fact_1272_inf_OboundedE,axiom,
% 2.39/2.73 ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o,C: product_prod_int_int > $o] :
% 2.39/2.73 ( ( ord_le8369615600986905444_int_o @ A @ ( inf_in3604695632404883862_int_o @ B @ C ) )
% 2.39/2.73 => ~ ( ( ord_le8369615600986905444_int_o @ A @ B )
% 2.39/2.73 => ~ ( ord_le8369615600986905444_int_o @ A @ C ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.boundedE
% 2.39/2.73 thf(fact_1273_inf_OboundedE,axiom,
% 2.39/2.73 ! [A: assn,B: assn,C: assn] :
% 2.39/2.73 ( ( ord_less_eq_assn @ A @ ( inf_inf_assn @ B @ C ) )
% 2.39/2.73 => ~ ( ( ord_less_eq_assn @ A @ B )
% 2.39/2.73 => ~ ( ord_less_eq_assn @ A @ C ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.boundedE
% 2.39/2.73 thf(fact_1274_inf_OboundedE,axiom,
% 2.39/2.73 ! [A: set_nat,B: set_nat,C: set_nat] :
% 2.39/2.73 ( ( ord_less_eq_set_nat @ A @ ( inf_inf_set_nat @ B @ C ) )
% 2.39/2.73 => ~ ( ( ord_less_eq_set_nat @ A @ B )
% 2.39/2.73 => ~ ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.boundedE
% 2.39/2.73 thf(fact_1275_inf_OboundedE,axiom,
% 2.39/2.73 ! [A: rat,B: rat,C: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ A @ ( inf_inf_rat @ B @ C ) )
% 2.39/2.73 => ~ ( ( ord_less_eq_rat @ A @ B )
% 2.39/2.73 => ~ ( ord_less_eq_rat @ A @ C ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.boundedE
% 2.39/2.73 thf(fact_1276_inf_OboundedE,axiom,
% 2.39/2.73 ! [A: nat,B: nat,C: nat] :
% 2.39/2.73 ( ( ord_less_eq_nat @ A @ ( inf_inf_nat @ B @ C ) )
% 2.39/2.73 => ~ ( ( ord_less_eq_nat @ A @ B )
% 2.39/2.73 => ~ ( ord_less_eq_nat @ A @ C ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.boundedE
% 2.39/2.73 thf(fact_1277_inf_OboundedE,axiom,
% 2.39/2.73 ! [A: int,B: int,C: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ A @ ( inf_inf_int @ B @ C ) )
% 2.39/2.73 => ~ ( ( ord_less_eq_int @ A @ B )
% 2.39/2.73 => ~ ( ord_less_eq_int @ A @ C ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.boundedE
% 2.39/2.73 thf(fact_1278_inf__absorb2,axiom,
% 2.39/2.73 ! [Y: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat] :
% 2.39/2.73 ( ( ord_le3146513528884898305at_nat @ Y @ X )
% 2.39/2.73 => ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 2.39/2.73 = Y ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf_absorb2
% 2.39/2.73 thf(fact_1279_inf__absorb2,axiom,
% 2.39/2.73 ! [Y: product_prod_int_int > $o,X: product_prod_int_int > $o] :
% 2.39/2.73 ( ( ord_le8369615600986905444_int_o @ Y @ X )
% 2.39/2.73 => ( ( inf_in3604695632404883862_int_o @ X @ Y )
% 2.39/2.73 = Y ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf_absorb2
% 2.39/2.73 thf(fact_1280_inf__absorb2,axiom,
% 2.39/2.73 ! [Y: assn,X: assn] :
% 2.39/2.73 ( ( ord_less_eq_assn @ Y @ X )
% 2.39/2.73 => ( ( inf_inf_assn @ X @ Y )
% 2.39/2.73 = Y ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf_absorb2
% 2.39/2.73 thf(fact_1281_inf__absorb2,axiom,
% 2.39/2.73 ! [Y: set_nat,X: set_nat] :
% 2.39/2.73 ( ( ord_less_eq_set_nat @ Y @ X )
% 2.39/2.73 => ( ( inf_inf_set_nat @ X @ Y )
% 2.39/2.73 = Y ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf_absorb2
% 2.39/2.73 thf(fact_1282_inf__absorb2,axiom,
% 2.39/2.73 ! [Y: rat,X: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ Y @ X )
% 2.39/2.73 => ( ( inf_inf_rat @ X @ Y )
% 2.39/2.73 = Y ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf_absorb2
% 2.39/2.73 thf(fact_1283_inf__absorb2,axiom,
% 2.39/2.73 ! [Y: nat,X: nat] :
% 2.39/2.73 ( ( ord_less_eq_nat @ Y @ X )
% 2.39/2.73 => ( ( inf_inf_nat @ X @ Y )
% 2.39/2.73 = Y ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf_absorb2
% 2.39/2.73 thf(fact_1284_inf__absorb2,axiom,
% 2.39/2.73 ! [Y: int,X: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ Y @ X )
% 2.39/2.73 => ( ( inf_inf_int @ X @ Y )
% 2.39/2.73 = Y ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf_absorb2
% 2.39/2.73 thf(fact_1285_inf__absorb1,axiom,
% 2.39/2.73 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 2.39/2.73 ( ( ord_le3146513528884898305at_nat @ X @ Y )
% 2.39/2.73 => ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 2.39/2.73 = X ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf_absorb1
% 2.39/2.73 thf(fact_1286_inf__absorb1,axiom,
% 2.39/2.73 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 2.39/2.73 ( ( ord_le8369615600986905444_int_o @ X @ Y )
% 2.39/2.73 => ( ( inf_in3604695632404883862_int_o @ X @ Y )
% 2.39/2.73 = X ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf_absorb1
% 2.39/2.73 thf(fact_1287_inf__absorb1,axiom,
% 2.39/2.73 ! [X: assn,Y: assn] :
% 2.39/2.73 ( ( ord_less_eq_assn @ X @ Y )
% 2.39/2.73 => ( ( inf_inf_assn @ X @ Y )
% 2.39/2.73 = X ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf_absorb1
% 2.39/2.73 thf(fact_1288_inf__absorb1,axiom,
% 2.39/2.73 ! [X: set_nat,Y: set_nat] :
% 2.39/2.73 ( ( ord_less_eq_set_nat @ X @ Y )
% 2.39/2.73 => ( ( inf_inf_set_nat @ X @ Y )
% 2.39/2.73 = X ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf_absorb1
% 2.39/2.73 thf(fact_1289_inf__absorb1,axiom,
% 2.39/2.73 ! [X: rat,Y: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ X @ Y )
% 2.39/2.73 => ( ( inf_inf_rat @ X @ Y )
% 2.39/2.73 = X ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf_absorb1
% 2.39/2.73 thf(fact_1290_inf__absorb1,axiom,
% 2.39/2.73 ! [X: nat,Y: nat] :
% 2.39/2.73 ( ( ord_less_eq_nat @ X @ Y )
% 2.39/2.73 => ( ( inf_inf_nat @ X @ Y )
% 2.39/2.73 = X ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf_absorb1
% 2.39/2.73 thf(fact_1291_inf__absorb1,axiom,
% 2.39/2.73 ! [X: int,Y: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ X @ Y )
% 2.39/2.73 => ( ( inf_inf_int @ X @ Y )
% 2.39/2.73 = X ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf_absorb1
% 2.39/2.73 thf(fact_1292_inf_Oabsorb2,axiom,
% 2.39/2.73 ! [B: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 2.39/2.73 ( ( ord_le3146513528884898305at_nat @ B @ A )
% 2.39/2.73 => ( ( inf_in2572325071724192079at_nat @ A @ B )
% 2.39/2.73 = B ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.absorb2
% 2.39/2.73 thf(fact_1293_inf_Oabsorb2,axiom,
% 2.39/2.73 ! [B: product_prod_int_int > $o,A: product_prod_int_int > $o] :
% 2.39/2.73 ( ( ord_le8369615600986905444_int_o @ B @ A )
% 2.39/2.73 => ( ( inf_in3604695632404883862_int_o @ A @ B )
% 2.39/2.73 = B ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.absorb2
% 2.39/2.73 thf(fact_1294_inf_Oabsorb2,axiom,
% 2.39/2.73 ! [B: assn,A: assn] :
% 2.39/2.73 ( ( ord_less_eq_assn @ B @ A )
% 2.39/2.73 => ( ( inf_inf_assn @ A @ B )
% 2.39/2.73 = B ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.absorb2
% 2.39/2.73 thf(fact_1295_inf_Oabsorb2,axiom,
% 2.39/2.73 ! [B: set_nat,A: set_nat] :
% 2.39/2.73 ( ( ord_less_eq_set_nat @ B @ A )
% 2.39/2.73 => ( ( inf_inf_set_nat @ A @ B )
% 2.39/2.73 = B ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.absorb2
% 2.39/2.73 thf(fact_1296_inf_Oabsorb2,axiom,
% 2.39/2.73 ! [B: rat,A: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ B @ A )
% 2.39/2.73 => ( ( inf_inf_rat @ A @ B )
% 2.39/2.73 = B ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.absorb2
% 2.39/2.73 thf(fact_1297_inf_Oabsorb2,axiom,
% 2.39/2.73 ! [B: nat,A: nat] :
% 2.39/2.73 ( ( ord_less_eq_nat @ B @ A )
% 2.39/2.73 => ( ( inf_inf_nat @ A @ B )
% 2.39/2.73 = B ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.absorb2
% 2.39/2.73 thf(fact_1298_inf_Oabsorb2,axiom,
% 2.39/2.73 ! [B: int,A: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ B @ A )
% 2.39/2.73 => ( ( inf_inf_int @ A @ B )
% 2.39/2.73 = B ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.absorb2
% 2.39/2.73 thf(fact_1299_inf_Oabsorb1,axiom,
% 2.39/2.73 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.39/2.73 ( ( ord_le3146513528884898305at_nat @ A @ B )
% 2.39/2.73 => ( ( inf_in2572325071724192079at_nat @ A @ B )
% 2.39/2.73 = A ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.absorb1
% 2.39/2.73 thf(fact_1300_inf_Oabsorb1,axiom,
% 2.39/2.73 ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 2.39/2.73 ( ( ord_le8369615600986905444_int_o @ A @ B )
% 2.39/2.73 => ( ( inf_in3604695632404883862_int_o @ A @ B )
% 2.39/2.73 = A ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.absorb1
% 2.39/2.73 thf(fact_1301_inf_Oabsorb1,axiom,
% 2.39/2.73 ! [A: assn,B: assn] :
% 2.39/2.73 ( ( ord_less_eq_assn @ A @ B )
% 2.39/2.73 => ( ( inf_inf_assn @ A @ B )
% 2.39/2.73 = A ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.absorb1
% 2.39/2.73 thf(fact_1302_inf_Oabsorb1,axiom,
% 2.39/2.73 ! [A: set_nat,B: set_nat] :
% 2.39/2.73 ( ( ord_less_eq_set_nat @ A @ B )
% 2.39/2.73 => ( ( inf_inf_set_nat @ A @ B )
% 2.39/2.73 = A ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.absorb1
% 2.39/2.73 thf(fact_1303_inf_Oabsorb1,axiom,
% 2.39/2.73 ! [A: rat,B: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ A @ B )
% 2.39/2.73 => ( ( inf_inf_rat @ A @ B )
% 2.39/2.73 = A ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.absorb1
% 2.39/2.73 thf(fact_1304_inf_Oabsorb1,axiom,
% 2.39/2.73 ! [A: nat,B: nat] :
% 2.39/2.73 ( ( ord_less_eq_nat @ A @ B )
% 2.39/2.73 => ( ( inf_inf_nat @ A @ B )
% 2.39/2.73 = A ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.absorb1
% 2.39/2.73 thf(fact_1305_inf_Oabsorb1,axiom,
% 2.39/2.73 ! [A: int,B: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ A @ B )
% 2.39/2.73 => ( ( inf_inf_int @ A @ B )
% 2.39/2.73 = A ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.absorb1
% 2.39/2.73 thf(fact_1306_le__iff__inf,axiom,
% 2.39/2.73 ( ord_le3146513528884898305at_nat
% 2.39/2.73 = ( ^ [X2: set_Pr1261947904930325089at_nat,Y2: set_Pr1261947904930325089at_nat] :
% 2.39/2.73 ( ( inf_in2572325071724192079at_nat @ X2 @ Y2 )
% 2.39/2.73 = X2 ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_iff_inf
% 2.39/2.73 thf(fact_1307_le__iff__inf,axiom,
% 2.39/2.73 ( ord_le8369615600986905444_int_o
% 2.39/2.73 = ( ^ [X2: product_prod_int_int > $o,Y2: product_prod_int_int > $o] :
% 2.39/2.73 ( ( inf_in3604695632404883862_int_o @ X2 @ Y2 )
% 2.39/2.73 = X2 ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_iff_inf
% 2.39/2.73 thf(fact_1308_le__iff__inf,axiom,
% 2.39/2.73 ( ord_less_eq_assn
% 2.39/2.73 = ( ^ [X2: assn,Y2: assn] :
% 2.39/2.73 ( ( inf_inf_assn @ X2 @ Y2 )
% 2.39/2.73 = X2 ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_iff_inf
% 2.39/2.73 thf(fact_1309_le__iff__inf,axiom,
% 2.39/2.73 ( ord_less_eq_set_nat
% 2.39/2.73 = ( ^ [X2: set_nat,Y2: set_nat] :
% 2.39/2.73 ( ( inf_inf_set_nat @ X2 @ Y2 )
% 2.39/2.73 = X2 ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_iff_inf
% 2.39/2.73 thf(fact_1310_le__iff__inf,axiom,
% 2.39/2.73 ( ord_less_eq_rat
% 2.39/2.73 = ( ^ [X2: rat,Y2: rat] :
% 2.39/2.73 ( ( inf_inf_rat @ X2 @ Y2 )
% 2.39/2.73 = X2 ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_iff_inf
% 2.39/2.73 thf(fact_1311_le__iff__inf,axiom,
% 2.39/2.73 ( ord_less_eq_nat
% 2.39/2.73 = ( ^ [X2: nat,Y2: nat] :
% 2.39/2.73 ( ( inf_inf_nat @ X2 @ Y2 )
% 2.39/2.73 = X2 ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_iff_inf
% 2.39/2.73 thf(fact_1312_le__iff__inf,axiom,
% 2.39/2.73 ( ord_less_eq_int
% 2.39/2.73 = ( ^ [X2: int,Y2: int] :
% 2.39/2.73 ( ( inf_inf_int @ X2 @ Y2 )
% 2.39/2.73 = X2 ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_iff_inf
% 2.39/2.73 thf(fact_1313_inf__unique,axiom,
% 2.39/2.73 ! [F2: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 2.39/2.73 ( ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( F2 @ X3 @ Y3 ) @ X3 )
% 2.39/2.73 => ( ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( F2 @ X3 @ Y3 ) @ Y3 )
% 2.39/2.73 => ( ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,Z2: set_Pr1261947904930325089at_nat] :
% 2.39/2.73 ( ( ord_le3146513528884898305at_nat @ X3 @ Y3 )
% 2.39/2.73 => ( ( ord_le3146513528884898305at_nat @ X3 @ Z2 )
% 2.39/2.73 => ( ord_le3146513528884898305at_nat @ X3 @ ( F2 @ Y3 @ Z2 ) ) ) )
% 2.39/2.73 => ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 2.39/2.73 = ( F2 @ X @ Y ) ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf_unique
% 2.39/2.73 thf(fact_1314_inf__unique,axiom,
% 2.39/2.73 ! [F2: ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int > $o,X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 2.39/2.73 ( ! [X3: product_prod_int_int > $o,Y3: product_prod_int_int > $o] : ( ord_le8369615600986905444_int_o @ ( F2 @ X3 @ Y3 ) @ X3 )
% 2.39/2.73 => ( ! [X3: product_prod_int_int > $o,Y3: product_prod_int_int > $o] : ( ord_le8369615600986905444_int_o @ ( F2 @ X3 @ Y3 ) @ Y3 )
% 2.39/2.73 => ( ! [X3: product_prod_int_int > $o,Y3: product_prod_int_int > $o,Z2: product_prod_int_int > $o] :
% 2.39/2.73 ( ( ord_le8369615600986905444_int_o @ X3 @ Y3 )
% 2.39/2.73 => ( ( ord_le8369615600986905444_int_o @ X3 @ Z2 )
% 2.39/2.73 => ( ord_le8369615600986905444_int_o @ X3 @ ( F2 @ Y3 @ Z2 ) ) ) )
% 2.39/2.73 => ( ( inf_in3604695632404883862_int_o @ X @ Y )
% 2.39/2.73 = ( F2 @ X @ Y ) ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf_unique
% 2.39/2.73 thf(fact_1315_inf__unique,axiom,
% 2.39/2.73 ! [F2: assn > assn > assn,X: assn,Y: assn] :
% 2.39/2.73 ( ! [X3: assn,Y3: assn] : ( ord_less_eq_assn @ ( F2 @ X3 @ Y3 ) @ X3 )
% 2.39/2.73 => ( ! [X3: assn,Y3: assn] : ( ord_less_eq_assn @ ( F2 @ X3 @ Y3 ) @ Y3 )
% 2.39/2.73 => ( ! [X3: assn,Y3: assn,Z2: assn] :
% 2.39/2.73 ( ( ord_less_eq_assn @ X3 @ Y3 )
% 2.39/2.73 => ( ( ord_less_eq_assn @ X3 @ Z2 )
% 2.39/2.73 => ( ord_less_eq_assn @ X3 @ ( F2 @ Y3 @ Z2 ) ) ) )
% 2.39/2.73 => ( ( inf_inf_assn @ X @ Y )
% 2.39/2.73 = ( F2 @ X @ Y ) ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf_unique
% 2.39/2.73 thf(fact_1316_inf__unique,axiom,
% 2.39/2.73 ! [F2: set_nat > set_nat > set_nat,X: set_nat,Y: set_nat] :
% 2.39/2.73 ( ! [X3: set_nat,Y3: set_nat] : ( ord_less_eq_set_nat @ ( F2 @ X3 @ Y3 ) @ X3 )
% 2.39/2.73 => ( ! [X3: set_nat,Y3: set_nat] : ( ord_less_eq_set_nat @ ( F2 @ X3 @ Y3 ) @ Y3 )
% 2.39/2.73 => ( ! [X3: set_nat,Y3: set_nat,Z2: set_nat] :
% 2.39/2.73 ( ( ord_less_eq_set_nat @ X3 @ Y3 )
% 2.39/2.73 => ( ( ord_less_eq_set_nat @ X3 @ Z2 )
% 2.39/2.73 => ( ord_less_eq_set_nat @ X3 @ ( F2 @ Y3 @ Z2 ) ) ) )
% 2.39/2.73 => ( ( inf_inf_set_nat @ X @ Y )
% 2.39/2.73 = ( F2 @ X @ Y ) ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf_unique
% 2.39/2.73 thf(fact_1317_inf__unique,axiom,
% 2.39/2.73 ! [F2: rat > rat > rat,X: rat,Y: rat] :
% 2.39/2.73 ( ! [X3: rat,Y3: rat] : ( ord_less_eq_rat @ ( F2 @ X3 @ Y3 ) @ X3 )
% 2.39/2.73 => ( ! [X3: rat,Y3: rat] : ( ord_less_eq_rat @ ( F2 @ X3 @ Y3 ) @ Y3 )
% 2.39/2.73 => ( ! [X3: rat,Y3: rat,Z2: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 2.39/2.73 => ( ( ord_less_eq_rat @ X3 @ Z2 )
% 2.39/2.73 => ( ord_less_eq_rat @ X3 @ ( F2 @ Y3 @ Z2 ) ) ) )
% 2.39/2.73 => ( ( inf_inf_rat @ X @ Y )
% 2.39/2.73 = ( F2 @ X @ Y ) ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf_unique
% 2.39/2.73 thf(fact_1318_inf__unique,axiom,
% 2.39/2.73 ! [F2: nat > nat > nat,X: nat,Y: nat] :
% 2.39/2.73 ( ! [X3: nat,Y3: nat] : ( ord_less_eq_nat @ ( F2 @ X3 @ Y3 ) @ X3 )
% 2.39/2.73 => ( ! [X3: nat,Y3: nat] : ( ord_less_eq_nat @ ( F2 @ X3 @ Y3 ) @ Y3 )
% 2.39/2.73 => ( ! [X3: nat,Y3: nat,Z2: nat] :
% 2.39/2.73 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 2.39/2.73 => ( ( ord_less_eq_nat @ X3 @ Z2 )
% 2.39/2.73 => ( ord_less_eq_nat @ X3 @ ( F2 @ Y3 @ Z2 ) ) ) )
% 2.39/2.73 => ( ( inf_inf_nat @ X @ Y )
% 2.39/2.73 = ( F2 @ X @ Y ) ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf_unique
% 2.39/2.73 thf(fact_1319_inf__unique,axiom,
% 2.39/2.73 ! [F2: int > int > int,X: int,Y: int] :
% 2.39/2.73 ( ! [X3: int,Y3: int] : ( ord_less_eq_int @ ( F2 @ X3 @ Y3 ) @ X3 )
% 2.39/2.73 => ( ! [X3: int,Y3: int] : ( ord_less_eq_int @ ( F2 @ X3 @ Y3 ) @ Y3 )
% 2.39/2.73 => ( ! [X3: int,Y3: int,Z2: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ X3 @ Y3 )
% 2.39/2.73 => ( ( ord_less_eq_int @ X3 @ Z2 )
% 2.39/2.73 => ( ord_less_eq_int @ X3 @ ( F2 @ Y3 @ Z2 ) ) ) )
% 2.39/2.73 => ( ( inf_inf_int @ X @ Y )
% 2.39/2.73 = ( F2 @ X @ Y ) ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf_unique
% 2.39/2.73 thf(fact_1320_inf_OorderI,axiom,
% 2.39/2.73 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.39/2.73 ( ( A
% 2.39/2.73 = ( inf_in2572325071724192079at_nat @ A @ B ) )
% 2.39/2.73 => ( ord_le3146513528884898305at_nat @ A @ B ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.orderI
% 2.39/2.73 thf(fact_1321_inf_OorderI,axiom,
% 2.39/2.73 ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 2.39/2.73 ( ( A
% 2.39/2.73 = ( inf_in3604695632404883862_int_o @ A @ B ) )
% 2.39/2.73 => ( ord_le8369615600986905444_int_o @ A @ B ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.orderI
% 2.39/2.73 thf(fact_1322_inf_OorderI,axiom,
% 2.39/2.73 ! [A: assn,B: assn] :
% 2.39/2.73 ( ( A
% 2.39/2.73 = ( inf_inf_assn @ A @ B ) )
% 2.39/2.73 => ( ord_less_eq_assn @ A @ B ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.orderI
% 2.39/2.73 thf(fact_1323_inf_OorderI,axiom,
% 2.39/2.73 ! [A: set_nat,B: set_nat] :
% 2.39/2.73 ( ( A
% 2.39/2.73 = ( inf_inf_set_nat @ A @ B ) )
% 2.39/2.73 => ( ord_less_eq_set_nat @ A @ B ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.orderI
% 2.39/2.73 thf(fact_1324_inf_OorderI,axiom,
% 2.39/2.73 ! [A: rat,B: rat] :
% 2.39/2.73 ( ( A
% 2.39/2.73 = ( inf_inf_rat @ A @ B ) )
% 2.39/2.73 => ( ord_less_eq_rat @ A @ B ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.orderI
% 2.39/2.73 thf(fact_1325_inf_OorderI,axiom,
% 2.39/2.73 ! [A: nat,B: nat] :
% 2.39/2.73 ( ( A
% 2.39/2.73 = ( inf_inf_nat @ A @ B ) )
% 2.39/2.73 => ( ord_less_eq_nat @ A @ B ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.orderI
% 2.39/2.73 thf(fact_1326_inf_OorderI,axiom,
% 2.39/2.73 ! [A: int,B: int] :
% 2.39/2.73 ( ( A
% 2.39/2.73 = ( inf_inf_int @ A @ B ) )
% 2.39/2.73 => ( ord_less_eq_int @ A @ B ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.orderI
% 2.39/2.73 thf(fact_1327_inf_OorderE,axiom,
% 2.39/2.73 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.39/2.73 ( ( ord_le3146513528884898305at_nat @ A @ B )
% 2.39/2.73 => ( A
% 2.39/2.73 = ( inf_in2572325071724192079at_nat @ A @ B ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.orderE
% 2.39/2.73 thf(fact_1328_inf_OorderE,axiom,
% 2.39/2.73 ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 2.39/2.73 ( ( ord_le8369615600986905444_int_o @ A @ B )
% 2.39/2.73 => ( A
% 2.39/2.73 = ( inf_in3604695632404883862_int_o @ A @ B ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.orderE
% 2.39/2.73 thf(fact_1329_inf_OorderE,axiom,
% 2.39/2.73 ! [A: assn,B: assn] :
% 2.39/2.73 ( ( ord_less_eq_assn @ A @ B )
% 2.39/2.73 => ( A
% 2.39/2.73 = ( inf_inf_assn @ A @ B ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.orderE
% 2.39/2.73 thf(fact_1330_inf_OorderE,axiom,
% 2.39/2.73 ! [A: set_nat,B: set_nat] :
% 2.39/2.73 ( ( ord_less_eq_set_nat @ A @ B )
% 2.39/2.73 => ( A
% 2.39/2.73 = ( inf_inf_set_nat @ A @ B ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.orderE
% 2.39/2.73 thf(fact_1331_inf_OorderE,axiom,
% 2.39/2.73 ! [A: rat,B: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ A @ B )
% 2.39/2.73 => ( A
% 2.39/2.73 = ( inf_inf_rat @ A @ B ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.orderE
% 2.39/2.73 thf(fact_1332_inf_OorderE,axiom,
% 2.39/2.73 ! [A: nat,B: nat] :
% 2.39/2.73 ( ( ord_less_eq_nat @ A @ B )
% 2.39/2.73 => ( A
% 2.39/2.73 = ( inf_inf_nat @ A @ B ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.orderE
% 2.39/2.73 thf(fact_1333_inf_OorderE,axiom,
% 2.39/2.73 ! [A: int,B: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ A @ B )
% 2.39/2.73 => ( A
% 2.39/2.73 = ( inf_inf_int @ A @ B ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf.orderE
% 2.39/2.73 thf(fact_1334_le__infI2,axiom,
% 2.39/2.73 ! [B: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 2.39/2.73 ( ( ord_le3146513528884898305at_nat @ B @ X )
% 2.39/2.73 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ X ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_infI2
% 2.39/2.73 thf(fact_1335_le__infI2,axiom,
% 2.39/2.73 ! [B: product_prod_int_int > $o,X: product_prod_int_int > $o,A: product_prod_int_int > $o] :
% 2.39/2.73 ( ( ord_le8369615600986905444_int_o @ B @ X )
% 2.39/2.73 => ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ X ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_infI2
% 2.39/2.73 thf(fact_1336_le__infI2,axiom,
% 2.39/2.73 ! [B: assn,X: assn,A: assn] :
% 2.39/2.73 ( ( ord_less_eq_assn @ B @ X )
% 2.39/2.73 => ( ord_less_eq_assn @ ( inf_inf_assn @ A @ B ) @ X ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_infI2
% 2.39/2.73 thf(fact_1337_le__infI2,axiom,
% 2.39/2.73 ! [B: set_nat,X: set_nat,A: set_nat] :
% 2.39/2.73 ( ( ord_less_eq_set_nat @ B @ X )
% 2.39/2.73 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ X ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_infI2
% 2.39/2.73 thf(fact_1338_le__infI2,axiom,
% 2.39/2.73 ! [B: rat,X: rat,A: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ B @ X )
% 2.39/2.73 => ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ X ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_infI2
% 2.39/2.73 thf(fact_1339_le__infI2,axiom,
% 2.39/2.73 ! [B: nat,X: nat,A: nat] :
% 2.39/2.73 ( ( ord_less_eq_nat @ B @ X )
% 2.39/2.73 => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ X ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_infI2
% 2.39/2.73 thf(fact_1340_le__infI2,axiom,
% 2.39/2.73 ! [B: int,X: int,A: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ B @ X )
% 2.39/2.73 => ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ X ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_infI2
% 2.39/2.73 thf(fact_1341_le__infI1,axiom,
% 2.39/2.73 ! [A: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.39/2.73 ( ( ord_le3146513528884898305at_nat @ A @ X )
% 2.39/2.73 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ X ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_infI1
% 2.39/2.73 thf(fact_1342_le__infI1,axiom,
% 2.39/2.73 ! [A: product_prod_int_int > $o,X: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 2.39/2.73 ( ( ord_le8369615600986905444_int_o @ A @ X )
% 2.39/2.73 => ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ X ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_infI1
% 2.39/2.73 thf(fact_1343_le__infI1,axiom,
% 2.39/2.73 ! [A: assn,X: assn,B: assn] :
% 2.39/2.73 ( ( ord_less_eq_assn @ A @ X )
% 2.39/2.73 => ( ord_less_eq_assn @ ( inf_inf_assn @ A @ B ) @ X ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_infI1
% 2.39/2.73 thf(fact_1344_le__infI1,axiom,
% 2.39/2.73 ! [A: set_nat,X: set_nat,B: set_nat] :
% 2.39/2.73 ( ( ord_less_eq_set_nat @ A @ X )
% 2.39/2.73 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ X ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_infI1
% 2.39/2.73 thf(fact_1345_le__infI1,axiom,
% 2.39/2.73 ! [A: rat,X: rat,B: rat] :
% 2.39/2.73 ( ( ord_less_eq_rat @ A @ X )
% 2.39/2.73 => ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ X ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_infI1
% 2.39/2.73 thf(fact_1346_le__infI1,axiom,
% 2.39/2.73 ! [A: nat,X: nat,B: nat] :
% 2.39/2.73 ( ( ord_less_eq_nat @ A @ X )
% 2.39/2.73 => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ X ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_infI1
% 2.39/2.73 thf(fact_1347_le__infI1,axiom,
% 2.39/2.73 ! [A: int,X: int,B: int] :
% 2.39/2.73 ( ( ord_less_eq_int @ A @ X )
% 2.39/2.73 => ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ X ) ) ).
% 2.39/2.73
% 2.39/2.73 % le_infI1
% 2.39/2.73 thf(fact_1348_inf__mono,axiom,
% 2.39/2.73 ! [A: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,D2: set_Pr1261947904930325089at_nat] :
% 2.39/2.73 ( ( ord_le3146513528884898305at_nat @ A @ C )
% 2.39/2.73 => ( ( ord_le3146513528884898305at_nat @ B @ D2 )
% 2.39/2.73 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ ( inf_in2572325071724192079at_nat @ C @ D2 ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf_mono
% 2.39/2.73 thf(fact_1349_inf__mono,axiom,
% 2.39/2.73 ! [A: product_prod_int_int > $o,C: product_prod_int_int > $o,B: product_prod_int_int > $o,D2: product_prod_int_int > $o] :
% 2.39/2.73 ( ( ord_le8369615600986905444_int_o @ A @ C )
% 2.39/2.73 => ( ( ord_le8369615600986905444_int_o @ B @ D2 )
% 2.39/2.73 => ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ ( inf_in3604695632404883862_int_o @ C @ D2 ) ) ) ) ).
% 2.39/2.73
% 2.39/2.73 % inf_mono
% 2.39/2.73 thf(fact_1350_inf__mono,axiom,
% 2.39/2.73 ! [A: assn,C: assn,B: assn,D2: assn] :
% 2.39/2.74 ( ( ord_less_eq_assn @ A @ C )
% 2.39/2.74 => ( ( ord_less_eq_assn @ B @ D2 )
% 2.39/2.74 => ( ord_less_eq_assn @ ( inf_inf_assn @ A @ B ) @ ( inf_inf_assn @ C @ D2 ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % inf_mono
% 2.39/2.74 thf(fact_1351_inf__mono,axiom,
% 2.39/2.74 ! [A: set_nat,C: set_nat,B: set_nat,D2: set_nat] :
% 2.39/2.74 ( ( ord_less_eq_set_nat @ A @ C )
% 2.39/2.74 => ( ( ord_less_eq_set_nat @ B @ D2 )
% 2.39/2.74 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ ( inf_inf_set_nat @ C @ D2 ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % inf_mono
% 2.39/2.74 thf(fact_1352_inf__mono,axiom,
% 2.39/2.74 ! [A: rat,C: rat,B: rat,D2: rat] :
% 2.39/2.74 ( ( ord_less_eq_rat @ A @ C )
% 2.39/2.74 => ( ( ord_less_eq_rat @ B @ D2 )
% 2.39/2.74 => ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ ( inf_inf_rat @ C @ D2 ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % inf_mono
% 2.39/2.74 thf(fact_1353_inf__mono,axiom,
% 2.39/2.74 ! [A: nat,C: nat,B: nat,D2: nat] :
% 2.39/2.74 ( ( ord_less_eq_nat @ A @ C )
% 2.39/2.74 => ( ( ord_less_eq_nat @ B @ D2 )
% 2.39/2.74 => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ ( inf_inf_nat @ C @ D2 ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % inf_mono
% 2.39/2.74 thf(fact_1354_inf__mono,axiom,
% 2.39/2.74 ! [A: int,C: int,B: int,D2: int] :
% 2.39/2.74 ( ( ord_less_eq_int @ A @ C )
% 2.39/2.74 => ( ( ord_less_eq_int @ B @ D2 )
% 2.39/2.74 => ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ ( inf_inf_int @ C @ D2 ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % inf_mono
% 2.39/2.74 thf(fact_1355_le__infI,axiom,
% 2.39/2.74 ! [X: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.39/2.74 ( ( ord_le3146513528884898305at_nat @ X @ A )
% 2.39/2.74 => ( ( ord_le3146513528884898305at_nat @ X @ B )
% 2.39/2.74 => ( ord_le3146513528884898305at_nat @ X @ ( inf_in2572325071724192079at_nat @ A @ B ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_infI
% 2.39/2.74 thf(fact_1356_le__infI,axiom,
% 2.39/2.74 ! [X: product_prod_int_int > $o,A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 2.39/2.74 ( ( ord_le8369615600986905444_int_o @ X @ A )
% 2.39/2.74 => ( ( ord_le8369615600986905444_int_o @ X @ B )
% 2.39/2.74 => ( ord_le8369615600986905444_int_o @ X @ ( inf_in3604695632404883862_int_o @ A @ B ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_infI
% 2.39/2.74 thf(fact_1357_le__infI,axiom,
% 2.39/2.74 ! [X: assn,A: assn,B: assn] :
% 2.39/2.74 ( ( ord_less_eq_assn @ X @ A )
% 2.39/2.74 => ( ( ord_less_eq_assn @ X @ B )
% 2.39/2.74 => ( ord_less_eq_assn @ X @ ( inf_inf_assn @ A @ B ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_infI
% 2.39/2.74 thf(fact_1358_le__infI,axiom,
% 2.39/2.74 ! [X: set_nat,A: set_nat,B: set_nat] :
% 2.39/2.74 ( ( ord_less_eq_set_nat @ X @ A )
% 2.39/2.74 => ( ( ord_less_eq_set_nat @ X @ B )
% 2.39/2.74 => ( ord_less_eq_set_nat @ X @ ( inf_inf_set_nat @ A @ B ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_infI
% 2.39/2.74 thf(fact_1359_le__infI,axiom,
% 2.39/2.74 ! [X: rat,A: rat,B: rat] :
% 2.39/2.74 ( ( ord_less_eq_rat @ X @ A )
% 2.39/2.74 => ( ( ord_less_eq_rat @ X @ B )
% 2.39/2.74 => ( ord_less_eq_rat @ X @ ( inf_inf_rat @ A @ B ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_infI
% 2.39/2.74 thf(fact_1360_le__infI,axiom,
% 2.39/2.74 ! [X: nat,A: nat,B: nat] :
% 2.39/2.74 ( ( ord_less_eq_nat @ X @ A )
% 2.39/2.74 => ( ( ord_less_eq_nat @ X @ B )
% 2.39/2.74 => ( ord_less_eq_nat @ X @ ( inf_inf_nat @ A @ B ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_infI
% 2.39/2.74 thf(fact_1361_le__infI,axiom,
% 2.39/2.74 ! [X: int,A: int,B: int] :
% 2.39/2.74 ( ( ord_less_eq_int @ X @ A )
% 2.39/2.74 => ( ( ord_less_eq_int @ X @ B )
% 2.39/2.74 => ( ord_less_eq_int @ X @ ( inf_inf_int @ A @ B ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_infI
% 2.39/2.74 thf(fact_1362_le__infE,axiom,
% 2.39/2.74 ! [X: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.39/2.74 ( ( ord_le3146513528884898305at_nat @ X @ ( inf_in2572325071724192079at_nat @ A @ B ) )
% 2.39/2.74 => ~ ( ( ord_le3146513528884898305at_nat @ X @ A )
% 2.39/2.74 => ~ ( ord_le3146513528884898305at_nat @ X @ B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_infE
% 2.39/2.74 thf(fact_1363_le__infE,axiom,
% 2.39/2.74 ! [X: product_prod_int_int > $o,A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 2.39/2.74 ( ( ord_le8369615600986905444_int_o @ X @ ( inf_in3604695632404883862_int_o @ A @ B ) )
% 2.39/2.74 => ~ ( ( ord_le8369615600986905444_int_o @ X @ A )
% 2.39/2.74 => ~ ( ord_le8369615600986905444_int_o @ X @ B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_infE
% 2.39/2.74 thf(fact_1364_le__infE,axiom,
% 2.39/2.74 ! [X: assn,A: assn,B: assn] :
% 2.39/2.74 ( ( ord_less_eq_assn @ X @ ( inf_inf_assn @ A @ B ) )
% 2.39/2.74 => ~ ( ( ord_less_eq_assn @ X @ A )
% 2.39/2.74 => ~ ( ord_less_eq_assn @ X @ B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_infE
% 2.39/2.74 thf(fact_1365_le__infE,axiom,
% 2.39/2.74 ! [X: set_nat,A: set_nat,B: set_nat] :
% 2.39/2.74 ( ( ord_less_eq_set_nat @ X @ ( inf_inf_set_nat @ A @ B ) )
% 2.39/2.74 => ~ ( ( ord_less_eq_set_nat @ X @ A )
% 2.39/2.74 => ~ ( ord_less_eq_set_nat @ X @ B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_infE
% 2.39/2.74 thf(fact_1366_le__infE,axiom,
% 2.39/2.74 ! [X: rat,A: rat,B: rat] :
% 2.39/2.74 ( ( ord_less_eq_rat @ X @ ( inf_inf_rat @ A @ B ) )
% 2.39/2.74 => ~ ( ( ord_less_eq_rat @ X @ A )
% 2.39/2.74 => ~ ( ord_less_eq_rat @ X @ B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_infE
% 2.39/2.74 thf(fact_1367_le__infE,axiom,
% 2.39/2.74 ! [X: nat,A: nat,B: nat] :
% 2.39/2.74 ( ( ord_less_eq_nat @ X @ ( inf_inf_nat @ A @ B ) )
% 2.39/2.74 => ~ ( ( ord_less_eq_nat @ X @ A )
% 2.39/2.74 => ~ ( ord_less_eq_nat @ X @ B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_infE
% 2.39/2.74 thf(fact_1368_le__infE,axiom,
% 2.39/2.74 ! [X: int,A: int,B: int] :
% 2.39/2.74 ( ( ord_less_eq_int @ X @ ( inf_inf_int @ A @ B ) )
% 2.39/2.74 => ~ ( ( ord_less_eq_int @ X @ A )
% 2.39/2.74 => ~ ( ord_less_eq_int @ X @ B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_infE
% 2.39/2.74 thf(fact_1369_inf__le2,axiom,
% 2.39/2.74 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ Y ) ).
% 2.39/2.74
% 2.39/2.74 % inf_le2
% 2.39/2.74 thf(fact_1370_inf__le2,axiom,
% 2.39/2.74 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] : ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ Y ) ).
% 2.39/2.74
% 2.39/2.74 % inf_le2
% 2.39/2.74 thf(fact_1371_inf__le2,axiom,
% 2.39/2.74 ! [X: assn,Y: assn] : ( ord_less_eq_assn @ ( inf_inf_assn @ X @ Y ) @ Y ) ).
% 2.39/2.74
% 2.39/2.74 % inf_le2
% 2.39/2.74 thf(fact_1372_inf__le2,axiom,
% 2.39/2.74 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ Y ) ).
% 2.39/2.74
% 2.39/2.74 % inf_le2
% 2.39/2.74 thf(fact_1373_inf__le2,axiom,
% 2.39/2.74 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ X @ Y ) @ Y ) ).
% 2.39/2.74
% 2.39/2.74 % inf_le2
% 2.39/2.74 thf(fact_1374_inf__le2,axiom,
% 2.39/2.74 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ Y ) ).
% 2.39/2.74
% 2.39/2.74 % inf_le2
% 2.39/2.74 thf(fact_1375_inf__le2,axiom,
% 2.39/2.74 ! [X: int,Y: int] : ( ord_less_eq_int @ ( inf_inf_int @ X @ Y ) @ Y ) ).
% 2.39/2.74
% 2.39/2.74 % inf_le2
% 2.39/2.74 thf(fact_1376_inf__le1,axiom,
% 2.39/2.74 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ X ) ).
% 2.39/2.74
% 2.39/2.74 % inf_le1
% 2.39/2.74 thf(fact_1377_inf__le1,axiom,
% 2.39/2.74 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] : ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ X ) ).
% 2.39/2.74
% 2.39/2.74 % inf_le1
% 2.39/2.74 thf(fact_1378_inf__le1,axiom,
% 2.39/2.74 ! [X: assn,Y: assn] : ( ord_less_eq_assn @ ( inf_inf_assn @ X @ Y ) @ X ) ).
% 2.39/2.74
% 2.39/2.74 % inf_le1
% 2.39/2.74 thf(fact_1379_inf__le1,axiom,
% 2.39/2.74 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ X ) ).
% 2.39/2.74
% 2.39/2.74 % inf_le1
% 2.39/2.74 thf(fact_1380_inf__le1,axiom,
% 2.39/2.74 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ X @ Y ) @ X ) ).
% 2.39/2.74
% 2.39/2.74 % inf_le1
% 2.39/2.74 thf(fact_1381_inf__le1,axiom,
% 2.39/2.74 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ X ) ).
% 2.39/2.74
% 2.39/2.74 % inf_le1
% 2.39/2.74 thf(fact_1382_inf__le1,axiom,
% 2.39/2.74 ! [X: int,Y: int] : ( ord_less_eq_int @ ( inf_inf_int @ X @ Y ) @ X ) ).
% 2.39/2.74
% 2.39/2.74 % inf_le1
% 2.39/2.74 thf(fact_1383_inf__sup__ord_I1_J,axiom,
% 2.39/2.74 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ X ) ).
% 2.39/2.74
% 2.39/2.74 % inf_sup_ord(1)
% 2.39/2.74 thf(fact_1384_inf__sup__ord_I1_J,axiom,
% 2.39/2.74 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] : ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ X ) ).
% 2.39/2.74
% 2.39/2.74 % inf_sup_ord(1)
% 2.39/2.74 thf(fact_1385_inf__sup__ord_I1_J,axiom,
% 2.39/2.74 ! [X: assn,Y: assn] : ( ord_less_eq_assn @ ( inf_inf_assn @ X @ Y ) @ X ) ).
% 2.39/2.74
% 2.39/2.74 % inf_sup_ord(1)
% 2.39/2.74 thf(fact_1386_inf__sup__ord_I1_J,axiom,
% 2.39/2.74 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ X ) ).
% 2.39/2.74
% 2.39/2.74 % inf_sup_ord(1)
% 2.39/2.74 thf(fact_1387_inf__sup__ord_I1_J,axiom,
% 2.39/2.74 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ X @ Y ) @ X ) ).
% 2.39/2.74
% 2.39/2.74 % inf_sup_ord(1)
% 2.39/2.74 thf(fact_1388_inf__sup__ord_I1_J,axiom,
% 2.39/2.74 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ X ) ).
% 2.39/2.74
% 2.39/2.74 % inf_sup_ord(1)
% 2.39/2.74 thf(fact_1389_inf__sup__ord_I1_J,axiom,
% 2.39/2.74 ! [X: int,Y: int] : ( ord_less_eq_int @ ( inf_inf_int @ X @ Y ) @ X ) ).
% 2.39/2.74
% 2.39/2.74 % inf_sup_ord(1)
% 2.39/2.74 thf(fact_1390_inf__sup__ord_I2_J,axiom,
% 2.39/2.74 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ Y ) ).
% 2.39/2.74
% 2.39/2.74 % inf_sup_ord(2)
% 2.39/2.74 thf(fact_1391_inf__sup__ord_I2_J,axiom,
% 2.39/2.74 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] : ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ Y ) ).
% 2.39/2.74
% 2.39/2.74 % inf_sup_ord(2)
% 2.39/2.74 thf(fact_1392_inf__sup__ord_I2_J,axiom,
% 2.39/2.74 ! [X: assn,Y: assn] : ( ord_less_eq_assn @ ( inf_inf_assn @ X @ Y ) @ Y ) ).
% 2.39/2.74
% 2.39/2.74 % inf_sup_ord(2)
% 2.39/2.74 thf(fact_1393_inf__sup__ord_I2_J,axiom,
% 2.39/2.74 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ Y ) ).
% 2.39/2.74
% 2.39/2.74 % inf_sup_ord(2)
% 2.39/2.74 thf(fact_1394_inf__sup__ord_I2_J,axiom,
% 2.39/2.74 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ X @ Y ) @ Y ) ).
% 2.39/2.74
% 2.39/2.74 % inf_sup_ord(2)
% 2.39/2.74 thf(fact_1395_inf__sup__ord_I2_J,axiom,
% 2.39/2.74 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ Y ) ).
% 2.39/2.74
% 2.39/2.74 % inf_sup_ord(2)
% 2.39/2.74 thf(fact_1396_inf__sup__ord_I2_J,axiom,
% 2.39/2.74 ! [X: int,Y: int] : ( ord_less_eq_int @ ( inf_inf_int @ X @ Y ) @ Y ) ).
% 2.39/2.74
% 2.39/2.74 % inf_sup_ord(2)
% 2.39/2.74 thf(fact_1397_inf__sup__ord_I4_J,axiom,
% 2.39/2.74 ! [Y: assn,X: assn] : ( ord_less_eq_assn @ Y @ ( sup_sup_assn @ X @ Y ) ) ).
% 2.39/2.74
% 2.39/2.74 % inf_sup_ord(4)
% 2.39/2.74 thf(fact_1398_inf__sup__ord_I4_J,axiom,
% 2.39/2.74 ! [Y: set_nat,X: set_nat] : ( ord_less_eq_set_nat @ Y @ ( sup_sup_set_nat @ X @ Y ) ) ).
% 2.39/2.74
% 2.39/2.74 % inf_sup_ord(4)
% 2.39/2.74 thf(fact_1399_inf__sup__ord_I4_J,axiom,
% 2.39/2.74 ! [Y: rat,X: rat] : ( ord_less_eq_rat @ Y @ ( sup_sup_rat @ X @ Y ) ) ).
% 2.39/2.74
% 2.39/2.74 % inf_sup_ord(4)
% 2.39/2.74 thf(fact_1400_inf__sup__ord_I4_J,axiom,
% 2.39/2.74 ! [Y: nat,X: nat] : ( ord_less_eq_nat @ Y @ ( sup_sup_nat @ X @ Y ) ) ).
% 2.39/2.74
% 2.39/2.74 % inf_sup_ord(4)
% 2.39/2.74 thf(fact_1401_inf__sup__ord_I4_J,axiom,
% 2.39/2.74 ! [Y: int,X: int] : ( ord_less_eq_int @ Y @ ( sup_sup_int @ X @ Y ) ) ).
% 2.39/2.74
% 2.39/2.74 % inf_sup_ord(4)
% 2.39/2.74 thf(fact_1402_inf__sup__ord_I3_J,axiom,
% 2.39/2.74 ! [X: assn,Y: assn] : ( ord_less_eq_assn @ X @ ( sup_sup_assn @ X @ Y ) ) ).
% 2.39/2.74
% 2.39/2.74 % inf_sup_ord(3)
% 2.39/2.74 thf(fact_1403_inf__sup__ord_I3_J,axiom,
% 2.39/2.74 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ X @ Y ) ) ).
% 2.39/2.74
% 2.39/2.74 % inf_sup_ord(3)
% 2.39/2.74 thf(fact_1404_inf__sup__ord_I3_J,axiom,
% 2.39/2.74 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ X @ ( sup_sup_rat @ X @ Y ) ) ).
% 2.39/2.74
% 2.39/2.74 % inf_sup_ord(3)
% 2.39/2.74 thf(fact_1405_inf__sup__ord_I3_J,axiom,
% 2.39/2.74 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ X @ ( sup_sup_nat @ X @ Y ) ) ).
% 2.39/2.74
% 2.39/2.74 % inf_sup_ord(3)
% 2.39/2.74 thf(fact_1406_inf__sup__ord_I3_J,axiom,
% 2.39/2.74 ! [X: int,Y: int] : ( ord_less_eq_int @ X @ ( sup_sup_int @ X @ Y ) ) ).
% 2.39/2.74
% 2.39/2.74 % inf_sup_ord(3)
% 2.39/2.74 thf(fact_1407_le__supE,axiom,
% 2.39/2.74 ! [A: assn,B: assn,X: assn] :
% 2.39/2.74 ( ( ord_less_eq_assn @ ( sup_sup_assn @ A @ B ) @ X )
% 2.39/2.74 => ~ ( ( ord_less_eq_assn @ A @ X )
% 2.39/2.74 => ~ ( ord_less_eq_assn @ B @ X ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_supE
% 2.39/2.74 thf(fact_1408_le__supE,axiom,
% 2.39/2.74 ! [A: set_nat,B: set_nat,X: set_nat] :
% 2.39/2.74 ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A @ B ) @ X )
% 2.39/2.74 => ~ ( ( ord_less_eq_set_nat @ A @ X )
% 2.39/2.74 => ~ ( ord_less_eq_set_nat @ B @ X ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_supE
% 2.39/2.74 thf(fact_1409_le__supE,axiom,
% 2.39/2.74 ! [A: rat,B: rat,X: rat] :
% 2.39/2.74 ( ( ord_less_eq_rat @ ( sup_sup_rat @ A @ B ) @ X )
% 2.39/2.74 => ~ ( ( ord_less_eq_rat @ A @ X )
% 2.39/2.74 => ~ ( ord_less_eq_rat @ B @ X ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_supE
% 2.39/2.74 thf(fact_1410_le__supE,axiom,
% 2.39/2.74 ! [A: nat,B: nat,X: nat] :
% 2.39/2.74 ( ( ord_less_eq_nat @ ( sup_sup_nat @ A @ B ) @ X )
% 2.39/2.74 => ~ ( ( ord_less_eq_nat @ A @ X )
% 2.39/2.74 => ~ ( ord_less_eq_nat @ B @ X ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_supE
% 2.39/2.74 thf(fact_1411_le__supE,axiom,
% 2.39/2.74 ! [A: int,B: int,X: int] :
% 2.39/2.74 ( ( ord_less_eq_int @ ( sup_sup_int @ A @ B ) @ X )
% 2.39/2.74 => ~ ( ( ord_less_eq_int @ A @ X )
% 2.39/2.74 => ~ ( ord_less_eq_int @ B @ X ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_supE
% 2.39/2.74 thf(fact_1412_le__supI,axiom,
% 2.39/2.74 ! [A: assn,X: assn,B: assn] :
% 2.39/2.74 ( ( ord_less_eq_assn @ A @ X )
% 2.39/2.74 => ( ( ord_less_eq_assn @ B @ X )
% 2.39/2.74 => ( ord_less_eq_assn @ ( sup_sup_assn @ A @ B ) @ X ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_supI
% 2.39/2.74 thf(fact_1413_le__supI,axiom,
% 2.39/2.74 ! [A: set_nat,X: set_nat,B: set_nat] :
% 2.39/2.74 ( ( ord_less_eq_set_nat @ A @ X )
% 2.39/2.74 => ( ( ord_less_eq_set_nat @ B @ X )
% 2.39/2.74 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A @ B ) @ X ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_supI
% 2.39/2.74 thf(fact_1414_le__supI,axiom,
% 2.39/2.74 ! [A: rat,X: rat,B: rat] :
% 2.39/2.74 ( ( ord_less_eq_rat @ A @ X )
% 2.39/2.74 => ( ( ord_less_eq_rat @ B @ X )
% 2.39/2.74 => ( ord_less_eq_rat @ ( sup_sup_rat @ A @ B ) @ X ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_supI
% 2.39/2.74 thf(fact_1415_le__supI,axiom,
% 2.39/2.74 ! [A: nat,X: nat,B: nat] :
% 2.39/2.74 ( ( ord_less_eq_nat @ A @ X )
% 2.39/2.74 => ( ( ord_less_eq_nat @ B @ X )
% 2.39/2.74 => ( ord_less_eq_nat @ ( sup_sup_nat @ A @ B ) @ X ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_supI
% 2.39/2.74 thf(fact_1416_le__supI,axiom,
% 2.39/2.74 ! [A: int,X: int,B: int] :
% 2.39/2.74 ( ( ord_less_eq_int @ A @ X )
% 2.39/2.74 => ( ( ord_less_eq_int @ B @ X )
% 2.39/2.74 => ( ord_less_eq_int @ ( sup_sup_int @ A @ B ) @ X ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_supI
% 2.39/2.74 thf(fact_1417_sup__ge1,axiom,
% 2.39/2.74 ! [X: assn,Y: assn] : ( ord_less_eq_assn @ X @ ( sup_sup_assn @ X @ Y ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup_ge1
% 2.39/2.74 thf(fact_1418_sup__ge1,axiom,
% 2.39/2.74 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ X @ Y ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup_ge1
% 2.39/2.74 thf(fact_1419_sup__ge1,axiom,
% 2.39/2.74 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ X @ ( sup_sup_rat @ X @ Y ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup_ge1
% 2.39/2.74 thf(fact_1420_sup__ge1,axiom,
% 2.39/2.74 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ X @ ( sup_sup_nat @ X @ Y ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup_ge1
% 2.39/2.74 thf(fact_1421_sup__ge1,axiom,
% 2.39/2.74 ! [X: int,Y: int] : ( ord_less_eq_int @ X @ ( sup_sup_int @ X @ Y ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup_ge1
% 2.39/2.74 thf(fact_1422_sup__ge2,axiom,
% 2.39/2.74 ! [Y: assn,X: assn] : ( ord_less_eq_assn @ Y @ ( sup_sup_assn @ X @ Y ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup_ge2
% 2.39/2.74 thf(fact_1423_sup__ge2,axiom,
% 2.39/2.74 ! [Y: set_nat,X: set_nat] : ( ord_less_eq_set_nat @ Y @ ( sup_sup_set_nat @ X @ Y ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup_ge2
% 2.39/2.74 thf(fact_1424_sup__ge2,axiom,
% 2.39/2.74 ! [Y: rat,X: rat] : ( ord_less_eq_rat @ Y @ ( sup_sup_rat @ X @ Y ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup_ge2
% 2.39/2.74 thf(fact_1425_sup__ge2,axiom,
% 2.39/2.74 ! [Y: nat,X: nat] : ( ord_less_eq_nat @ Y @ ( sup_sup_nat @ X @ Y ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup_ge2
% 2.39/2.74 thf(fact_1426_sup__ge2,axiom,
% 2.39/2.74 ! [Y: int,X: int] : ( ord_less_eq_int @ Y @ ( sup_sup_int @ X @ Y ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup_ge2
% 2.39/2.74 thf(fact_1427_le__supI1,axiom,
% 2.39/2.74 ! [X: assn,A: assn,B: assn] :
% 2.39/2.74 ( ( ord_less_eq_assn @ X @ A )
% 2.39/2.74 => ( ord_less_eq_assn @ X @ ( sup_sup_assn @ A @ B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_supI1
% 2.39/2.74 thf(fact_1428_le__supI1,axiom,
% 2.39/2.74 ! [X: set_nat,A: set_nat,B: set_nat] :
% 2.39/2.74 ( ( ord_less_eq_set_nat @ X @ A )
% 2.39/2.74 => ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_supI1
% 2.39/2.74 thf(fact_1429_le__supI1,axiom,
% 2.39/2.74 ! [X: rat,A: rat,B: rat] :
% 2.39/2.74 ( ( ord_less_eq_rat @ X @ A )
% 2.39/2.74 => ( ord_less_eq_rat @ X @ ( sup_sup_rat @ A @ B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_supI1
% 2.39/2.74 thf(fact_1430_le__supI1,axiom,
% 2.39/2.74 ! [X: nat,A: nat,B: nat] :
% 2.39/2.74 ( ( ord_less_eq_nat @ X @ A )
% 2.39/2.74 => ( ord_less_eq_nat @ X @ ( sup_sup_nat @ A @ B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_supI1
% 2.39/2.74 thf(fact_1431_le__supI1,axiom,
% 2.39/2.74 ! [X: int,A: int,B: int] :
% 2.39/2.74 ( ( ord_less_eq_int @ X @ A )
% 2.39/2.74 => ( ord_less_eq_int @ X @ ( sup_sup_int @ A @ B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_supI1
% 2.39/2.74 thf(fact_1432_le__supI2,axiom,
% 2.39/2.74 ! [X: assn,B: assn,A: assn] :
% 2.39/2.74 ( ( ord_less_eq_assn @ X @ B )
% 2.39/2.74 => ( ord_less_eq_assn @ X @ ( sup_sup_assn @ A @ B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_supI2
% 2.39/2.74 thf(fact_1433_le__supI2,axiom,
% 2.39/2.74 ! [X: set_nat,B: set_nat,A: set_nat] :
% 2.39/2.74 ( ( ord_less_eq_set_nat @ X @ B )
% 2.39/2.74 => ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_supI2
% 2.39/2.74 thf(fact_1434_le__supI2,axiom,
% 2.39/2.74 ! [X: rat,B: rat,A: rat] :
% 2.39/2.74 ( ( ord_less_eq_rat @ X @ B )
% 2.39/2.74 => ( ord_less_eq_rat @ X @ ( sup_sup_rat @ A @ B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_supI2
% 2.39/2.74 thf(fact_1435_le__supI2,axiom,
% 2.39/2.74 ! [X: nat,B: nat,A: nat] :
% 2.39/2.74 ( ( ord_less_eq_nat @ X @ B )
% 2.39/2.74 => ( ord_less_eq_nat @ X @ ( sup_sup_nat @ A @ B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_supI2
% 2.39/2.74 thf(fact_1436_le__supI2,axiom,
% 2.39/2.74 ! [X: int,B: int,A: int] :
% 2.39/2.74 ( ( ord_less_eq_int @ X @ B )
% 2.39/2.74 => ( ord_less_eq_int @ X @ ( sup_sup_int @ A @ B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_supI2
% 2.39/2.74 thf(fact_1437_sup_Omono,axiom,
% 2.39/2.74 ! [C: assn,A: assn,D2: assn,B: assn] :
% 2.39/2.74 ( ( ord_less_eq_assn @ C @ A )
% 2.39/2.74 => ( ( ord_less_eq_assn @ D2 @ B )
% 2.39/2.74 => ( ord_less_eq_assn @ ( sup_sup_assn @ C @ D2 ) @ ( sup_sup_assn @ A @ B ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.mono
% 2.39/2.74 thf(fact_1438_sup_Omono,axiom,
% 2.39/2.74 ! [C: set_nat,A: set_nat,D2: set_nat,B: set_nat] :
% 2.39/2.74 ( ( ord_less_eq_set_nat @ C @ A )
% 2.39/2.74 => ( ( ord_less_eq_set_nat @ D2 @ B )
% 2.39/2.74 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ C @ D2 ) @ ( sup_sup_set_nat @ A @ B ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.mono
% 2.39/2.74 thf(fact_1439_sup_Omono,axiom,
% 2.39/2.74 ! [C: rat,A: rat,D2: rat,B: rat] :
% 2.39/2.74 ( ( ord_less_eq_rat @ C @ A )
% 2.39/2.74 => ( ( ord_less_eq_rat @ D2 @ B )
% 2.39/2.74 => ( ord_less_eq_rat @ ( sup_sup_rat @ C @ D2 ) @ ( sup_sup_rat @ A @ B ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.mono
% 2.39/2.74 thf(fact_1440_sup_Omono,axiom,
% 2.39/2.74 ! [C: nat,A: nat,D2: nat,B: nat] :
% 2.39/2.74 ( ( ord_less_eq_nat @ C @ A )
% 2.39/2.74 => ( ( ord_less_eq_nat @ D2 @ B )
% 2.39/2.74 => ( ord_less_eq_nat @ ( sup_sup_nat @ C @ D2 ) @ ( sup_sup_nat @ A @ B ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.mono
% 2.39/2.74 thf(fact_1441_sup_Omono,axiom,
% 2.39/2.74 ! [C: int,A: int,D2: int,B: int] :
% 2.39/2.74 ( ( ord_less_eq_int @ C @ A )
% 2.39/2.74 => ( ( ord_less_eq_int @ D2 @ B )
% 2.39/2.74 => ( ord_less_eq_int @ ( sup_sup_int @ C @ D2 ) @ ( sup_sup_int @ A @ B ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.mono
% 2.39/2.74 thf(fact_1442_sup__mono,axiom,
% 2.39/2.74 ! [A: assn,C: assn,B: assn,D2: assn] :
% 2.39/2.74 ( ( ord_less_eq_assn @ A @ C )
% 2.39/2.74 => ( ( ord_less_eq_assn @ B @ D2 )
% 2.39/2.74 => ( ord_less_eq_assn @ ( sup_sup_assn @ A @ B ) @ ( sup_sup_assn @ C @ D2 ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup_mono
% 2.39/2.74 thf(fact_1443_sup__mono,axiom,
% 2.39/2.74 ! [A: set_nat,C: set_nat,B: set_nat,D2: set_nat] :
% 2.39/2.74 ( ( ord_less_eq_set_nat @ A @ C )
% 2.39/2.74 => ( ( ord_less_eq_set_nat @ B @ D2 )
% 2.39/2.74 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A @ B ) @ ( sup_sup_set_nat @ C @ D2 ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup_mono
% 2.39/2.74 thf(fact_1444_sup__mono,axiom,
% 2.39/2.74 ! [A: rat,C: rat,B: rat,D2: rat] :
% 2.39/2.74 ( ( ord_less_eq_rat @ A @ C )
% 2.39/2.74 => ( ( ord_less_eq_rat @ B @ D2 )
% 2.39/2.74 => ( ord_less_eq_rat @ ( sup_sup_rat @ A @ B ) @ ( sup_sup_rat @ C @ D2 ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup_mono
% 2.39/2.74 thf(fact_1445_sup__mono,axiom,
% 2.39/2.74 ! [A: nat,C: nat,B: nat,D2: nat] :
% 2.39/2.74 ( ( ord_less_eq_nat @ A @ C )
% 2.39/2.74 => ( ( ord_less_eq_nat @ B @ D2 )
% 2.39/2.74 => ( ord_less_eq_nat @ ( sup_sup_nat @ A @ B ) @ ( sup_sup_nat @ C @ D2 ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup_mono
% 2.39/2.74 thf(fact_1446_sup__mono,axiom,
% 2.39/2.74 ! [A: int,C: int,B: int,D2: int] :
% 2.39/2.74 ( ( ord_less_eq_int @ A @ C )
% 2.39/2.74 => ( ( ord_less_eq_int @ B @ D2 )
% 2.39/2.74 => ( ord_less_eq_int @ ( sup_sup_int @ A @ B ) @ ( sup_sup_int @ C @ D2 ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup_mono
% 2.39/2.74 thf(fact_1447_sup__least,axiom,
% 2.39/2.74 ! [Y: assn,X: assn,Z: assn] :
% 2.39/2.74 ( ( ord_less_eq_assn @ Y @ X )
% 2.39/2.74 => ( ( ord_less_eq_assn @ Z @ X )
% 2.39/2.74 => ( ord_less_eq_assn @ ( sup_sup_assn @ Y @ Z ) @ X ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup_least
% 2.39/2.74 thf(fact_1448_sup__least,axiom,
% 2.39/2.74 ! [Y: set_nat,X: set_nat,Z: set_nat] :
% 2.39/2.74 ( ( ord_less_eq_set_nat @ Y @ X )
% 2.39/2.74 => ( ( ord_less_eq_set_nat @ Z @ X )
% 2.39/2.74 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ Y @ Z ) @ X ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup_least
% 2.39/2.74 thf(fact_1449_sup__least,axiom,
% 2.39/2.74 ! [Y: rat,X: rat,Z: rat] :
% 2.39/2.74 ( ( ord_less_eq_rat @ Y @ X )
% 2.39/2.74 => ( ( ord_less_eq_rat @ Z @ X )
% 2.39/2.74 => ( ord_less_eq_rat @ ( sup_sup_rat @ Y @ Z ) @ X ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup_least
% 2.39/2.74 thf(fact_1450_sup__least,axiom,
% 2.39/2.74 ! [Y: nat,X: nat,Z: nat] :
% 2.39/2.74 ( ( ord_less_eq_nat @ Y @ X )
% 2.39/2.74 => ( ( ord_less_eq_nat @ Z @ X )
% 2.39/2.74 => ( ord_less_eq_nat @ ( sup_sup_nat @ Y @ Z ) @ X ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup_least
% 2.39/2.74 thf(fact_1451_sup__least,axiom,
% 2.39/2.74 ! [Y: int,X: int,Z: int] :
% 2.39/2.74 ( ( ord_less_eq_int @ Y @ X )
% 2.39/2.74 => ( ( ord_less_eq_int @ Z @ X )
% 2.39/2.74 => ( ord_less_eq_int @ ( sup_sup_int @ Y @ Z ) @ X ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup_least
% 2.39/2.74 thf(fact_1452_le__iff__sup,axiom,
% 2.39/2.74 ( ord_less_eq_assn
% 2.39/2.74 = ( ^ [X2: assn,Y2: assn] :
% 2.39/2.74 ( ( sup_sup_assn @ X2 @ Y2 )
% 2.39/2.74 = Y2 ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_iff_sup
% 2.39/2.74 thf(fact_1453_le__iff__sup,axiom,
% 2.39/2.74 ( ord_less_eq_set_nat
% 2.39/2.74 = ( ^ [X2: set_nat,Y2: set_nat] :
% 2.39/2.74 ( ( sup_sup_set_nat @ X2 @ Y2 )
% 2.39/2.74 = Y2 ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_iff_sup
% 2.39/2.74 thf(fact_1454_le__iff__sup,axiom,
% 2.39/2.74 ( ord_less_eq_rat
% 2.39/2.74 = ( ^ [X2: rat,Y2: rat] :
% 2.39/2.74 ( ( sup_sup_rat @ X2 @ Y2 )
% 2.39/2.74 = Y2 ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_iff_sup
% 2.39/2.74 thf(fact_1455_le__iff__sup,axiom,
% 2.39/2.74 ( ord_less_eq_nat
% 2.39/2.74 = ( ^ [X2: nat,Y2: nat] :
% 2.39/2.74 ( ( sup_sup_nat @ X2 @ Y2 )
% 2.39/2.74 = Y2 ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_iff_sup
% 2.39/2.74 thf(fact_1456_le__iff__sup,axiom,
% 2.39/2.74 ( ord_less_eq_int
% 2.39/2.74 = ( ^ [X2: int,Y2: int] :
% 2.39/2.74 ( ( sup_sup_int @ X2 @ Y2 )
% 2.39/2.74 = Y2 ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_iff_sup
% 2.39/2.74 thf(fact_1457_sup_OorderE,axiom,
% 2.39/2.74 ! [B: assn,A: assn] :
% 2.39/2.74 ( ( ord_less_eq_assn @ B @ A )
% 2.39/2.74 => ( A
% 2.39/2.74 = ( sup_sup_assn @ A @ B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.orderE
% 2.39/2.74 thf(fact_1458_sup_OorderE,axiom,
% 2.39/2.74 ! [B: set_nat,A: set_nat] :
% 2.39/2.74 ( ( ord_less_eq_set_nat @ B @ A )
% 2.39/2.74 => ( A
% 2.39/2.74 = ( sup_sup_set_nat @ A @ B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.orderE
% 2.39/2.74 thf(fact_1459_sup_OorderE,axiom,
% 2.39/2.74 ! [B: rat,A: rat] :
% 2.39/2.74 ( ( ord_less_eq_rat @ B @ A )
% 2.39/2.74 => ( A
% 2.39/2.74 = ( sup_sup_rat @ A @ B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.orderE
% 2.39/2.74 thf(fact_1460_sup_OorderE,axiom,
% 2.39/2.74 ! [B: nat,A: nat] :
% 2.39/2.74 ( ( ord_less_eq_nat @ B @ A )
% 2.39/2.74 => ( A
% 2.39/2.74 = ( sup_sup_nat @ A @ B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.orderE
% 2.39/2.74 thf(fact_1461_sup_OorderE,axiom,
% 2.39/2.74 ! [B: int,A: int] :
% 2.39/2.74 ( ( ord_less_eq_int @ B @ A )
% 2.39/2.74 => ( A
% 2.39/2.74 = ( sup_sup_int @ A @ B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.orderE
% 2.39/2.74 thf(fact_1462_sup_OorderI,axiom,
% 2.39/2.74 ! [A: assn,B: assn] :
% 2.39/2.74 ( ( A
% 2.39/2.74 = ( sup_sup_assn @ A @ B ) )
% 2.39/2.74 => ( ord_less_eq_assn @ B @ A ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.orderI
% 2.39/2.74 thf(fact_1463_sup_OorderI,axiom,
% 2.39/2.74 ! [A: set_nat,B: set_nat] :
% 2.39/2.74 ( ( A
% 2.39/2.74 = ( sup_sup_set_nat @ A @ B ) )
% 2.39/2.74 => ( ord_less_eq_set_nat @ B @ A ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.orderI
% 2.39/2.74 thf(fact_1464_sup_OorderI,axiom,
% 2.39/2.74 ! [A: rat,B: rat] :
% 2.39/2.74 ( ( A
% 2.39/2.74 = ( sup_sup_rat @ A @ B ) )
% 2.39/2.74 => ( ord_less_eq_rat @ B @ A ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.orderI
% 2.39/2.74 thf(fact_1465_sup_OorderI,axiom,
% 2.39/2.74 ! [A: nat,B: nat] :
% 2.39/2.74 ( ( A
% 2.39/2.74 = ( sup_sup_nat @ A @ B ) )
% 2.39/2.74 => ( ord_less_eq_nat @ B @ A ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.orderI
% 2.39/2.74 thf(fact_1466_sup_OorderI,axiom,
% 2.39/2.74 ! [A: int,B: int] :
% 2.39/2.74 ( ( A
% 2.39/2.74 = ( sup_sup_int @ A @ B ) )
% 2.39/2.74 => ( ord_less_eq_int @ B @ A ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.orderI
% 2.39/2.74 thf(fact_1467_sup__unique,axiom,
% 2.39/2.74 ! [F2: assn > assn > assn,X: assn,Y: assn] :
% 2.39/2.74 ( ! [X3: assn,Y3: assn] : ( ord_less_eq_assn @ X3 @ ( F2 @ X3 @ Y3 ) )
% 2.39/2.74 => ( ! [X3: assn,Y3: assn] : ( ord_less_eq_assn @ Y3 @ ( F2 @ X3 @ Y3 ) )
% 2.39/2.74 => ( ! [X3: assn,Y3: assn,Z2: assn] :
% 2.39/2.74 ( ( ord_less_eq_assn @ Y3 @ X3 )
% 2.39/2.74 => ( ( ord_less_eq_assn @ Z2 @ X3 )
% 2.39/2.74 => ( ord_less_eq_assn @ ( F2 @ Y3 @ Z2 ) @ X3 ) ) )
% 2.39/2.74 => ( ( sup_sup_assn @ X @ Y )
% 2.39/2.74 = ( F2 @ X @ Y ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup_unique
% 2.39/2.74 thf(fact_1468_sup__unique,axiom,
% 2.39/2.74 ! [F2: set_nat > set_nat > set_nat,X: set_nat,Y: set_nat] :
% 2.39/2.74 ( ! [X3: set_nat,Y3: set_nat] : ( ord_less_eq_set_nat @ X3 @ ( F2 @ X3 @ Y3 ) )
% 2.39/2.74 => ( ! [X3: set_nat,Y3: set_nat] : ( ord_less_eq_set_nat @ Y3 @ ( F2 @ X3 @ Y3 ) )
% 2.39/2.74 => ( ! [X3: set_nat,Y3: set_nat,Z2: set_nat] :
% 2.39/2.74 ( ( ord_less_eq_set_nat @ Y3 @ X3 )
% 2.39/2.74 => ( ( ord_less_eq_set_nat @ Z2 @ X3 )
% 2.39/2.74 => ( ord_less_eq_set_nat @ ( F2 @ Y3 @ Z2 ) @ X3 ) ) )
% 2.39/2.74 => ( ( sup_sup_set_nat @ X @ Y )
% 2.39/2.74 = ( F2 @ X @ Y ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup_unique
% 2.39/2.74 thf(fact_1469_sup__unique,axiom,
% 2.39/2.74 ! [F2: rat > rat > rat,X: rat,Y: rat] :
% 2.39/2.74 ( ! [X3: rat,Y3: rat] : ( ord_less_eq_rat @ X3 @ ( F2 @ X3 @ Y3 ) )
% 2.39/2.74 => ( ! [X3: rat,Y3: rat] : ( ord_less_eq_rat @ Y3 @ ( F2 @ X3 @ Y3 ) )
% 2.39/2.74 => ( ! [X3: rat,Y3: rat,Z2: rat] :
% 2.39/2.74 ( ( ord_less_eq_rat @ Y3 @ X3 )
% 2.39/2.74 => ( ( ord_less_eq_rat @ Z2 @ X3 )
% 2.39/2.74 => ( ord_less_eq_rat @ ( F2 @ Y3 @ Z2 ) @ X3 ) ) )
% 2.39/2.74 => ( ( sup_sup_rat @ X @ Y )
% 2.39/2.74 = ( F2 @ X @ Y ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup_unique
% 2.39/2.74 thf(fact_1470_sup__unique,axiom,
% 2.39/2.74 ! [F2: nat > nat > nat,X: nat,Y: nat] :
% 2.39/2.74 ( ! [X3: nat,Y3: nat] : ( ord_less_eq_nat @ X3 @ ( F2 @ X3 @ Y3 ) )
% 2.39/2.74 => ( ! [X3: nat,Y3: nat] : ( ord_less_eq_nat @ Y3 @ ( F2 @ X3 @ Y3 ) )
% 2.39/2.74 => ( ! [X3: nat,Y3: nat,Z2: nat] :
% 2.39/2.74 ( ( ord_less_eq_nat @ Y3 @ X3 )
% 2.39/2.74 => ( ( ord_less_eq_nat @ Z2 @ X3 )
% 2.39/2.74 => ( ord_less_eq_nat @ ( F2 @ Y3 @ Z2 ) @ X3 ) ) )
% 2.39/2.74 => ( ( sup_sup_nat @ X @ Y )
% 2.39/2.74 = ( F2 @ X @ Y ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup_unique
% 2.39/2.74 thf(fact_1471_sup__unique,axiom,
% 2.39/2.74 ! [F2: int > int > int,X: int,Y: int] :
% 2.39/2.74 ( ! [X3: int,Y3: int] : ( ord_less_eq_int @ X3 @ ( F2 @ X3 @ Y3 ) )
% 2.39/2.74 => ( ! [X3: int,Y3: int] : ( ord_less_eq_int @ Y3 @ ( F2 @ X3 @ Y3 ) )
% 2.39/2.74 => ( ! [X3: int,Y3: int,Z2: int] :
% 2.39/2.74 ( ( ord_less_eq_int @ Y3 @ X3 )
% 2.39/2.74 => ( ( ord_less_eq_int @ Z2 @ X3 )
% 2.39/2.74 => ( ord_less_eq_int @ ( F2 @ Y3 @ Z2 ) @ X3 ) ) )
% 2.39/2.74 => ( ( sup_sup_int @ X @ Y )
% 2.39/2.74 = ( F2 @ X @ Y ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup_unique
% 2.39/2.74 thf(fact_1472_sup_Oabsorb1,axiom,
% 2.39/2.74 ! [B: assn,A: assn] :
% 2.39/2.74 ( ( ord_less_eq_assn @ B @ A )
% 2.39/2.74 => ( ( sup_sup_assn @ A @ B )
% 2.39/2.74 = A ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.absorb1
% 2.39/2.74 thf(fact_1473_sup_Oabsorb1,axiom,
% 2.39/2.74 ! [B: set_nat,A: set_nat] :
% 2.39/2.74 ( ( ord_less_eq_set_nat @ B @ A )
% 2.39/2.74 => ( ( sup_sup_set_nat @ A @ B )
% 2.39/2.74 = A ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.absorb1
% 2.39/2.74 thf(fact_1474_sup_Oabsorb1,axiom,
% 2.39/2.74 ! [B: rat,A: rat] :
% 2.39/2.74 ( ( ord_less_eq_rat @ B @ A )
% 2.39/2.74 => ( ( sup_sup_rat @ A @ B )
% 2.39/2.74 = A ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.absorb1
% 2.39/2.74 thf(fact_1475_sup_Oabsorb1,axiom,
% 2.39/2.74 ! [B: nat,A: nat] :
% 2.39/2.74 ( ( ord_less_eq_nat @ B @ A )
% 2.39/2.74 => ( ( sup_sup_nat @ A @ B )
% 2.39/2.74 = A ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.absorb1
% 2.39/2.74 thf(fact_1476_sup_Oabsorb1,axiom,
% 2.39/2.74 ! [B: int,A: int] :
% 2.39/2.74 ( ( ord_less_eq_int @ B @ A )
% 2.39/2.74 => ( ( sup_sup_int @ A @ B )
% 2.39/2.74 = A ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.absorb1
% 2.39/2.74 thf(fact_1477_sup_Oabsorb2,axiom,
% 2.39/2.74 ! [A: assn,B: assn] :
% 2.39/2.74 ( ( ord_less_eq_assn @ A @ B )
% 2.39/2.74 => ( ( sup_sup_assn @ A @ B )
% 2.39/2.74 = B ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.absorb2
% 2.39/2.74 thf(fact_1478_sup_Oabsorb2,axiom,
% 2.39/2.74 ! [A: set_nat,B: set_nat] :
% 2.39/2.74 ( ( ord_less_eq_set_nat @ A @ B )
% 2.39/2.74 => ( ( sup_sup_set_nat @ A @ B )
% 2.39/2.74 = B ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.absorb2
% 2.39/2.74 thf(fact_1479_sup_Oabsorb2,axiom,
% 2.39/2.74 ! [A: rat,B: rat] :
% 2.39/2.74 ( ( ord_less_eq_rat @ A @ B )
% 2.39/2.74 => ( ( sup_sup_rat @ A @ B )
% 2.39/2.74 = B ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.absorb2
% 2.39/2.74 thf(fact_1480_sup_Oabsorb2,axiom,
% 2.39/2.74 ! [A: nat,B: nat] :
% 2.39/2.74 ( ( ord_less_eq_nat @ A @ B )
% 2.39/2.74 => ( ( sup_sup_nat @ A @ B )
% 2.39/2.74 = B ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.absorb2
% 2.39/2.74 thf(fact_1481_sup_Oabsorb2,axiom,
% 2.39/2.74 ! [A: int,B: int] :
% 2.39/2.74 ( ( ord_less_eq_int @ A @ B )
% 2.39/2.74 => ( ( sup_sup_int @ A @ B )
% 2.39/2.74 = B ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.absorb2
% 2.39/2.74 thf(fact_1482_sup__absorb1,axiom,
% 2.39/2.74 ! [Y: assn,X: assn] :
% 2.39/2.74 ( ( ord_less_eq_assn @ Y @ X )
% 2.39/2.74 => ( ( sup_sup_assn @ X @ Y )
% 2.39/2.74 = X ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup_absorb1
% 2.39/2.74 thf(fact_1483_sup__absorb1,axiom,
% 2.39/2.74 ! [Y: set_nat,X: set_nat] :
% 2.39/2.74 ( ( ord_less_eq_set_nat @ Y @ X )
% 2.39/2.74 => ( ( sup_sup_set_nat @ X @ Y )
% 2.39/2.74 = X ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup_absorb1
% 2.39/2.74 thf(fact_1484_sup__absorb1,axiom,
% 2.39/2.74 ! [Y: rat,X: rat] :
% 2.39/2.74 ( ( ord_less_eq_rat @ Y @ X )
% 2.39/2.74 => ( ( sup_sup_rat @ X @ Y )
% 2.39/2.74 = X ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup_absorb1
% 2.39/2.74 thf(fact_1485_sup__absorb1,axiom,
% 2.39/2.74 ! [Y: nat,X: nat] :
% 2.39/2.74 ( ( ord_less_eq_nat @ Y @ X )
% 2.39/2.74 => ( ( sup_sup_nat @ X @ Y )
% 2.39/2.74 = X ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup_absorb1
% 2.39/2.74 thf(fact_1486_sup__absorb1,axiom,
% 2.39/2.74 ! [Y: int,X: int] :
% 2.39/2.74 ( ( ord_less_eq_int @ Y @ X )
% 2.39/2.74 => ( ( sup_sup_int @ X @ Y )
% 2.39/2.74 = X ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup_absorb1
% 2.39/2.74 thf(fact_1487_sup__absorb2,axiom,
% 2.39/2.74 ! [X: assn,Y: assn] :
% 2.39/2.74 ( ( ord_less_eq_assn @ X @ Y )
% 2.39/2.74 => ( ( sup_sup_assn @ X @ Y )
% 2.39/2.74 = Y ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup_absorb2
% 2.39/2.74 thf(fact_1488_sup__absorb2,axiom,
% 2.39/2.74 ! [X: set_nat,Y: set_nat] :
% 2.39/2.74 ( ( ord_less_eq_set_nat @ X @ Y )
% 2.39/2.74 => ( ( sup_sup_set_nat @ X @ Y )
% 2.39/2.74 = Y ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup_absorb2
% 2.39/2.74 thf(fact_1489_sup__absorb2,axiom,
% 2.39/2.74 ! [X: rat,Y: rat] :
% 2.39/2.74 ( ( ord_less_eq_rat @ X @ Y )
% 2.39/2.74 => ( ( sup_sup_rat @ X @ Y )
% 2.39/2.74 = Y ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup_absorb2
% 2.39/2.74 thf(fact_1490_sup__absorb2,axiom,
% 2.39/2.74 ! [X: nat,Y: nat] :
% 2.39/2.74 ( ( ord_less_eq_nat @ X @ Y )
% 2.39/2.74 => ( ( sup_sup_nat @ X @ Y )
% 2.39/2.74 = Y ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup_absorb2
% 2.39/2.74 thf(fact_1491_sup__absorb2,axiom,
% 2.39/2.74 ! [X: int,Y: int] :
% 2.39/2.74 ( ( ord_less_eq_int @ X @ Y )
% 2.39/2.74 => ( ( sup_sup_int @ X @ Y )
% 2.39/2.74 = Y ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup_absorb2
% 2.39/2.74 thf(fact_1492_sup_OboundedE,axiom,
% 2.39/2.74 ! [B: assn,C: assn,A: assn] :
% 2.39/2.74 ( ( ord_less_eq_assn @ ( sup_sup_assn @ B @ C ) @ A )
% 2.39/2.74 => ~ ( ( ord_less_eq_assn @ B @ A )
% 2.39/2.74 => ~ ( ord_less_eq_assn @ C @ A ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.boundedE
% 2.39/2.74 thf(fact_1493_sup_OboundedE,axiom,
% 2.39/2.74 ! [B: set_nat,C: set_nat,A: set_nat] :
% 2.39/2.74 ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ B @ C ) @ A )
% 2.39/2.74 => ~ ( ( ord_less_eq_set_nat @ B @ A )
% 2.39/2.74 => ~ ( ord_less_eq_set_nat @ C @ A ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.boundedE
% 2.39/2.74 thf(fact_1494_sup_OboundedE,axiom,
% 2.39/2.74 ! [B: rat,C: rat,A: rat] :
% 2.39/2.74 ( ( ord_less_eq_rat @ ( sup_sup_rat @ B @ C ) @ A )
% 2.39/2.74 => ~ ( ( ord_less_eq_rat @ B @ A )
% 2.39/2.74 => ~ ( ord_less_eq_rat @ C @ A ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.boundedE
% 2.39/2.74 thf(fact_1495_sup_OboundedE,axiom,
% 2.39/2.74 ! [B: nat,C: nat,A: nat] :
% 2.39/2.74 ( ( ord_less_eq_nat @ ( sup_sup_nat @ B @ C ) @ A )
% 2.39/2.74 => ~ ( ( ord_less_eq_nat @ B @ A )
% 2.39/2.74 => ~ ( ord_less_eq_nat @ C @ A ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.boundedE
% 2.39/2.74 thf(fact_1496_sup_OboundedE,axiom,
% 2.39/2.74 ! [B: int,C: int,A: int] :
% 2.39/2.74 ( ( ord_less_eq_int @ ( sup_sup_int @ B @ C ) @ A )
% 2.39/2.74 => ~ ( ( ord_less_eq_int @ B @ A )
% 2.39/2.74 => ~ ( ord_less_eq_int @ C @ A ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.boundedE
% 2.39/2.74 thf(fact_1497_sup_OboundedI,axiom,
% 2.39/2.74 ! [B: assn,A: assn,C: assn] :
% 2.39/2.74 ( ( ord_less_eq_assn @ B @ A )
% 2.39/2.74 => ( ( ord_less_eq_assn @ C @ A )
% 2.39/2.74 => ( ord_less_eq_assn @ ( sup_sup_assn @ B @ C ) @ A ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.boundedI
% 2.39/2.74 thf(fact_1498_sup_OboundedI,axiom,
% 2.39/2.74 ! [B: set_nat,A: set_nat,C: set_nat] :
% 2.39/2.74 ( ( ord_less_eq_set_nat @ B @ A )
% 2.39/2.74 => ( ( ord_less_eq_set_nat @ C @ A )
% 2.39/2.74 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ B @ C ) @ A ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.boundedI
% 2.39/2.74 thf(fact_1499_sup_OboundedI,axiom,
% 2.39/2.74 ! [B: rat,A: rat,C: rat] :
% 2.39/2.74 ( ( ord_less_eq_rat @ B @ A )
% 2.39/2.74 => ( ( ord_less_eq_rat @ C @ A )
% 2.39/2.74 => ( ord_less_eq_rat @ ( sup_sup_rat @ B @ C ) @ A ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.boundedI
% 2.39/2.74 thf(fact_1500_sup_OboundedI,axiom,
% 2.39/2.74 ! [B: nat,A: nat,C: nat] :
% 2.39/2.74 ( ( ord_less_eq_nat @ B @ A )
% 2.39/2.74 => ( ( ord_less_eq_nat @ C @ A )
% 2.39/2.74 => ( ord_less_eq_nat @ ( sup_sup_nat @ B @ C ) @ A ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.boundedI
% 2.39/2.74 thf(fact_1501_sup_OboundedI,axiom,
% 2.39/2.74 ! [B: int,A: int,C: int] :
% 2.39/2.74 ( ( ord_less_eq_int @ B @ A )
% 2.39/2.74 => ( ( ord_less_eq_int @ C @ A )
% 2.39/2.74 => ( ord_less_eq_int @ ( sup_sup_int @ B @ C ) @ A ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.boundedI
% 2.39/2.74 thf(fact_1502_sup_Oorder__iff,axiom,
% 2.39/2.74 ( ord_less_eq_assn
% 2.39/2.74 = ( ^ [B2: assn,A2: assn] :
% 2.39/2.74 ( A2
% 2.39/2.74 = ( sup_sup_assn @ A2 @ B2 ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.order_iff
% 2.39/2.74 thf(fact_1503_sup_Oorder__iff,axiom,
% 2.39/2.74 ( ord_less_eq_set_nat
% 2.39/2.74 = ( ^ [B2: set_nat,A2: set_nat] :
% 2.39/2.74 ( A2
% 2.39/2.74 = ( sup_sup_set_nat @ A2 @ B2 ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.order_iff
% 2.39/2.74 thf(fact_1504_sup_Oorder__iff,axiom,
% 2.39/2.74 ( ord_less_eq_rat
% 2.39/2.74 = ( ^ [B2: rat,A2: rat] :
% 2.39/2.74 ( A2
% 2.39/2.74 = ( sup_sup_rat @ A2 @ B2 ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.order_iff
% 2.39/2.74 thf(fact_1505_sup_Oorder__iff,axiom,
% 2.39/2.74 ( ord_less_eq_nat
% 2.39/2.74 = ( ^ [B2: nat,A2: nat] :
% 2.39/2.74 ( A2
% 2.39/2.74 = ( sup_sup_nat @ A2 @ B2 ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.order_iff
% 2.39/2.74 thf(fact_1506_sup_Oorder__iff,axiom,
% 2.39/2.74 ( ord_less_eq_int
% 2.39/2.74 = ( ^ [B2: int,A2: int] :
% 2.39/2.74 ( A2
% 2.39/2.74 = ( sup_sup_int @ A2 @ B2 ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.order_iff
% 2.39/2.74 thf(fact_1507_sup_Ocobounded1,axiom,
% 2.39/2.74 ! [A: assn,B: assn] : ( ord_less_eq_assn @ A @ ( sup_sup_assn @ A @ B ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.cobounded1
% 2.39/2.74 thf(fact_1508_sup_Ocobounded1,axiom,
% 2.39/2.74 ! [A: set_nat,B: set_nat] : ( ord_less_eq_set_nat @ A @ ( sup_sup_set_nat @ A @ B ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.cobounded1
% 2.39/2.74 thf(fact_1509_sup_Ocobounded1,axiom,
% 2.39/2.74 ! [A: rat,B: rat] : ( ord_less_eq_rat @ A @ ( sup_sup_rat @ A @ B ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.cobounded1
% 2.39/2.74 thf(fact_1510_sup_Ocobounded1,axiom,
% 2.39/2.74 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( sup_sup_nat @ A @ B ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.cobounded1
% 2.39/2.74 thf(fact_1511_sup_Ocobounded1,axiom,
% 2.39/2.74 ! [A: int,B: int] : ( ord_less_eq_int @ A @ ( sup_sup_int @ A @ B ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.cobounded1
% 2.39/2.74 thf(fact_1512_sup_Ocobounded2,axiom,
% 2.39/2.74 ! [B: assn,A: assn] : ( ord_less_eq_assn @ B @ ( sup_sup_assn @ A @ B ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.cobounded2
% 2.39/2.74 thf(fact_1513_sup_Ocobounded2,axiom,
% 2.39/2.74 ! [B: set_nat,A: set_nat] : ( ord_less_eq_set_nat @ B @ ( sup_sup_set_nat @ A @ B ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.cobounded2
% 2.39/2.74 thf(fact_1514_sup_Ocobounded2,axiom,
% 2.39/2.74 ! [B: rat,A: rat] : ( ord_less_eq_rat @ B @ ( sup_sup_rat @ A @ B ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.cobounded2
% 2.39/2.74 thf(fact_1515_sup_Ocobounded2,axiom,
% 2.39/2.74 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( sup_sup_nat @ A @ B ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.cobounded2
% 2.39/2.74 thf(fact_1516_sup_Ocobounded2,axiom,
% 2.39/2.74 ! [B: int,A: int] : ( ord_less_eq_int @ B @ ( sup_sup_int @ A @ B ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.cobounded2
% 2.39/2.74 thf(fact_1517_sup_Oabsorb__iff1,axiom,
% 2.39/2.74 ( ord_less_eq_assn
% 2.39/2.74 = ( ^ [B2: assn,A2: assn] :
% 2.39/2.74 ( ( sup_sup_assn @ A2 @ B2 )
% 2.39/2.74 = A2 ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.absorb_iff1
% 2.39/2.74 thf(fact_1518_sup_Oabsorb__iff1,axiom,
% 2.39/2.74 ( ord_less_eq_set_nat
% 2.39/2.74 = ( ^ [B2: set_nat,A2: set_nat] :
% 2.39/2.74 ( ( sup_sup_set_nat @ A2 @ B2 )
% 2.39/2.74 = A2 ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.absorb_iff1
% 2.39/2.74 thf(fact_1519_sup_Oabsorb__iff1,axiom,
% 2.39/2.74 ( ord_less_eq_rat
% 2.39/2.74 = ( ^ [B2: rat,A2: rat] :
% 2.39/2.74 ( ( sup_sup_rat @ A2 @ B2 )
% 2.39/2.74 = A2 ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.absorb_iff1
% 2.39/2.74 thf(fact_1520_sup_Oabsorb__iff1,axiom,
% 2.39/2.74 ( ord_less_eq_nat
% 2.39/2.74 = ( ^ [B2: nat,A2: nat] :
% 2.39/2.74 ( ( sup_sup_nat @ A2 @ B2 )
% 2.39/2.74 = A2 ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.absorb_iff1
% 2.39/2.74 thf(fact_1521_sup_Oabsorb__iff1,axiom,
% 2.39/2.74 ( ord_less_eq_int
% 2.39/2.74 = ( ^ [B2: int,A2: int] :
% 2.39/2.74 ( ( sup_sup_int @ A2 @ B2 )
% 2.39/2.74 = A2 ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.absorb_iff1
% 2.39/2.74 thf(fact_1522_sup_Oabsorb__iff2,axiom,
% 2.39/2.74 ( ord_less_eq_assn
% 2.39/2.74 = ( ^ [A2: assn,B2: assn] :
% 2.39/2.74 ( ( sup_sup_assn @ A2 @ B2 )
% 2.39/2.74 = B2 ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.absorb_iff2
% 2.39/2.74 thf(fact_1523_sup_Oabsorb__iff2,axiom,
% 2.39/2.74 ( ord_less_eq_set_nat
% 2.39/2.74 = ( ^ [A2: set_nat,B2: set_nat] :
% 2.39/2.74 ( ( sup_sup_set_nat @ A2 @ B2 )
% 2.39/2.74 = B2 ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.absorb_iff2
% 2.39/2.74 thf(fact_1524_sup_Oabsorb__iff2,axiom,
% 2.39/2.74 ( ord_less_eq_rat
% 2.39/2.74 = ( ^ [A2: rat,B2: rat] :
% 2.39/2.74 ( ( sup_sup_rat @ A2 @ B2 )
% 2.39/2.74 = B2 ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.absorb_iff2
% 2.39/2.74 thf(fact_1525_sup_Oabsorb__iff2,axiom,
% 2.39/2.74 ( ord_less_eq_nat
% 2.39/2.74 = ( ^ [A2: nat,B2: nat] :
% 2.39/2.74 ( ( sup_sup_nat @ A2 @ B2 )
% 2.39/2.74 = B2 ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.absorb_iff2
% 2.39/2.74 thf(fact_1526_sup_Oabsorb__iff2,axiom,
% 2.39/2.74 ( ord_less_eq_int
% 2.39/2.74 = ( ^ [A2: int,B2: int] :
% 2.39/2.74 ( ( sup_sup_int @ A2 @ B2 )
% 2.39/2.74 = B2 ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.absorb_iff2
% 2.39/2.74 thf(fact_1527_sup_OcoboundedI1,axiom,
% 2.39/2.74 ! [C: assn,A: assn,B: assn] :
% 2.39/2.74 ( ( ord_less_eq_assn @ C @ A )
% 2.39/2.74 => ( ord_less_eq_assn @ C @ ( sup_sup_assn @ A @ B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.coboundedI1
% 2.39/2.74 thf(fact_1528_sup_OcoboundedI1,axiom,
% 2.39/2.74 ! [C: set_nat,A: set_nat,B: set_nat] :
% 2.39/2.74 ( ( ord_less_eq_set_nat @ C @ A )
% 2.39/2.74 => ( ord_less_eq_set_nat @ C @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.coboundedI1
% 2.39/2.74 thf(fact_1529_sup_OcoboundedI1,axiom,
% 2.39/2.74 ! [C: rat,A: rat,B: rat] :
% 2.39/2.74 ( ( ord_less_eq_rat @ C @ A )
% 2.39/2.74 => ( ord_less_eq_rat @ C @ ( sup_sup_rat @ A @ B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.coboundedI1
% 2.39/2.74 thf(fact_1530_sup_OcoboundedI1,axiom,
% 2.39/2.74 ! [C: nat,A: nat,B: nat] :
% 2.39/2.74 ( ( ord_less_eq_nat @ C @ A )
% 2.39/2.74 => ( ord_less_eq_nat @ C @ ( sup_sup_nat @ A @ B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.coboundedI1
% 2.39/2.74 thf(fact_1531_sup_OcoboundedI1,axiom,
% 2.39/2.74 ! [C: int,A: int,B: int] :
% 2.39/2.74 ( ( ord_less_eq_int @ C @ A )
% 2.39/2.74 => ( ord_less_eq_int @ C @ ( sup_sup_int @ A @ B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.coboundedI1
% 2.39/2.74 thf(fact_1532_sup_OcoboundedI2,axiom,
% 2.39/2.74 ! [C: assn,B: assn,A: assn] :
% 2.39/2.74 ( ( ord_less_eq_assn @ C @ B )
% 2.39/2.74 => ( ord_less_eq_assn @ C @ ( sup_sup_assn @ A @ B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.coboundedI2
% 2.39/2.74 thf(fact_1533_sup_OcoboundedI2,axiom,
% 2.39/2.74 ! [C: set_nat,B: set_nat,A: set_nat] :
% 2.39/2.74 ( ( ord_less_eq_set_nat @ C @ B )
% 2.39/2.74 => ( ord_less_eq_set_nat @ C @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.coboundedI2
% 2.39/2.74 thf(fact_1534_sup_OcoboundedI2,axiom,
% 2.39/2.74 ! [C: rat,B: rat,A: rat] :
% 2.39/2.74 ( ( ord_less_eq_rat @ C @ B )
% 2.39/2.74 => ( ord_less_eq_rat @ C @ ( sup_sup_rat @ A @ B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.coboundedI2
% 2.39/2.74 thf(fact_1535_sup_OcoboundedI2,axiom,
% 2.39/2.74 ! [C: nat,B: nat,A: nat] :
% 2.39/2.74 ( ( ord_less_eq_nat @ C @ B )
% 2.39/2.74 => ( ord_less_eq_nat @ C @ ( sup_sup_nat @ A @ B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.coboundedI2
% 2.39/2.74 thf(fact_1536_sup_OcoboundedI2,axiom,
% 2.39/2.74 ! [C: int,B: int,A: int] :
% 2.39/2.74 ( ( ord_less_eq_int @ C @ B )
% 2.39/2.74 => ( ord_less_eq_int @ C @ ( sup_sup_int @ A @ B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sup.coboundedI2
% 2.39/2.74 thf(fact_1537_Int__Collect__mono,axiom,
% 2.39/2.74 ! [A3: set_int,B3: set_int,P2: int > $o,Q2: int > $o] :
% 2.39/2.74 ( ( ord_less_eq_set_int @ A3 @ B3 )
% 2.39/2.74 => ( ! [X3: int] :
% 2.39/2.74 ( ( member_int2 @ X3 @ A3 )
% 2.39/2.74 => ( ( P2 @ X3 )
% 2.39/2.74 => ( Q2 @ X3 ) ) )
% 2.39/2.74 => ( ord_less_eq_set_int @ ( inf_inf_set_int @ A3 @ ( collect_int @ P2 ) ) @ ( inf_inf_set_int @ B3 @ ( collect_int @ Q2 ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % Int_Collect_mono
% 2.39/2.74 thf(fact_1538_Int__Collect__mono,axiom,
% 2.39/2.74 ! [A3: set_Pr4532377907799695533_nat_o,B3: set_Pr4532377907799695533_nat_o,P2: ( produc3658429121746597890et_nat > $o ) > $o,Q2: ( produc3658429121746597890et_nat > $o ) > $o] :
% 2.39/2.74 ( ( ord_le2965882846123202637_nat_o @ A3 @ B3 )
% 2.39/2.74 => ( ! [X3: produc3658429121746597890et_nat > $o] :
% 2.39/2.74 ( ( member6576561426505652726_nat_o @ X3 @ A3 )
% 2.39/2.74 => ( ( P2 @ X3 )
% 2.39/2.74 => ( Q2 @ X3 ) ) )
% 2.39/2.74 => ( ord_le2965882846123202637_nat_o @ ( inf_in1906310914598751387_nat_o @ A3 @ ( collec939566748876313656_nat_o @ P2 ) ) @ ( inf_in1906310914598751387_nat_o @ B3 @ ( collec939566748876313656_nat_o @ Q2 ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % Int_Collect_mono
% 2.39/2.74 thf(fact_1539_Int__Collect__mono,axiom,
% 2.39/2.74 ! [A3: set_list_nat,B3: set_list_nat,P2: list_nat > $o,Q2: list_nat > $o] :
% 2.39/2.74 ( ( ord_le6045566169113846134st_nat @ A3 @ B3 )
% 2.39/2.74 => ( ! [X3: list_nat] :
% 2.39/2.74 ( ( member_list_nat @ X3 @ A3 )
% 2.39/2.74 => ( ( P2 @ X3 )
% 2.39/2.74 => ( Q2 @ X3 ) ) )
% 2.39/2.74 => ( ord_le6045566169113846134st_nat @ ( inf_inf_set_list_nat @ A3 @ ( collect_list_nat @ P2 ) ) @ ( inf_inf_set_list_nat @ B3 @ ( collect_list_nat @ Q2 ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % Int_Collect_mono
% 2.39/2.74 thf(fact_1540_Int__Collect__mono,axiom,
% 2.39/2.74 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,P2: product_prod_nat_nat > $o,Q2: product_prod_nat_nat > $o] :
% 2.39/2.74 ( ( ord_le3146513528884898305at_nat @ A3 @ B3 )
% 2.39/2.74 => ( ! [X3: product_prod_nat_nat] :
% 2.39/2.74 ( ( member8440522571783428010at_nat @ X3 @ A3 )
% 2.39/2.74 => ( ( P2 @ X3 )
% 2.39/2.74 => ( Q2 @ X3 ) ) )
% 2.39/2.74 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ ( collec3392354462482085612at_nat @ P2 ) ) @ ( inf_in2572325071724192079at_nat @ B3 @ ( collec3392354462482085612at_nat @ Q2 ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % Int_Collect_mono
% 2.39/2.74 thf(fact_1541_Int__Collect__mono,axiom,
% 2.39/2.74 ! [A3: set_nat,B3: set_nat,P2: nat > $o,Q2: nat > $o] :
% 2.39/2.74 ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 2.39/2.74 => ( ! [X3: nat] :
% 2.39/2.74 ( ( member_nat2 @ X3 @ A3 )
% 2.39/2.74 => ( ( P2 @ X3 )
% 2.39/2.74 => ( Q2 @ X3 ) ) )
% 2.39/2.74 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A3 @ ( collect_nat @ P2 ) ) @ ( inf_inf_set_nat @ B3 @ ( collect_nat @ Q2 ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % Int_Collect_mono
% 2.39/2.74 thf(fact_1542_Int__greatest,axiom,
% 2.39/2.74 ! [C2: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.74 ( ( ord_le3146513528884898305at_nat @ C2 @ A3 )
% 2.39/2.74 => ( ( ord_le3146513528884898305at_nat @ C2 @ B3 )
% 2.39/2.74 => ( ord_le3146513528884898305at_nat @ C2 @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % Int_greatest
% 2.39/2.74 thf(fact_1543_Int__greatest,axiom,
% 2.39/2.74 ! [C2: set_nat,A3: set_nat,B3: set_nat] :
% 2.39/2.74 ( ( ord_less_eq_set_nat @ C2 @ A3 )
% 2.39/2.74 => ( ( ord_less_eq_set_nat @ C2 @ B3 )
% 2.39/2.74 => ( ord_less_eq_set_nat @ C2 @ ( inf_inf_set_nat @ A3 @ B3 ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % Int_greatest
% 2.39/2.74 thf(fact_1544_Int__absorb2,axiom,
% 2.39/2.74 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.74 ( ( ord_le3146513528884898305at_nat @ A3 @ B3 )
% 2.39/2.74 => ( ( inf_in2572325071724192079at_nat @ A3 @ B3 )
% 2.39/2.74 = A3 ) ) ).
% 2.39/2.74
% 2.39/2.74 % Int_absorb2
% 2.39/2.74 thf(fact_1545_Int__absorb2,axiom,
% 2.39/2.74 ! [A3: set_nat,B3: set_nat] :
% 2.39/2.74 ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 2.39/2.74 => ( ( inf_inf_set_nat @ A3 @ B3 )
% 2.39/2.74 = A3 ) ) ).
% 2.39/2.74
% 2.39/2.74 % Int_absorb2
% 2.39/2.74 thf(fact_1546_Int__absorb1,axiom,
% 2.39/2.74 ! [B3: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat] :
% 2.39/2.74 ( ( ord_le3146513528884898305at_nat @ B3 @ A3 )
% 2.39/2.74 => ( ( inf_in2572325071724192079at_nat @ A3 @ B3 )
% 2.39/2.74 = B3 ) ) ).
% 2.39/2.74
% 2.39/2.74 % Int_absorb1
% 2.39/2.74 thf(fact_1547_Int__absorb1,axiom,
% 2.39/2.74 ! [B3: set_nat,A3: set_nat] :
% 2.39/2.74 ( ( ord_less_eq_set_nat @ B3 @ A3 )
% 2.39/2.74 => ( ( inf_inf_set_nat @ A3 @ B3 )
% 2.39/2.74 = B3 ) ) ).
% 2.39/2.74
% 2.39/2.74 % Int_absorb1
% 2.39/2.74 thf(fact_1548_Int__lower2,axiom,
% 2.39/2.74 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) @ B3 ) ).
% 2.39/2.74
% 2.39/2.74 % Int_lower2
% 2.39/2.74 thf(fact_1549_Int__lower2,axiom,
% 2.39/2.74 ! [A3: set_nat,B3: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A3 @ B3 ) @ B3 ) ).
% 2.39/2.74
% 2.39/2.74 % Int_lower2
% 2.39/2.74 thf(fact_1550_Int__lower1,axiom,
% 2.39/2.74 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) @ A3 ) ).
% 2.39/2.74
% 2.39/2.74 % Int_lower1
% 2.39/2.74 thf(fact_1551_Int__lower1,axiom,
% 2.39/2.74 ! [A3: set_nat,B3: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A3 @ B3 ) @ A3 ) ).
% 2.39/2.74
% 2.39/2.74 % Int_lower1
% 2.39/2.74 thf(fact_1552_Int__mono,axiom,
% 2.39/2.74 ! [A3: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,D: set_Pr1261947904930325089at_nat] :
% 2.39/2.74 ( ( ord_le3146513528884898305at_nat @ A3 @ C2 )
% 2.39/2.74 => ( ( ord_le3146513528884898305at_nat @ B3 @ D )
% 2.39/2.74 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) @ ( inf_in2572325071724192079at_nat @ C2 @ D ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % Int_mono
% 2.39/2.74 thf(fact_1553_Int__mono,axiom,
% 2.39/2.74 ! [A3: set_nat,C2: set_nat,B3: set_nat,D: set_nat] :
% 2.39/2.74 ( ( ord_less_eq_set_nat @ A3 @ C2 )
% 2.39/2.74 => ( ( ord_less_eq_set_nat @ B3 @ D )
% 2.39/2.74 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A3 @ B3 ) @ ( inf_inf_set_nat @ C2 @ D ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % Int_mono
% 2.39/2.74 thf(fact_1554_inter__eq__subsetI,axiom,
% 2.39/2.74 ! [S: set_Pr1261947904930325089at_nat,S2: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.74 ( ( ord_le3146513528884898305at_nat @ S @ S2 )
% 2.39/2.74 => ( ( ( inf_in2572325071724192079at_nat @ A3 @ S2 )
% 2.39/2.74 = ( inf_in2572325071724192079at_nat @ B3 @ S2 ) )
% 2.39/2.74 => ( ( inf_in2572325071724192079at_nat @ A3 @ S )
% 2.39/2.74 = ( inf_in2572325071724192079at_nat @ B3 @ S ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % inter_eq_subsetI
% 2.39/2.74 thf(fact_1555_inter__eq__subsetI,axiom,
% 2.39/2.74 ! [S: set_nat,S2: set_nat,A3: set_nat,B3: set_nat] :
% 2.39/2.74 ( ( ord_less_eq_set_nat @ S @ S2 )
% 2.39/2.74 => ( ( ( inf_inf_set_nat @ A3 @ S2 )
% 2.39/2.74 = ( inf_inf_set_nat @ B3 @ S2 ) )
% 2.39/2.74 => ( ( inf_inf_set_nat @ A3 @ S )
% 2.39/2.74 = ( inf_inf_set_nat @ B3 @ S ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % inter_eq_subsetI
% 2.39/2.74 thf(fact_1556_mult__right__cancel,axiom,
% 2.39/2.74 ! [C: rat,A: rat,B: rat] :
% 2.39/2.74 ( ( C != zero_zero_rat )
% 2.39/2.74 => ( ( ( times_times_rat @ A @ C )
% 2.39/2.74 = ( times_times_rat @ B @ C ) )
% 2.39/2.74 = ( A = B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % mult_right_cancel
% 2.39/2.74 thf(fact_1557_mult__right__cancel,axiom,
% 2.39/2.74 ! [C: nat,A: nat,B: nat] :
% 2.39/2.74 ( ( C != zero_zero_nat )
% 2.39/2.74 => ( ( ( times_times_nat @ A @ C )
% 2.39/2.74 = ( times_times_nat @ B @ C ) )
% 2.39/2.74 = ( A = B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % mult_right_cancel
% 2.39/2.74 thf(fact_1558_mult__right__cancel,axiom,
% 2.39/2.74 ! [C: int,A: int,B: int] :
% 2.39/2.74 ( ( C != zero_zero_int )
% 2.39/2.74 => ( ( ( times_times_int @ A @ C )
% 2.39/2.74 = ( times_times_int @ B @ C ) )
% 2.39/2.74 = ( A = B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % mult_right_cancel
% 2.39/2.74 thf(fact_1559_mult__right__cancel,axiom,
% 2.39/2.74 ! [C: code_integer,A: code_integer,B: code_integer] :
% 2.39/2.74 ( ( C != zero_z3403309356797280102nteger )
% 2.39/2.74 => ( ( ( times_3573771949741848930nteger @ A @ C )
% 2.39/2.74 = ( times_3573771949741848930nteger @ B @ C ) )
% 2.39/2.74 = ( A = B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % mult_right_cancel
% 2.39/2.74 thf(fact_1560_mult__right__cancel,axiom,
% 2.39/2.74 ! [C: code_natural,A: code_natural,B: code_natural] :
% 2.39/2.74 ( ( C != zero_z2226904508553997617atural )
% 2.39/2.74 => ( ( ( times_2397367101498566445atural @ A @ C )
% 2.39/2.74 = ( times_2397367101498566445atural @ B @ C ) )
% 2.39/2.74 = ( A = B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % mult_right_cancel
% 2.39/2.74 thf(fact_1561_mult__left__cancel,axiom,
% 2.39/2.74 ! [C: rat,A: rat,B: rat] :
% 2.39/2.74 ( ( C != zero_zero_rat )
% 2.39/2.74 => ( ( ( times_times_rat @ C @ A )
% 2.39/2.74 = ( times_times_rat @ C @ B ) )
% 2.39/2.74 = ( A = B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % mult_left_cancel
% 2.39/2.74 thf(fact_1562_mult__left__cancel,axiom,
% 2.39/2.74 ! [C: nat,A: nat,B: nat] :
% 2.39/2.74 ( ( C != zero_zero_nat )
% 2.39/2.74 => ( ( ( times_times_nat @ C @ A )
% 2.39/2.74 = ( times_times_nat @ C @ B ) )
% 2.39/2.74 = ( A = B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % mult_left_cancel
% 2.39/2.74 thf(fact_1563_mult__left__cancel,axiom,
% 2.39/2.74 ! [C: int,A: int,B: int] :
% 2.39/2.74 ( ( C != zero_zero_int )
% 2.39/2.74 => ( ( ( times_times_int @ C @ A )
% 2.39/2.74 = ( times_times_int @ C @ B ) )
% 2.39/2.74 = ( A = B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % mult_left_cancel
% 2.39/2.74 thf(fact_1564_mult__left__cancel,axiom,
% 2.39/2.74 ! [C: code_integer,A: code_integer,B: code_integer] :
% 2.39/2.74 ( ( C != zero_z3403309356797280102nteger )
% 2.39/2.74 => ( ( ( times_3573771949741848930nteger @ C @ A )
% 2.39/2.74 = ( times_3573771949741848930nteger @ C @ B ) )
% 2.39/2.74 = ( A = B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % mult_left_cancel
% 2.39/2.74 thf(fact_1565_mult__left__cancel,axiom,
% 2.39/2.74 ! [C: code_natural,A: code_natural,B: code_natural] :
% 2.39/2.74 ( ( C != zero_z2226904508553997617atural )
% 2.39/2.74 => ( ( ( times_2397367101498566445atural @ C @ A )
% 2.39/2.74 = ( times_2397367101498566445atural @ C @ B ) )
% 2.39/2.74 = ( A = B ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % mult_left_cancel
% 2.39/2.74 thf(fact_1566_no__zero__divisors,axiom,
% 2.39/2.74 ! [A: rat,B: rat] :
% 2.39/2.74 ( ( A != zero_zero_rat )
% 2.39/2.74 => ( ( B != zero_zero_rat )
% 2.39/2.74 => ( ( times_times_rat @ A @ B )
% 2.39/2.74 != zero_zero_rat ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % no_zero_divisors
% 2.39/2.74 thf(fact_1567_no__zero__divisors,axiom,
% 2.39/2.74 ! [A: nat,B: nat] :
% 2.39/2.74 ( ( A != zero_zero_nat )
% 2.39/2.74 => ( ( B != zero_zero_nat )
% 2.39/2.74 => ( ( times_times_nat @ A @ B )
% 2.39/2.74 != zero_zero_nat ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % no_zero_divisors
% 2.39/2.74 thf(fact_1568_no__zero__divisors,axiom,
% 2.39/2.74 ! [A: int,B: int] :
% 2.39/2.74 ( ( A != zero_zero_int )
% 2.39/2.74 => ( ( B != zero_zero_int )
% 2.39/2.74 => ( ( times_times_int @ A @ B )
% 2.39/2.74 != zero_zero_int ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % no_zero_divisors
% 2.39/2.74 thf(fact_1569_no__zero__divisors,axiom,
% 2.39/2.74 ! [A: code_integer,B: code_integer] :
% 2.39/2.74 ( ( A != zero_z3403309356797280102nteger )
% 2.39/2.74 => ( ( B != zero_z3403309356797280102nteger )
% 2.39/2.74 => ( ( times_3573771949741848930nteger @ A @ B )
% 2.39/2.74 != zero_z3403309356797280102nteger ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % no_zero_divisors
% 2.39/2.74 thf(fact_1570_no__zero__divisors,axiom,
% 2.39/2.74 ! [A: code_natural,B: code_natural] :
% 2.39/2.74 ( ( A != zero_z2226904508553997617atural )
% 2.39/2.74 => ( ( B != zero_z2226904508553997617atural )
% 2.39/2.74 => ( ( times_2397367101498566445atural @ A @ B )
% 2.39/2.74 != zero_z2226904508553997617atural ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % no_zero_divisors
% 2.39/2.74 thf(fact_1571_divisors__zero,axiom,
% 2.39/2.74 ! [A: rat,B: rat] :
% 2.39/2.74 ( ( ( times_times_rat @ A @ B )
% 2.39/2.74 = zero_zero_rat )
% 2.39/2.74 => ( ( A = zero_zero_rat )
% 2.39/2.74 | ( B = zero_zero_rat ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % divisors_zero
% 2.39/2.74 thf(fact_1572_divisors__zero,axiom,
% 2.39/2.74 ! [A: nat,B: nat] :
% 2.39/2.74 ( ( ( times_times_nat @ A @ B )
% 2.39/2.74 = zero_zero_nat )
% 2.39/2.74 => ( ( A = zero_zero_nat )
% 2.39/2.74 | ( B = zero_zero_nat ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % divisors_zero
% 2.39/2.74 thf(fact_1573_divisors__zero,axiom,
% 2.39/2.74 ! [A: int,B: int] :
% 2.39/2.74 ( ( ( times_times_int @ A @ B )
% 2.39/2.74 = zero_zero_int )
% 2.39/2.74 => ( ( A = zero_zero_int )
% 2.39/2.74 | ( B = zero_zero_int ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % divisors_zero
% 2.39/2.74 thf(fact_1574_divisors__zero,axiom,
% 2.39/2.74 ! [A: code_integer,B: code_integer] :
% 2.39/2.74 ( ( ( times_3573771949741848930nteger @ A @ B )
% 2.39/2.74 = zero_z3403309356797280102nteger )
% 2.39/2.74 => ( ( A = zero_z3403309356797280102nteger )
% 2.39/2.74 | ( B = zero_z3403309356797280102nteger ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % divisors_zero
% 2.39/2.74 thf(fact_1575_divisors__zero,axiom,
% 2.39/2.74 ! [A: code_natural,B: code_natural] :
% 2.39/2.74 ( ( ( times_2397367101498566445atural @ A @ B )
% 2.39/2.74 = zero_z2226904508553997617atural )
% 2.39/2.74 => ( ( A = zero_z2226904508553997617atural )
% 2.39/2.74 | ( B = zero_z2226904508553997617atural ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % divisors_zero
% 2.39/2.74 thf(fact_1576_mult__not__zero,axiom,
% 2.39/2.74 ! [A: rat,B: rat] :
% 2.39/2.74 ( ( ( times_times_rat @ A @ B )
% 2.39/2.74 != zero_zero_rat )
% 2.39/2.74 => ( ( A != zero_zero_rat )
% 2.39/2.74 & ( B != zero_zero_rat ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % mult_not_zero
% 2.39/2.74 thf(fact_1577_mult__not__zero,axiom,
% 2.39/2.74 ! [A: nat,B: nat] :
% 2.39/2.74 ( ( ( times_times_nat @ A @ B )
% 2.39/2.74 != zero_zero_nat )
% 2.39/2.74 => ( ( A != zero_zero_nat )
% 2.39/2.74 & ( B != zero_zero_nat ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % mult_not_zero
% 2.39/2.74 thf(fact_1578_mult__not__zero,axiom,
% 2.39/2.74 ! [A: int,B: int] :
% 2.39/2.74 ( ( ( times_times_int @ A @ B )
% 2.39/2.74 != zero_zero_int )
% 2.39/2.74 => ( ( A != zero_zero_int )
% 2.39/2.74 & ( B != zero_zero_int ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % mult_not_zero
% 2.39/2.74 thf(fact_1579_mult__not__zero,axiom,
% 2.39/2.74 ! [A: code_integer,B: code_integer] :
% 2.39/2.74 ( ( ( times_3573771949741848930nteger @ A @ B )
% 2.39/2.74 != zero_z3403309356797280102nteger )
% 2.39/2.74 => ( ( A != zero_z3403309356797280102nteger )
% 2.39/2.74 & ( B != zero_z3403309356797280102nteger ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % mult_not_zero
% 2.39/2.74 thf(fact_1580_mult__not__zero,axiom,
% 2.39/2.74 ! [A: code_natural,B: code_natural] :
% 2.39/2.74 ( ( ( times_2397367101498566445atural @ A @ B )
% 2.39/2.74 != zero_z2226904508553997617atural )
% 2.39/2.74 => ( ( A != zero_z2226904508553997617atural )
% 2.39/2.74 & ( B != zero_z2226904508553997617atural ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % mult_not_zero
% 2.39/2.74 thf(fact_1581_zero__neq__one,axiom,
% 2.39/2.74 zero_zero_nat != one_one_nat ).
% 2.39/2.74
% 2.39/2.74 % zero_neq_one
% 2.39/2.74 thf(fact_1582_zero__neq__one,axiom,
% 2.39/2.74 zero_zero_int != one_one_int ).
% 2.39/2.74
% 2.39/2.74 % zero_neq_one
% 2.39/2.74 thf(fact_1583_zero__neq__one,axiom,
% 2.39/2.74 zero_zero_rat != one_one_rat ).
% 2.39/2.74
% 2.39/2.74 % zero_neq_one
% 2.39/2.74 thf(fact_1584_zero__neq__one,axiom,
% 2.39/2.74 zero_z3403309356797280102nteger != one_one_Code_integer ).
% 2.39/2.74
% 2.39/2.74 % zero_neq_one
% 2.39/2.74 thf(fact_1585_zero__neq__one,axiom,
% 2.39/2.74 zero_z2226904508553997617atural != one_one_Code_natural ).
% 2.39/2.74
% 2.39/2.74 % zero_neq_one
% 2.39/2.74 thf(fact_1586_rotate1__map,axiom,
% 2.39/2.74 ! [F2: nat > nat,Xs: list_nat] :
% 2.39/2.74 ( ( rotate1_nat @ ( map_nat_nat @ F2 @ Xs ) )
% 2.39/2.74 = ( map_nat_nat @ F2 @ ( rotate1_nat @ Xs ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % rotate1_map
% 2.39/2.74 thf(fact_1587_rotate1__map,axiom,
% 2.39/2.74 ! [F2: produc6575502325842934193n_assn > assn,Xs: list_P8527749157015355191n_assn] :
% 2.39/2.74 ( ( rotate1_assn @ ( map_Pr8991440229025900053n_assn @ F2 @ Xs ) )
% 2.39/2.74 = ( map_Pr8991440229025900053n_assn @ F2 @ ( rotate328796349445179396n_assn @ Xs ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % rotate1_map
% 2.39/2.74 thf(fact_1588_sorted__list__of__set_Osorted__key__list__of__set__inject,axiom,
% 2.39/2.74 ! [A3: set_nat,B3: set_nat] :
% 2.39/2.74 ( ( ( linord2614967742042102400et_nat @ A3 )
% 2.39/2.74 = ( linord2614967742042102400et_nat @ B3 ) )
% 2.39/2.74 => ( ( finite_finite_nat @ A3 )
% 2.39/2.74 => ( ( finite_finite_nat @ B3 )
% 2.39/2.74 => ( A3 = B3 ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % sorted_list_of_set.sorted_key_list_of_set_inject
% 2.39/2.74 thf(fact_1589_less__eq__assn__def,axiom,
% 2.39/2.74 ( ord_less_eq_assn
% 2.39/2.74 = ( ^ [A2: assn,B2: assn] :
% 2.39/2.74 ( A2
% 2.39/2.74 = ( inf_inf_assn @ A2 @ B2 ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % less_eq_assn_def
% 2.39/2.74 thf(fact_1590_relH__subset,axiom,
% 2.39/2.74 ! [Bs: set_nat,H2: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit,As2: set_nat] :
% 2.39/2.74 ( ( relH @ Bs @ H2 @ H5 )
% 2.39/2.74 => ( ( ord_less_eq_set_nat @ As2 @ Bs )
% 2.39/2.74 => ( relH @ As2 @ H2 @ H5 ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % relH_subset
% 2.39/2.74 thf(fact_1591_le__minus__one__simps_I2_J,axiom,
% 2.39/2.74 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 2.39/2.74
% 2.39/2.74 % le_minus_one_simps(2)
% 2.39/2.74 thf(fact_1592_le__minus__one__simps_I2_J,axiom,
% 2.39/2.74 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 2.39/2.74
% 2.39/2.74 % le_minus_one_simps(2)
% 2.39/2.74 thf(fact_1593_le__minus__one__simps_I2_J,axiom,
% 2.39/2.74 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 2.39/2.74
% 2.39/2.74 % le_minus_one_simps(2)
% 2.39/2.74 thf(fact_1594_le__minus__one__simps_I4_J,axiom,
% 2.39/2.74 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_minus_one_simps(4)
% 2.39/2.74 thf(fact_1595_le__minus__one__simps_I4_J,axiom,
% 2.39/2.74 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_minus_one_simps(4)
% 2.39/2.74 thf(fact_1596_le__minus__one__simps_I4_J,axiom,
% 2.39/2.74 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 2.39/2.74
% 2.39/2.74 % le_minus_one_simps(4)
% 2.39/2.74 thf(fact_1597_distrib__inf__le,axiom,
% 2.39/2.74 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ ( inf_in2572325071724192079at_nat @ X @ Z ) ) @ ( inf_in2572325071724192079at_nat @ X @ ( sup_su6327502436637775413at_nat @ Y @ Z ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % distrib_inf_le
% 2.39/2.74 thf(fact_1598_distrib__inf__le,axiom,
% 2.39/2.74 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] : ( ord_le8369615600986905444_int_o @ ( sup_su8463660629351352368_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ ( inf_in3604695632404883862_int_o @ X @ Z ) ) @ ( inf_in3604695632404883862_int_o @ X @ ( sup_su8463660629351352368_int_o @ Y @ Z ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % distrib_inf_le
% 2.39/2.74 thf(fact_1599_distrib__inf__le,axiom,
% 2.39/2.74 ! [X: assn,Y: assn,Z: assn] : ( ord_less_eq_assn @ ( sup_sup_assn @ ( inf_inf_assn @ X @ Y ) @ ( inf_inf_assn @ X @ Z ) ) @ ( inf_inf_assn @ X @ ( sup_sup_assn @ Y @ Z ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % distrib_inf_le
% 2.39/2.74 thf(fact_1600_distrib__inf__le,axiom,
% 2.39/2.74 ! [X: set_nat,Y: set_nat,Z: set_nat] : ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ ( inf_inf_set_nat @ X @ Z ) ) @ ( inf_inf_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % distrib_inf_le
% 2.39/2.74 thf(fact_1601_distrib__inf__le,axiom,
% 2.39/2.74 ! [X: rat,Y: rat,Z: rat] : ( ord_less_eq_rat @ ( sup_sup_rat @ ( inf_inf_rat @ X @ Y ) @ ( inf_inf_rat @ X @ Z ) ) @ ( inf_inf_rat @ X @ ( sup_sup_rat @ Y @ Z ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % distrib_inf_le
% 2.39/2.74 thf(fact_1602_distrib__inf__le,axiom,
% 2.39/2.74 ! [X: nat,Y: nat,Z: nat] : ( ord_less_eq_nat @ ( sup_sup_nat @ ( inf_inf_nat @ X @ Y ) @ ( inf_inf_nat @ X @ Z ) ) @ ( inf_inf_nat @ X @ ( sup_sup_nat @ Y @ Z ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % distrib_inf_le
% 2.39/2.74 thf(fact_1603_distrib__inf__le,axiom,
% 2.39/2.74 ! [X: int,Y: int,Z: int] : ( ord_less_eq_int @ ( sup_sup_int @ ( inf_inf_int @ X @ Y ) @ ( inf_inf_int @ X @ Z ) ) @ ( inf_inf_int @ X @ ( sup_sup_int @ Y @ Z ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % distrib_inf_le
% 2.39/2.74 thf(fact_1604_distrib__sup__le,axiom,
% 2.39/2.74 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( sup_su6327502436637775413at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) ) @ ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ X @ Y ) @ ( sup_su6327502436637775413at_nat @ X @ Z ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % distrib_sup_le
% 2.39/2.74 thf(fact_1605_distrib__sup__le,axiom,
% 2.39/2.74 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] : ( ord_le8369615600986905444_int_o @ ( sup_su8463660629351352368_int_o @ X @ ( inf_in3604695632404883862_int_o @ Y @ Z ) ) @ ( inf_in3604695632404883862_int_o @ ( sup_su8463660629351352368_int_o @ X @ Y ) @ ( sup_su8463660629351352368_int_o @ X @ Z ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % distrib_sup_le
% 2.39/2.74 thf(fact_1606_distrib__sup__le,axiom,
% 2.39/2.74 ! [X: assn,Y: assn,Z: assn] : ( ord_less_eq_assn @ ( sup_sup_assn @ X @ ( inf_inf_assn @ Y @ Z ) ) @ ( inf_inf_assn @ ( sup_sup_assn @ X @ Y ) @ ( sup_sup_assn @ X @ Z ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % distrib_sup_le
% 2.39/2.74 thf(fact_1607_distrib__sup__le,axiom,
% 2.39/2.74 ! [X: set_nat,Y: set_nat,Z: set_nat] : ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) ) @ ( inf_inf_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ ( sup_sup_set_nat @ X @ Z ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % distrib_sup_le
% 2.39/2.74 thf(fact_1608_distrib__sup__le,axiom,
% 2.39/2.74 ! [X: rat,Y: rat,Z: rat] : ( ord_less_eq_rat @ ( sup_sup_rat @ X @ ( inf_inf_rat @ Y @ Z ) ) @ ( inf_inf_rat @ ( sup_sup_rat @ X @ Y ) @ ( sup_sup_rat @ X @ Z ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % distrib_sup_le
% 2.39/2.74 thf(fact_1609_distrib__sup__le,axiom,
% 2.39/2.74 ! [X: nat,Y: nat,Z: nat] : ( ord_less_eq_nat @ ( sup_sup_nat @ X @ ( inf_inf_nat @ Y @ Z ) ) @ ( inf_inf_nat @ ( sup_sup_nat @ X @ Y ) @ ( sup_sup_nat @ X @ Z ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % distrib_sup_le
% 2.39/2.74 thf(fact_1610_distrib__sup__le,axiom,
% 2.39/2.74 ! [X: int,Y: int,Z: int] : ( ord_less_eq_int @ ( sup_sup_int @ X @ ( inf_inf_int @ Y @ Z ) ) @ ( inf_inf_int @ ( sup_sup_int @ X @ Y ) @ ( sup_sup_int @ X @ Z ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % distrib_sup_le
% 2.39/2.74 thf(fact_1611_disjoint__mono,axiom,
% 2.39/2.74 ! [A: set_Pr1261947904930325089at_nat,A5: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 2.39/2.74 ( ( ord_le3146513528884898305at_nat @ A @ A5 )
% 2.39/2.74 => ( ( ord_le3146513528884898305at_nat @ B @ B6 )
% 2.39/2.74 => ( ( ( inf_in2572325071724192079at_nat @ A5 @ B6 )
% 2.39/2.74 = bot_bo2099793752762293965at_nat )
% 2.39/2.74 => ( ( inf_in2572325071724192079at_nat @ A @ B )
% 2.39/2.74 = bot_bo2099793752762293965at_nat ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % disjoint_mono
% 2.39/2.74 thf(fact_1612_disjoint__mono,axiom,
% 2.39/2.74 ! [A: set_int,A5: set_int,B: set_int,B6: set_int] :
% 2.39/2.74 ( ( ord_less_eq_set_int @ A @ A5 )
% 2.39/2.74 => ( ( ord_less_eq_set_int @ B @ B6 )
% 2.39/2.74 => ( ( ( inf_inf_set_int @ A5 @ B6 )
% 2.39/2.74 = bot_bot_set_int )
% 2.39/2.74 => ( ( inf_inf_set_int @ A @ B )
% 2.39/2.74 = bot_bot_set_int ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % disjoint_mono
% 2.39/2.74 thf(fact_1613_disjoint__mono,axiom,
% 2.39/2.74 ! [A: set_nat,A5: set_nat,B: set_nat,B6: set_nat] :
% 2.39/2.74 ( ( ord_less_eq_set_nat @ A @ A5 )
% 2.39/2.74 => ( ( ord_less_eq_set_nat @ B @ B6 )
% 2.39/2.74 => ( ( ( inf_inf_set_nat @ A5 @ B6 )
% 2.39/2.74 = bot_bot_set_nat )
% 2.39/2.74 => ( ( inf_inf_set_nat @ A @ B )
% 2.39/2.74 = bot_bot_set_nat ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % disjoint_mono
% 2.39/2.74 thf(fact_1614_Un__Int__assoc__eq,axiom,
% 2.39/2.74 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 2.39/2.74 ( ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) @ C2 )
% 2.39/2.74 = ( inf_in2572325071724192079at_nat @ A3 @ ( sup_su6327502436637775413at_nat @ B3 @ C2 ) ) )
% 2.39/2.74 = ( ord_le3146513528884898305at_nat @ C2 @ A3 ) ) ).
% 2.39/2.74
% 2.39/2.74 % Un_Int_assoc_eq
% 2.39/2.74 thf(fact_1615_Un__Int__assoc__eq,axiom,
% 2.39/2.74 ! [A3: set_nat,B3: set_nat,C2: set_nat] :
% 2.39/2.74 ( ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ A3 @ B3 ) @ C2 )
% 2.39/2.74 = ( inf_inf_set_nat @ A3 @ ( sup_sup_set_nat @ B3 @ C2 ) ) )
% 2.39/2.74 = ( ord_less_eq_set_nat @ C2 @ A3 ) ) ).
% 2.39/2.74
% 2.39/2.74 % Un_Int_assoc_eq
% 2.39/2.74 thf(fact_1616_zero__neq__neg__one,axiom,
% 2.39/2.74 ( zero_zero_int
% 2.39/2.74 != ( uminus_uminus_int @ one_one_int ) ) ).
% 2.39/2.74
% 2.39/2.74 % zero_neq_neg_one
% 2.39/2.74 thf(fact_1617_zero__neq__neg__one,axiom,
% 2.39/2.74 ( zero_zero_rat
% 2.39/2.74 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 2.39/2.74
% 2.39/2.74 % zero_neq_neg_one
% 2.39/2.74 thf(fact_1618_zero__neq__neg__one,axiom,
% 2.39/2.74 ( zero_z3403309356797280102nteger
% 2.39/2.74 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 2.39/2.74
% 2.39/2.74 % zero_neq_neg_one
% 2.39/2.74 thf(fact_1619_in__range__subset,axiom,
% 2.39/2.74 ! [As2: set_nat,As3: set_nat,H2: heap_e7401611519738050253t_unit] :
% 2.39/2.74 ( ( ord_less_eq_set_nat @ As2 @ As3 )
% 2.39/2.74 => ( ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As3 ) )
% 2.39/2.74 => ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As2 ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % in_range_subset
% 2.39/2.74 thf(fact_1620_inf__shunt,axiom,
% 2.39/2.74 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 2.39/2.74 ( ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 2.39/2.74 = bot_bo2099793752762293965at_nat )
% 2.39/2.74 = ( ord_le3146513528884898305at_nat @ X @ ( uminus6524753893492686040at_nat @ Y ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % inf_shunt
% 2.39/2.74 thf(fact_1621_inf__shunt,axiom,
% 2.39/2.74 ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 2.39/2.74 ( ( ( inf_in3604695632404883862_int_o @ X @ Y )
% 2.39/2.74 = bot_bo8147686125503663512_int_o )
% 2.39/2.74 = ( ord_le8369615600986905444_int_o @ X @ ( uminus7117520113953359693_int_o @ Y ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % inf_shunt
% 2.39/2.74 thf(fact_1622_inf__shunt,axiom,
% 2.39/2.74 ! [X: set_int,Y: set_int] :
% 2.39/2.74 ( ( ( inf_inf_set_int @ X @ Y )
% 2.39/2.74 = bot_bot_set_int )
% 2.39/2.74 = ( ord_less_eq_set_int @ X @ ( uminus1532241313380277803et_int @ Y ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % inf_shunt
% 2.39/2.74 thf(fact_1623_inf__shunt,axiom,
% 2.39/2.74 ! [X: assn,Y: assn] :
% 2.39/2.74 ( ( ( inf_inf_assn @ X @ Y )
% 2.39/2.74 = bot_bot_assn )
% 2.39/2.74 = ( ord_less_eq_assn @ X @ ( uminus_uminus_assn @ Y ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % inf_shunt
% 2.39/2.74 thf(fact_1624_inf__shunt,axiom,
% 2.39/2.74 ! [X: set_nat,Y: set_nat] :
% 2.39/2.74 ( ( ( inf_inf_set_nat @ X @ Y )
% 2.39/2.74 = bot_bot_set_nat )
% 2.39/2.74 = ( ord_less_eq_set_nat @ X @ ( uminus5710092332889474511et_nat @ Y ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % inf_shunt
% 2.39/2.74 thf(fact_1625_finite__Int,axiom,
% 2.39/2.74 ! [F4: set_Pr1261947904930325089at_nat,G2: set_Pr1261947904930325089at_nat] :
% 2.39/2.74 ( ( ( finite6177210948735845034at_nat @ F4 )
% 2.39/2.74 | ( finite6177210948735845034at_nat @ G2 ) )
% 2.39/2.74 => ( finite6177210948735845034at_nat @ ( inf_in2572325071724192079at_nat @ F4 @ G2 ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % finite_Int
% 2.39/2.74 thf(fact_1626_finite__Int,axiom,
% 2.39/2.74 ! [F4: set_nat,G2: set_nat] :
% 2.39/2.74 ( ( ( finite_finite_nat @ F4 )
% 2.39/2.74 | ( finite_finite_nat @ G2 ) )
% 2.39/2.74 => ( finite_finite_nat @ ( inf_inf_set_nat @ F4 @ G2 ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % finite_Int
% 2.39/2.74 thf(fact_1627_wand__raw_Opelims_I3_J,axiom,
% 2.39/2.74 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 2.39/2.74 ( ~ ( wand_raw @ X @ Xa @ Xb )
% 2.39/2.74 => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 2.39/2.74 => ~ ! [H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.39/2.74 ( ( Xb
% 2.39/2.74 = ( produc7507926704131184380et_nat @ H3 @ As ) )
% 2.39/2.74 => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H3 @ As ) ) ) )
% 2.39/2.74 => ( ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As ) )
% 2.39/2.74 & ! [H4: heap_e7401611519738050253t_unit,As4: set_nat] :
% 2.39/2.74 ( ( ( ( inf_inf_set_nat @ As @ As4 )
% 2.39/2.74 = bot_bot_set_nat )
% 2.39/2.74 & ( relH @ As @ H3 @ H4 )
% 2.39/2.74 & ( in_range @ ( produc7507926704131184380et_nat @ H4 @ As ) )
% 2.39/2.74 & ( X @ ( produc7507926704131184380et_nat @ H4 @ As4 ) ) )
% 2.39/2.74 => ( Xa @ ( produc7507926704131184380et_nat @ H4 @ ( sup_sup_set_nat @ As @ As4 ) ) ) ) ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % wand_raw.pelims(3)
% 2.39/2.74 thf(fact_1628_wand__raw_Opelims_I2_J,axiom,
% 2.39/2.74 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 2.39/2.74 ( ( wand_raw @ X @ Xa @ Xb )
% 2.39/2.74 => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 2.39/2.74 => ~ ! [H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.39/2.74 ( ( Xb
% 2.39/2.74 = ( produc7507926704131184380et_nat @ H3 @ As ) )
% 2.39/2.74 => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H3 @ As ) ) ) )
% 2.39/2.74 => ~ ( ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As ) )
% 2.39/2.74 & ! [H6: heap_e7401611519738050253t_unit,As5: set_nat] :
% 2.39/2.74 ( ( ( ( inf_inf_set_nat @ As @ As5 )
% 2.39/2.74 = bot_bot_set_nat )
% 2.39/2.74 & ( relH @ As @ H3 @ H6 )
% 2.39/2.74 & ( in_range @ ( produc7507926704131184380et_nat @ H6 @ As ) )
% 2.39/2.74 & ( X @ ( produc7507926704131184380et_nat @ H6 @ As5 ) ) )
% 2.39/2.74 => ( Xa @ ( produc7507926704131184380et_nat @ H6 @ ( sup_sup_set_nat @ As @ As5 ) ) ) ) ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % wand_raw.pelims(2)
% 2.39/2.74 thf(fact_1629_wand__raw_Opelims_I1_J,axiom,
% 2.39/2.74 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat,Y: $o] :
% 2.39/2.74 ( ( ( wand_raw @ X @ Xa @ Xb )
% 2.39/2.74 = Y )
% 2.39/2.74 => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 2.39/2.74 => ~ ! [H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.39/2.74 ( ( Xb
% 2.39/2.74 = ( produc7507926704131184380et_nat @ H3 @ As ) )
% 2.39/2.74 => ( ( Y
% 2.39/2.74 = ( ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As ) )
% 2.39/2.74 & ! [H7: heap_e7401611519738050253t_unit,As6: set_nat] :
% 2.39/2.74 ( ( ( ( inf_inf_set_nat @ As @ As6 )
% 2.39/2.74 = bot_bot_set_nat )
% 2.39/2.74 & ( relH @ As @ H3 @ H7 )
% 2.39/2.74 & ( in_range @ ( produc7507926704131184380et_nat @ H7 @ As ) )
% 2.39/2.74 & ( X @ ( produc7507926704131184380et_nat @ H7 @ As6 ) ) )
% 2.39/2.74 => ( Xa @ ( produc7507926704131184380et_nat @ H7 @ ( sup_sup_set_nat @ As @ As6 ) ) ) ) ) )
% 2.39/2.74 => ~ ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H3 @ As ) ) ) ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % wand_raw.pelims(1)
% 2.39/2.74 thf(fact_1630_mod__star__trueE_H,axiom,
% 2.39/2.74 ! [P2: assn,H2: produc3658429121746597890et_nat] :
% 2.39/2.74 ( ( rep_assn @ ( times_times_assn @ P2 @ top_top_assn ) @ H2 )
% 2.39/2.74 => ~ ! [H4: produc3658429121746597890et_nat] :
% 2.39/2.74 ( ( ( produc1824681642469235216et_nat @ H4 )
% 2.39/2.74 = ( produc1824681642469235216et_nat @ H2 ) )
% 2.39/2.74 => ( ( ord_less_eq_set_nat @ ( produc8586169260539613262et_nat @ H4 ) @ ( produc8586169260539613262et_nat @ H2 ) )
% 2.39/2.74 => ~ ( rep_assn @ P2 @ H4 ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % mod_star_trueE'
% 2.39/2.74 thf(fact_1631_map__eq__map__tailrec,axiom,
% 2.39/2.74 map_nat_nat = map_tailrec_nat_nat ).
% 2.39/2.74
% 2.39/2.74 % map_eq_map_tailrec
% 2.39/2.74 thf(fact_1632_map__eq__map__tailrec,axiom,
% 2.39/2.74 map_Pr8991440229025900053n_assn = map_ta2194206859901583947n_assn ).
% 2.39/2.74
% 2.39/2.74 % map_eq_map_tailrec
% 2.39/2.74 thf(fact_1633_times__assn__raw_Opelims_I1_J,axiom,
% 2.39/2.74 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat,Y: $o] :
% 2.39/2.74 ( ( ( times_assn_raw @ X @ Xa @ Xb )
% 2.39/2.74 = Y )
% 2.39/2.74 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 2.39/2.74 => ~ ! [H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.39/2.74 ( ( Xb
% 2.39/2.74 = ( produc7507926704131184380et_nat @ H3 @ As ) )
% 2.39/2.74 => ( ( Y
% 2.39/2.74 = ( ? [As1: set_nat,As22: set_nat] :
% 2.39/2.74 ( ( As
% 2.39/2.74 = ( sup_sup_set_nat @ As1 @ As22 ) )
% 2.39/2.74 & ( ( inf_inf_set_nat @ As1 @ As22 )
% 2.39/2.74 = bot_bot_set_nat )
% 2.39/2.74 & ( X @ ( produc7507926704131184380et_nat @ H3 @ As1 ) )
% 2.39/2.74 & ( Xa @ ( produc7507926704131184380et_nat @ H3 @ As22 ) ) ) ) )
% 2.39/2.74 => ~ ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H3 @ As ) ) ) ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % times_assn_raw.pelims(1)
% 2.39/2.74 thf(fact_1634_times__assn__raw_Opelims_I2_J,axiom,
% 2.39/2.74 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 2.39/2.74 ( ( times_assn_raw @ X @ Xa @ Xb )
% 2.39/2.74 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 2.39/2.74 => ~ ! [H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.39/2.74 ( ( Xb
% 2.39/2.74 = ( produc7507926704131184380et_nat @ H3 @ As ) )
% 2.39/2.74 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H3 @ As ) ) ) )
% 2.39/2.74 => ~ ? [As13: set_nat,As24: set_nat] :
% 2.39/2.74 ( ( As
% 2.39/2.74 = ( sup_sup_set_nat @ As13 @ As24 ) )
% 2.39/2.74 & ( ( inf_inf_set_nat @ As13 @ As24 )
% 2.39/2.74 = bot_bot_set_nat )
% 2.39/2.74 & ( X @ ( produc7507926704131184380et_nat @ H3 @ As13 ) )
% 2.39/2.74 & ( Xa @ ( produc7507926704131184380et_nat @ H3 @ As24 ) ) ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % times_assn_raw.pelims(2)
% 2.39/2.74 thf(fact_1635_times__assn__raw_Opelims_I3_J,axiom,
% 2.39/2.74 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 2.39/2.74 ( ~ ( times_assn_raw @ X @ Xa @ Xb )
% 2.39/2.74 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 2.39/2.74 => ~ ! [H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.39/2.74 ( ( Xb
% 2.39/2.74 = ( produc7507926704131184380et_nat @ H3 @ As ) )
% 2.39/2.74 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H3 @ As ) ) ) )
% 2.39/2.74 => ? [As12: set_nat,As23: set_nat] :
% 2.39/2.74 ( ( As
% 2.39/2.74 = ( sup_sup_set_nat @ As12 @ As23 ) )
% 2.39/2.74 & ( ( inf_inf_set_nat @ As12 @ As23 )
% 2.39/2.74 = bot_bot_set_nat )
% 2.39/2.74 & ( X @ ( produc7507926704131184380et_nat @ H3 @ As12 ) )
% 2.39/2.74 & ( Xa @ ( produc7507926704131184380et_nat @ H3 @ As23 ) ) ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % times_assn_raw.pelims(3)
% 2.39/2.74 thf(fact_1636_mult__le__cancel__left1,axiom,
% 2.39/2.74 ! [C: code_integer,B: code_integer] :
% 2.39/2.74 ( ( ord_le3102999989581377725nteger @ C @ ( times_3573771949741848930nteger @ C @ B ) )
% 2.39/2.74 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 2.39/2.74 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ B ) )
% 2.39/2.74 & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 2.39/2.74 => ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % mult_le_cancel_left1
% 2.39/2.74 thf(fact_1637_mult__le__cancel__left1,axiom,
% 2.39/2.74 ! [C: rat,B: rat] :
% 2.39/2.74 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ C @ B ) )
% 2.39/2.74 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.74 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 2.39/2.74 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.74 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % mult_le_cancel_left1
% 2.39/2.74 thf(fact_1638_mult__le__cancel__left1,axiom,
% 2.39/2.74 ! [C: int,B: int] :
% 2.39/2.74 ( ( ord_less_eq_int @ C @ ( times_times_int @ C @ B ) )
% 2.39/2.74 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 2.39/2.74 => ( ord_less_eq_int @ one_one_int @ B ) )
% 2.39/2.74 & ( ( ord_less_int @ C @ zero_zero_int )
% 2.39/2.74 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % mult_le_cancel_left1
% 2.39/2.74 thf(fact_1639_list_Oinject,axiom,
% 2.39/2.74 ! [X21: int,X22: list_int,Y21: int,Y22: list_int] :
% 2.39/2.74 ( ( ( cons_int @ X21 @ X22 )
% 2.39/2.74 = ( cons_int @ Y21 @ Y22 ) )
% 2.39/2.74 = ( ( X21 = Y21 )
% 2.39/2.74 & ( X22 = Y22 ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % list.inject
% 2.39/2.74 thf(fact_1640_list_Oinject,axiom,
% 2.39/2.74 ! [X21: nat,X22: list_nat,Y21: nat,Y22: list_nat] :
% 2.39/2.74 ( ( ( cons_nat @ X21 @ X22 )
% 2.39/2.74 = ( cons_nat @ Y21 @ Y22 ) )
% 2.39/2.74 = ( ( X21 = Y21 )
% 2.39/2.74 & ( X22 = Y22 ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % list.inject
% 2.39/2.74 thf(fact_1641_not__gr__zero,axiom,
% 2.39/2.74 ! [N: nat] :
% 2.39/2.74 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 2.39/2.74 = ( N = zero_zero_nat ) ) ).
% 2.39/2.74
% 2.39/2.74 % not_gr_zero
% 2.39/2.74 thf(fact_1642_neg__less__iff__less,axiom,
% 2.39/2.74 ! [B: int,A: int] :
% 2.39/2.74 ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 2.39/2.74 = ( ord_less_int @ A @ B ) ) ).
% 2.39/2.74
% 2.39/2.74 % neg_less_iff_less
% 2.39/2.74 thf(fact_1643_neg__less__iff__less,axiom,
% 2.39/2.74 ! [B: rat,A: rat] :
% 2.39/2.74 ( ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 2.39/2.74 = ( ord_less_rat @ A @ B ) ) ).
% 2.39/2.74
% 2.39/2.74 % neg_less_iff_less
% 2.39/2.74 thf(fact_1644_neg__less__iff__less,axiom,
% 2.39/2.74 ! [B: code_integer,A: code_integer] :
% 2.39/2.74 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 2.39/2.74 = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 2.39/2.74
% 2.39/2.74 % neg_less_iff_less
% 2.39/2.74 thf(fact_1645_list__ex__simps_I1_J,axiom,
% 2.39/2.74 ! [P2: int > $o,X: int,Xs: list_int] :
% 2.39/2.74 ( ( list_ex_int @ P2 @ ( cons_int @ X @ Xs ) )
% 2.39/2.74 = ( ( P2 @ X )
% 2.39/2.74 | ( list_ex_int @ P2 @ Xs ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % list_ex_simps(1)
% 2.39/2.74 thf(fact_1646_list__ex__simps_I1_J,axiom,
% 2.39/2.74 ! [P2: nat > $o,X: nat,Xs: list_nat] :
% 2.39/2.74 ( ( list_ex_nat @ P2 @ ( cons_nat @ X @ Xs ) )
% 2.39/2.74 = ( ( P2 @ X )
% 2.39/2.74 | ( list_ex_nat @ P2 @ Xs ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % list_ex_simps(1)
% 2.39/2.74 thf(fact_1647_in__measures_I2_J,axiom,
% 2.39/2.74 ! [X: nat,Y: nat,F2: nat > nat,Fs: list_nat_nat] :
% 2.39/2.74 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( measures_nat @ ( cons_nat_nat @ F2 @ Fs ) ) )
% 2.39/2.74 = ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 2.39/2.74 | ( ( ( F2 @ X )
% 2.39/2.74 = ( F2 @ Y ) )
% 2.39/2.74 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( measures_nat @ Fs ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % in_measures(2)
% 2.39/2.74 thf(fact_1648_in__measures_I2_J,axiom,
% 2.39/2.74 ! [X: int,Y: int,F2: int > nat,Fs: list_int_nat] :
% 2.39/2.74 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( measures_int @ ( cons_int_nat @ F2 @ Fs ) ) )
% 2.39/2.74 = ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 2.39/2.74 | ( ( ( F2 @ X )
% 2.39/2.74 = ( F2 @ Y ) )
% 2.39/2.74 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( measures_int @ Fs ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % in_measures(2)
% 2.39/2.74 thf(fact_1649_neg__less__0__iff__less,axiom,
% 2.39/2.74 ! [A: int] :
% 2.39/2.74 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 2.39/2.74 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 2.39/2.74
% 2.39/2.74 % neg_less_0_iff_less
% 2.39/2.74 thf(fact_1650_neg__less__0__iff__less,axiom,
% 2.39/2.74 ! [A: rat] :
% 2.39/2.74 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 2.39/2.74 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 2.39/2.74
% 2.39/2.74 % neg_less_0_iff_less
% 2.39/2.74 thf(fact_1651_neg__less__0__iff__less,axiom,
% 2.39/2.74 ! [A: code_integer] :
% 2.39/2.74 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 2.39/2.74 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 2.39/2.74
% 2.39/2.74 % neg_less_0_iff_less
% 2.39/2.74 thf(fact_1652_neg__0__less__iff__less,axiom,
% 2.39/2.74 ! [A: int] :
% 2.39/2.74 ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 2.39/2.74 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 2.39/2.74
% 2.39/2.74 % neg_0_less_iff_less
% 2.39/2.74 thf(fact_1653_neg__0__less__iff__less,axiom,
% 2.39/2.74 ! [A: rat] :
% 2.39/2.74 ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 2.39/2.74 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 2.39/2.74
% 2.39/2.74 % neg_0_less_iff_less
% 2.39/2.74 thf(fact_1654_neg__0__less__iff__less,axiom,
% 2.39/2.74 ! [A: code_integer] :
% 2.39/2.74 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 2.39/2.74 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 2.39/2.74
% 2.39/2.74 % neg_0_less_iff_less
% 2.39/2.74 thf(fact_1655_neg__less__pos,axiom,
% 2.39/2.74 ! [A: int] :
% 2.39/2.74 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 2.39/2.74 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 2.39/2.74
% 2.39/2.74 % neg_less_pos
% 2.39/2.74 thf(fact_1656_neg__less__pos,axiom,
% 2.39/2.74 ! [A: rat] :
% 2.39/2.74 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ A )
% 2.39/2.74 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 2.39/2.74
% 2.39/2.74 % neg_less_pos
% 2.39/2.74 thf(fact_1657_neg__less__pos,axiom,
% 2.39/2.74 ! [A: code_integer] :
% 2.39/2.74 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 2.39/2.74 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 2.39/2.74
% 2.39/2.74 % neg_less_pos
% 2.39/2.74 thf(fact_1658_less__neg__neg,axiom,
% 2.39/2.74 ! [A: int] :
% 2.39/2.74 ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 2.39/2.74 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 2.39/2.74
% 2.39/2.74 % less_neg_neg
% 2.39/2.74 thf(fact_1659_less__neg__neg,axiom,
% 2.39/2.74 ! [A: rat] :
% 2.39/2.74 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ A ) )
% 2.39/2.74 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 2.39/2.74
% 2.39/2.74 % less_neg_neg
% 2.39/2.74 thf(fact_1660_less__neg__neg,axiom,
% 2.39/2.74 ! [A: code_integer] :
% 2.39/2.74 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 2.39/2.74 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 2.39/2.74
% 2.39/2.74 % less_neg_neg
% 2.39/2.74 thf(fact_1661_zip__Cons__Cons,axiom,
% 2.39/2.74 ! [X: int,Xs: list_int,Y: nat,Ys: list_nat] :
% 2.39/2.74 ( ( zip_int_nat @ ( cons_int @ X @ Xs ) @ ( cons_nat @ Y @ Ys ) )
% 2.39/2.74 = ( cons_P7512249878480867347nt_nat @ ( product_Pair_int_nat @ X @ Y ) @ ( zip_int_nat @ Xs @ Ys ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % zip_Cons_Cons
% 2.39/2.74 thf(fact_1662_zip__Cons__Cons,axiom,
% 2.39/2.74 ! [X: nat,Xs: list_nat,Y: int,Ys: list_int] :
% 2.39/2.74 ( ( zip_nat_int @ ( cons_nat @ X @ Xs ) @ ( cons_int @ Y @ Ys ) )
% 2.39/2.74 = ( cons_P2335045147070616083at_int @ ( product_Pair_nat_int @ X @ Y ) @ ( zip_nat_int @ Xs @ Ys ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % zip_Cons_Cons
% 2.39/2.74 thf(fact_1663_zip__Cons__Cons,axiom,
% 2.39/2.74 ! [X: heap_e7401611519738050253t_unit,Xs: list_h2745205591237434579t_unit,Y: set_nat,Ys: list_set_nat] :
% 2.39/2.74 ( ( zip_he6711929980790699996et_nat @ ( cons_h4161061858534515843t_unit @ X @ Xs ) @ ( cons_set_nat @ Y @ Ys ) )
% 2.39/2.74 = ( cons_P2869003950965171916et_nat @ ( produc7507926704131184380et_nat @ X @ Y ) @ ( zip_he6711929980790699996et_nat @ Xs @ Ys ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % zip_Cons_Cons
% 2.39/2.74 thf(fact_1664_zip__Cons__Cons,axiom,
% 2.39/2.74 ! [X: nat,Xs: list_nat,Y: nat,Ys: list_nat] :
% 2.39/2.74 ( ( zip_nat_nat @ ( cons_nat @ X @ Xs ) @ ( cons_nat @ Y @ Ys ) )
% 2.39/2.74 = ( cons_P6512896166579812791at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( zip_nat_nat @ Xs @ Ys ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % zip_Cons_Cons
% 2.39/2.74 thf(fact_1665_zip__Cons__Cons,axiom,
% 2.39/2.74 ! [X: int,Xs: list_int,Y: int,Ys: list_int] :
% 2.39/2.74 ( ( zip_int_int @ ( cons_int @ X @ Xs ) @ ( cons_int @ Y @ Ys ) )
% 2.39/2.74 = ( cons_P3334398858971670639nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( zip_int_int @ Xs @ Ys ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % zip_Cons_Cons
% 2.39/2.74 thf(fact_1666_zip__Cons__Cons,axiom,
% 2.39/2.74 ! [X: produc3658429121746597890et_nat > $o,Xs: list_P7985473006766602707_nat_o,Y: produc3658429121746597890et_nat,Ys: list_P9062070895058802706et_nat] :
% 2.39/2.74 ( ( zip_Pr7134870689397686104et_nat @ ( cons_P6219271836124797827_nat_o @ X @ Xs ) @ ( cons_P2869003950965171916et_nat @ Y @ Ys ) )
% 2.39/2.74 = ( cons_P3419706843779801160et_nat @ ( produc5001842942810119800et_nat @ X @ Y ) @ ( zip_Pr7134870689397686104et_nat @ Xs @ Ys ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % zip_Cons_Cons
% 2.39/2.74 thf(fact_1667_zip__Cons__Cons,axiom,
% 2.39/2.74 ! [X: produc3658429121746597890et_nat > $o,Xs: list_P7985473006766602707_nat_o,Y: produc3925858234332021118et_nat,Ys: list_P2321686559999237006et_nat] :
% 2.39/2.74 ( ( zip_Pr8136144321567152340et_nat @ ( cons_P6219271836124797827_nat_o @ X @ Xs ) @ ( cons_P3419706843779801160et_nat @ Y @ Ys ) )
% 2.39/2.74 = ( cons_P6329468272379687876et_nat @ ( produc2245416461498447860et_nat @ X @ Y ) @ ( zip_Pr8136144321567152340et_nat @ Xs @ Ys ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % zip_Cons_Cons
% 2.39/2.74 thf(fact_1668_zip__map__fst__snd,axiom,
% 2.39/2.74 ! [Zs: list_P9062070895058802706et_nat] :
% 2.39/2.74 ( ( zip_he6711929980790699996et_nat @ ( map_Pr7042224834074979589t_unit @ produc1824681642469235216et_nat @ Zs ) @ ( map_Pr4871828589360411470et_nat @ produc8586169260539613262et_nat @ Zs ) )
% 2.39/2.74 = Zs ) ).
% 2.39/2.74
% 2.39/2.74 % zip_map_fst_snd
% 2.39/2.74 thf(fact_1669_zip__map__fst__snd,axiom,
% 2.39/2.74 ! [Zs: list_P5707943133018811711nt_int] :
% 2.39/2.74 ( ( zip_int_int @ ( map_Pr6494458893431244577nt_int @ product_fst_int_int @ Zs ) @ ( map_Pr6494458893431244577nt_int @ product_snd_int_int @ Zs ) )
% 2.39/2.74 = Zs ) ).
% 2.39/2.74
% 2.39/2.74 % zip_map_fst_snd
% 2.39/2.74 thf(fact_1670_zip__map__fst__snd,axiom,
% 2.39/2.74 ! [Zs: list_P8527749157015355191n_assn] :
% 2.39/2.74 ( ( zip_assn_assn @ ( map_Pr8991440229025900053n_assn @ produc9167289414957590229n_assn @ Zs ) @ ( map_Pr8991440229025900053n_assn @ produc2051961928117032727n_assn @ Zs ) )
% 2.39/2.74 = Zs ) ).
% 2.39/2.74
% 2.39/2.74 % zip_map_fst_snd
% 2.39/2.74 thf(fact_1671_nths__singleton,axiom,
% 2.39/2.74 ! [A3: set_nat,X: produc6575502325842934193n_assn] :
% 2.39/2.74 ( ( ( member_nat2 @ zero_zero_nat @ A3 )
% 2.39/2.74 => ( ( nths_P5537322223065504949n_assn @ ( cons_P2971678138204555879n_assn @ X @ nil_Pr5671120429643327159n_assn ) @ A3 )
% 2.39/2.74 = ( cons_P2971678138204555879n_assn @ X @ nil_Pr5671120429643327159n_assn ) ) )
% 2.39/2.74 & ( ~ ( member_nat2 @ zero_zero_nat @ A3 )
% 2.39/2.74 => ( ( nths_P5537322223065504949n_assn @ ( cons_P2971678138204555879n_assn @ X @ nil_Pr5671120429643327159n_assn ) @ A3 )
% 2.39/2.74 = nil_Pr5671120429643327159n_assn ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % nths_singleton
% 2.39/2.74 thf(fact_1672_nths__singleton,axiom,
% 2.39/2.74 ! [A3: set_nat,X: int] :
% 2.39/2.74 ( ( ( member_nat2 @ zero_zero_nat @ A3 )
% 2.39/2.74 => ( ( nths_int @ ( cons_int @ X @ nil_int ) @ A3 )
% 2.39/2.74 = ( cons_int @ X @ nil_int ) ) )
% 2.39/2.74 & ( ~ ( member_nat2 @ zero_zero_nat @ A3 )
% 2.39/2.74 => ( ( nths_int @ ( cons_int @ X @ nil_int ) @ A3 )
% 2.39/2.74 = nil_int ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % nths_singleton
% 2.39/2.74 thf(fact_1673_nths__singleton,axiom,
% 2.39/2.74 ! [A3: set_nat,X: nat] :
% 2.39/2.74 ( ( ( member_nat2 @ zero_zero_nat @ A3 )
% 2.39/2.74 => ( ( nths_nat @ ( cons_nat @ X @ nil_nat ) @ A3 )
% 2.39/2.74 = ( cons_nat @ X @ nil_nat ) ) )
% 2.39/2.74 & ( ~ ( member_nat2 @ zero_zero_nat @ A3 )
% 2.39/2.74 => ( ( nths_nat @ ( cons_nat @ X @ nil_nat ) @ A3 )
% 2.39/2.74 = nil_nat ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % nths_singleton
% 2.39/2.74 thf(fact_1674_less__assn__def,axiom,
% 2.39/2.74 ( ord_less_assn
% 2.39/2.74 = ( ^ [A2: assn,B2: assn] :
% 2.39/2.74 ( ( ord_less_eq_assn @ A2 @ B2 )
% 2.39/2.74 & ( A2 != B2 ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % less_assn_def
% 2.39/2.74 thf(fact_1675_not__Cons__self2,axiom,
% 2.39/2.74 ! [X: int,Xs: list_int] :
% 2.39/2.74 ( ( cons_int @ X @ Xs )
% 2.39/2.74 != Xs ) ).
% 2.39/2.74
% 2.39/2.74 % not_Cons_self2
% 2.39/2.74 thf(fact_1676_not__Cons__self2,axiom,
% 2.39/2.74 ! [X: nat,Xs: list_nat] :
% 2.39/2.74 ( ( cons_nat @ X @ Xs )
% 2.39/2.74 != Xs ) ).
% 2.39/2.74
% 2.39/2.74 % not_Cons_self2
% 2.39/2.74 thf(fact_1677_transpose_Ocases,axiom,
% 2.39/2.74 ! [X: list_l6351802567095793725n_assn] :
% 2.39/2.74 ( ( X != nil_li5476096274760905021n_assn )
% 2.39/2.74 => ( ! [Xss: list_l6351802567095793725n_assn] :
% 2.39/2.74 ( X
% 2.39/2.74 != ( cons_l2423627976422276333n_assn @ nil_Pr5671120429643327159n_assn @ Xss ) )
% 2.39/2.74 => ~ ! [X3: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn,Xss: list_l6351802567095793725n_assn] :
% 2.39/2.74 ( X
% 2.39/2.74 != ( cons_l2423627976422276333n_assn @ ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % transpose.cases
% 2.39/2.74 thf(fact_1678_transpose_Ocases,axiom,
% 2.39/2.74 ! [X: list_list_int] :
% 2.39/2.74 ( ( X != nil_list_int )
% 2.39/2.74 => ( ! [Xss: list_list_int] :
% 2.39/2.74 ( X
% 2.39/2.74 != ( cons_list_int @ nil_int @ Xss ) )
% 2.39/2.74 => ~ ! [X3: int,Xs2: list_int,Xss: list_list_int] :
% 2.39/2.74 ( X
% 2.39/2.74 != ( cons_list_int @ ( cons_int @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % transpose.cases
% 2.39/2.74 thf(fact_1679_transpose_Ocases,axiom,
% 2.39/2.74 ! [X: list_list_nat] :
% 2.39/2.74 ( ( X != nil_list_nat )
% 2.39/2.74 => ( ! [Xss: list_list_nat] :
% 2.39/2.74 ( X
% 2.39/2.74 != ( cons_list_nat @ nil_nat @ Xss ) )
% 2.39/2.74 => ~ ! [X3: nat,Xs2: list_nat,Xss: list_list_nat] :
% 2.39/2.74 ( X
% 2.39/2.74 != ( cons_list_nat @ ( cons_nat @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % transpose.cases
% 2.39/2.74 thf(fact_1680_zip__eq__ConsE,axiom,
% 2.39/2.74 ! [Xs: list_int,Ys: list_nat,Xy: product_prod_int_nat,Xys: list_P8198026277950538467nt_nat] :
% 2.39/2.74 ( ( ( zip_int_nat @ Xs @ Ys )
% 2.39/2.74 = ( cons_P7512249878480867347nt_nat @ Xy @ Xys ) )
% 2.39/2.74 => ~ ! [X3: int,Xs3: list_int] :
% 2.39/2.74 ( ( Xs
% 2.39/2.74 = ( cons_int @ X3 @ Xs3 ) )
% 2.39/2.74 => ! [Y3: nat,Ys2: list_nat] :
% 2.39/2.74 ( ( Ys
% 2.39/2.74 = ( cons_nat @ Y3 @ Ys2 ) )
% 2.39/2.74 => ( ( Xy
% 2.39/2.74 = ( product_Pair_int_nat @ X3 @ Y3 ) )
% 2.39/2.74 => ( Xys
% 2.39/2.74 != ( zip_int_nat @ Xs3 @ Ys2 ) ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % zip_eq_ConsE
% 2.39/2.74 thf(fact_1681_zip__eq__ConsE,axiom,
% 2.39/2.74 ! [Xs: list_nat,Ys: list_int,Xy: product_prod_nat_int,Xys: list_P3521021558325789923at_int] :
% 2.39/2.74 ( ( ( zip_nat_int @ Xs @ Ys )
% 2.39/2.74 = ( cons_P2335045147070616083at_int @ Xy @ Xys ) )
% 2.39/2.74 => ~ ! [X3: nat,Xs3: list_nat] :
% 2.39/2.74 ( ( Xs
% 2.39/2.74 = ( cons_nat @ X3 @ Xs3 ) )
% 2.39/2.74 => ! [Y3: int,Ys2: list_int] :
% 2.39/2.74 ( ( Ys
% 2.39/2.74 = ( cons_int @ Y3 @ Ys2 ) )
% 2.39/2.74 => ( ( Xy
% 2.39/2.74 = ( product_Pair_nat_int @ X3 @ Y3 ) )
% 2.39/2.74 => ( Xys
% 2.39/2.74 != ( zip_nat_int @ Xs3 @ Ys2 ) ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % zip_eq_ConsE
% 2.39/2.74 thf(fact_1682_zip__eq__ConsE,axiom,
% 2.39/2.74 ! [Xs: list_h2745205591237434579t_unit,Ys: list_set_nat,Xy: produc3658429121746597890et_nat,Xys: list_P9062070895058802706et_nat] :
% 2.39/2.74 ( ( ( zip_he6711929980790699996et_nat @ Xs @ Ys )
% 2.39/2.74 = ( cons_P2869003950965171916et_nat @ Xy @ Xys ) )
% 2.39/2.74 => ~ ! [X3: heap_e7401611519738050253t_unit,Xs3: list_h2745205591237434579t_unit] :
% 2.39/2.74 ( ( Xs
% 2.39/2.74 = ( cons_h4161061858534515843t_unit @ X3 @ Xs3 ) )
% 2.39/2.74 => ! [Y3: set_nat,Ys2: list_set_nat] :
% 2.39/2.74 ( ( Ys
% 2.39/2.74 = ( cons_set_nat @ Y3 @ Ys2 ) )
% 2.39/2.74 => ( ( Xy
% 2.39/2.74 = ( produc7507926704131184380et_nat @ X3 @ Y3 ) )
% 2.39/2.74 => ( Xys
% 2.39/2.74 != ( zip_he6711929980790699996et_nat @ Xs3 @ Ys2 ) ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % zip_eq_ConsE
% 2.39/2.74 thf(fact_1683_zip__eq__ConsE,axiom,
% 2.39/2.74 ! [Xs: list_nat,Ys: list_nat,Xy: product_prod_nat_nat,Xys: list_P6011104703257516679at_nat] :
% 2.39/2.74 ( ( ( zip_nat_nat @ Xs @ Ys )
% 2.39/2.74 = ( cons_P6512896166579812791at_nat @ Xy @ Xys ) )
% 2.39/2.74 => ~ ! [X3: nat,Xs3: list_nat] :
% 2.39/2.74 ( ( Xs
% 2.39/2.74 = ( cons_nat @ X3 @ Xs3 ) )
% 2.39/2.74 => ! [Y3: nat,Ys2: list_nat] :
% 2.39/2.74 ( ( Ys
% 2.39/2.74 = ( cons_nat @ Y3 @ Ys2 ) )
% 2.39/2.74 => ( ( Xy
% 2.39/2.74 = ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 2.39/2.74 => ( Xys
% 2.39/2.74 != ( zip_nat_nat @ Xs3 @ Ys2 ) ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % zip_eq_ConsE
% 2.39/2.74 thf(fact_1684_zip__eq__ConsE,axiom,
% 2.39/2.74 ! [Xs: list_int,Ys: list_int,Xy: product_prod_int_int,Xys: list_P5707943133018811711nt_int] :
% 2.39/2.74 ( ( ( zip_int_int @ Xs @ Ys )
% 2.39/2.74 = ( cons_P3334398858971670639nt_int @ Xy @ Xys ) )
% 2.39/2.74 => ~ ! [X3: int,Xs3: list_int] :
% 2.39/2.74 ( ( Xs
% 2.39/2.74 = ( cons_int @ X3 @ Xs3 ) )
% 2.39/2.74 => ! [Y3: int,Ys2: list_int] :
% 2.39/2.74 ( ( Ys
% 2.39/2.74 = ( cons_int @ Y3 @ Ys2 ) )
% 2.39/2.74 => ( ( Xy
% 2.39/2.74 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 2.39/2.74 => ( Xys
% 2.39/2.74 != ( zip_int_int @ Xs3 @ Ys2 ) ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % zip_eq_ConsE
% 2.39/2.74 thf(fact_1685_zip__eq__ConsE,axiom,
% 2.39/2.74 ! [Xs: list_P7985473006766602707_nat_o,Ys: list_P9062070895058802706et_nat,Xy: produc3925858234332021118et_nat,Xys: list_P2321686559999237006et_nat] :
% 2.39/2.74 ( ( ( zip_Pr7134870689397686104et_nat @ Xs @ Ys )
% 2.39/2.74 = ( cons_P3419706843779801160et_nat @ Xy @ Xys ) )
% 2.39/2.74 => ~ ! [X3: produc3658429121746597890et_nat > $o,Xs3: list_P7985473006766602707_nat_o] :
% 2.39/2.74 ( ( Xs
% 2.39/2.74 = ( cons_P6219271836124797827_nat_o @ X3 @ Xs3 ) )
% 2.39/2.74 => ! [Y3: produc3658429121746597890et_nat,Ys2: list_P9062070895058802706et_nat] :
% 2.39/2.74 ( ( Ys
% 2.39/2.74 = ( cons_P2869003950965171916et_nat @ Y3 @ Ys2 ) )
% 2.39/2.74 => ( ( Xy
% 2.39/2.74 = ( produc5001842942810119800et_nat @ X3 @ Y3 ) )
% 2.39/2.74 => ( Xys
% 2.39/2.74 != ( zip_Pr7134870689397686104et_nat @ Xs3 @ Ys2 ) ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % zip_eq_ConsE
% 2.39/2.74 thf(fact_1686_zip__eq__ConsE,axiom,
% 2.39/2.74 ! [Xs: list_P7985473006766602707_nat_o,Ys: list_P2321686559999237006et_nat,Xy: produc2732055786443039994et_nat,Xys: list_P362550909693114634et_nat] :
% 2.39/2.74 ( ( ( zip_Pr8136144321567152340et_nat @ Xs @ Ys )
% 2.39/2.74 = ( cons_P6329468272379687876et_nat @ Xy @ Xys ) )
% 2.39/2.74 => ~ ! [X3: produc3658429121746597890et_nat > $o,Xs3: list_P7985473006766602707_nat_o] :
% 2.39/2.74 ( ( Xs
% 2.39/2.74 = ( cons_P6219271836124797827_nat_o @ X3 @ Xs3 ) )
% 2.39/2.74 => ! [Y3: produc3925858234332021118et_nat,Ys2: list_P2321686559999237006et_nat] :
% 2.39/2.74 ( ( Ys
% 2.39/2.74 = ( cons_P3419706843779801160et_nat @ Y3 @ Ys2 ) )
% 2.39/2.74 => ( ( Xy
% 2.39/2.74 = ( produc2245416461498447860et_nat @ X3 @ Y3 ) )
% 2.39/2.74 => ( Xys
% 2.39/2.74 != ( zip_Pr8136144321567152340et_nat @ Xs3 @ Ys2 ) ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % zip_eq_ConsE
% 2.39/2.74 thf(fact_1687_pair__list__eqI,axiom,
% 2.39/2.74 ! [Xs: list_P9062070895058802706et_nat,Ys: list_P9062070895058802706et_nat] :
% 2.39/2.74 ( ( ( map_Pr7042224834074979589t_unit @ produc1824681642469235216et_nat @ Xs )
% 2.39/2.74 = ( map_Pr7042224834074979589t_unit @ produc1824681642469235216et_nat @ Ys ) )
% 2.39/2.74 => ( ( ( map_Pr4871828589360411470et_nat @ produc8586169260539613262et_nat @ Xs )
% 2.39/2.74 = ( map_Pr4871828589360411470et_nat @ produc8586169260539613262et_nat @ Ys ) )
% 2.39/2.74 => ( Xs = Ys ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % pair_list_eqI
% 2.39/2.74 thf(fact_1688_pair__list__eqI,axiom,
% 2.39/2.74 ! [Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int] :
% 2.39/2.74 ( ( ( map_Pr6494458893431244577nt_int @ product_fst_int_int @ Xs )
% 2.39/2.74 = ( map_Pr6494458893431244577nt_int @ product_fst_int_int @ Ys ) )
% 2.39/2.74 => ( ( ( map_Pr6494458893431244577nt_int @ product_snd_int_int @ Xs )
% 2.39/2.74 = ( map_Pr6494458893431244577nt_int @ product_snd_int_int @ Ys ) )
% 2.39/2.74 => ( Xs = Ys ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % pair_list_eqI
% 2.39/2.74 thf(fact_1689_pair__list__eqI,axiom,
% 2.39/2.74 ! [Xs: list_P8527749157015355191n_assn,Ys: list_P8527749157015355191n_assn] :
% 2.39/2.74 ( ( ( map_Pr8991440229025900053n_assn @ produc9167289414957590229n_assn @ Xs )
% 2.39/2.74 = ( map_Pr8991440229025900053n_assn @ produc9167289414957590229n_assn @ Ys ) )
% 2.39/2.74 => ( ( ( map_Pr8991440229025900053n_assn @ produc2051961928117032727n_assn @ Xs )
% 2.39/2.74 = ( map_Pr8991440229025900053n_assn @ produc2051961928117032727n_assn @ Ys ) )
% 2.39/2.74 => ( Xs = Ys ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % pair_list_eqI
% 2.39/2.74 thf(fact_1690_zero__less__iff__neq__zero,axiom,
% 2.39/2.74 ! [N: nat] :
% 2.39/2.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.39/2.74 = ( N != zero_zero_nat ) ) ).
% 2.39/2.74
% 2.39/2.74 % zero_less_iff_neq_zero
% 2.39/2.74 thf(fact_1691_gr__implies__not__zero,axiom,
% 2.39/2.74 ! [M2: nat,N: nat] :
% 2.39/2.74 ( ( ord_less_nat @ M2 @ N )
% 2.39/2.74 => ( N != zero_zero_nat ) ) ).
% 2.39/2.74
% 2.39/2.74 % gr_implies_not_zero
% 2.39/2.74 thf(fact_1692_not__less__zero,axiom,
% 2.39/2.74 ! [N: nat] :
% 2.39/2.74 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 2.39/2.74
% 2.39/2.74 % not_less_zero
% 2.39/2.74 thf(fact_1693_gr__zeroI,axiom,
% 2.39/2.74 ! [N: nat] :
% 2.39/2.74 ( ( N != zero_zero_nat )
% 2.39/2.74 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 2.39/2.74
% 2.39/2.74 % gr_zeroI
% 2.39/2.74 thf(fact_1694_less__numeral__extra_I4_J,axiom,
% 2.39/2.74 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ one_one_Code_integer ) ).
% 2.39/2.74
% 2.39/2.74 % less_numeral_extra(4)
% 2.39/2.74 thf(fact_1695_less__numeral__extra_I4_J,axiom,
% 2.39/2.74 ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 2.39/2.74
% 2.39/2.74 % less_numeral_extra(4)
% 2.39/2.74 thf(fact_1696_less__numeral__extra_I4_J,axiom,
% 2.39/2.74 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 2.39/2.74
% 2.39/2.74 % less_numeral_extra(4)
% 2.39/2.74 thf(fact_1697_less__numeral__extra_I4_J,axiom,
% 2.39/2.74 ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 2.39/2.74
% 2.39/2.74 % less_numeral_extra(4)
% 2.39/2.74 thf(fact_1698_neq__NilE,axiom,
% 2.39/2.74 ! [L: list_P8527749157015355191n_assn] :
% 2.39/2.74 ( ( L != nil_Pr5671120429643327159n_assn )
% 2.39/2.74 => ~ ! [X3: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn] :
% 2.39/2.74 ( L
% 2.39/2.74 != ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % neq_NilE
% 2.39/2.74 thf(fact_1699_neq__NilE,axiom,
% 2.39/2.74 ! [L: list_int] :
% 2.39/2.74 ( ( L != nil_int )
% 2.39/2.74 => ~ ! [X3: int,Xs2: list_int] :
% 2.39/2.74 ( L
% 2.39/2.74 != ( cons_int @ X3 @ Xs2 ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % neq_NilE
% 2.39/2.74 thf(fact_1700_neq__NilE,axiom,
% 2.39/2.74 ! [L: list_nat] :
% 2.39/2.74 ( ( L != nil_nat )
% 2.39/2.74 => ~ ! [X3: nat,Xs2: list_nat] :
% 2.39/2.74 ( L
% 2.39/2.74 != ( cons_nat @ X3 @ Xs2 ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % neq_NilE
% 2.39/2.74 thf(fact_1701_list__2pre__induct,axiom,
% 2.39/2.74 ! [P2: list_P8527749157015355191n_assn > list_P8527749157015355191n_assn > $o,W1: list_P8527749157015355191n_assn,W2: list_P8527749157015355191n_assn] :
% 2.39/2.74 ( ( P2 @ nil_Pr5671120429643327159n_assn @ nil_Pr5671120429643327159n_assn )
% 2.39/2.74 => ( ! [E: produc6575502325842934193n_assn,W12: list_P8527749157015355191n_assn,W22: list_P8527749157015355191n_assn] :
% 2.39/2.74 ( ( P2 @ W12 @ W22 )
% 2.39/2.74 => ( P2 @ ( cons_P2971678138204555879n_assn @ E @ W12 ) @ W22 ) )
% 2.39/2.74 => ( ! [E: produc6575502325842934193n_assn,W13: list_P8527749157015355191n_assn,W23: list_P8527749157015355191n_assn] :
% 2.39/2.74 ( ( P2 @ W13 @ W23 )
% 2.39/2.74 => ( P2 @ W13 @ ( cons_P2971678138204555879n_assn @ E @ W23 ) ) )
% 2.39/2.74 => ( P2 @ W1 @ W2 ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % list_2pre_induct
% 2.39/2.74 thf(fact_1702_list__2pre__induct,axiom,
% 2.39/2.74 ! [P2: list_P8527749157015355191n_assn > list_int > $o,W1: list_P8527749157015355191n_assn,W2: list_int] :
% 2.39/2.74 ( ( P2 @ nil_Pr5671120429643327159n_assn @ nil_int )
% 2.39/2.74 => ( ! [E: produc6575502325842934193n_assn,W12: list_P8527749157015355191n_assn,W22: list_int] :
% 2.39/2.74 ( ( P2 @ W12 @ W22 )
% 2.39/2.74 => ( P2 @ ( cons_P2971678138204555879n_assn @ E @ W12 ) @ W22 ) )
% 2.39/2.74 => ( ! [E: int,W13: list_P8527749157015355191n_assn,W23: list_int] :
% 2.39/2.74 ( ( P2 @ W13 @ W23 )
% 2.39/2.74 => ( P2 @ W13 @ ( cons_int @ E @ W23 ) ) )
% 2.39/2.74 => ( P2 @ W1 @ W2 ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % list_2pre_induct
% 2.39/2.74 thf(fact_1703_list__2pre__induct,axiom,
% 2.39/2.74 ! [P2: list_P8527749157015355191n_assn > list_nat > $o,W1: list_P8527749157015355191n_assn,W2: list_nat] :
% 2.39/2.74 ( ( P2 @ nil_Pr5671120429643327159n_assn @ nil_nat )
% 2.39/2.74 => ( ! [E: produc6575502325842934193n_assn,W12: list_P8527749157015355191n_assn,W22: list_nat] :
% 2.39/2.74 ( ( P2 @ W12 @ W22 )
% 2.39/2.74 => ( P2 @ ( cons_P2971678138204555879n_assn @ E @ W12 ) @ W22 ) )
% 2.39/2.74 => ( ! [E: nat,W13: list_P8527749157015355191n_assn,W23: list_nat] :
% 2.39/2.74 ( ( P2 @ W13 @ W23 )
% 2.39/2.74 => ( P2 @ W13 @ ( cons_nat @ E @ W23 ) ) )
% 2.39/2.74 => ( P2 @ W1 @ W2 ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % list_2pre_induct
% 2.39/2.74 thf(fact_1704_list__2pre__induct,axiom,
% 2.39/2.74 ! [P2: list_int > list_P8527749157015355191n_assn > $o,W1: list_int,W2: list_P8527749157015355191n_assn] :
% 2.39/2.74 ( ( P2 @ nil_int @ nil_Pr5671120429643327159n_assn )
% 2.39/2.74 => ( ! [E: int,W12: list_int,W22: list_P8527749157015355191n_assn] :
% 2.39/2.74 ( ( P2 @ W12 @ W22 )
% 2.39/2.74 => ( P2 @ ( cons_int @ E @ W12 ) @ W22 ) )
% 2.39/2.74 => ( ! [E: produc6575502325842934193n_assn,W13: list_int,W23: list_P8527749157015355191n_assn] :
% 2.39/2.74 ( ( P2 @ W13 @ W23 )
% 2.39/2.74 => ( P2 @ W13 @ ( cons_P2971678138204555879n_assn @ E @ W23 ) ) )
% 2.39/2.74 => ( P2 @ W1 @ W2 ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % list_2pre_induct
% 2.39/2.74 thf(fact_1705_list__2pre__induct,axiom,
% 2.39/2.74 ! [P2: list_int > list_int > $o,W1: list_int,W2: list_int] :
% 2.39/2.74 ( ( P2 @ nil_int @ nil_int )
% 2.39/2.74 => ( ! [E: int,W12: list_int,W22: list_int] :
% 2.39/2.74 ( ( P2 @ W12 @ W22 )
% 2.39/2.74 => ( P2 @ ( cons_int @ E @ W12 ) @ W22 ) )
% 2.39/2.74 => ( ! [E: int,W13: list_int,W23: list_int] :
% 2.39/2.74 ( ( P2 @ W13 @ W23 )
% 2.39/2.74 => ( P2 @ W13 @ ( cons_int @ E @ W23 ) ) )
% 2.39/2.74 => ( P2 @ W1 @ W2 ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % list_2pre_induct
% 2.39/2.74 thf(fact_1706_list__2pre__induct,axiom,
% 2.39/2.74 ! [P2: list_int > list_nat > $o,W1: list_int,W2: list_nat] :
% 2.39/2.74 ( ( P2 @ nil_int @ nil_nat )
% 2.39/2.74 => ( ! [E: int,W12: list_int,W22: list_nat] :
% 2.39/2.74 ( ( P2 @ W12 @ W22 )
% 2.39/2.74 => ( P2 @ ( cons_int @ E @ W12 ) @ W22 ) )
% 2.39/2.74 => ( ! [E: nat,W13: list_int,W23: list_nat] :
% 2.39/2.74 ( ( P2 @ W13 @ W23 )
% 2.39/2.74 => ( P2 @ W13 @ ( cons_nat @ E @ W23 ) ) )
% 2.39/2.74 => ( P2 @ W1 @ W2 ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % list_2pre_induct
% 2.39/2.74 thf(fact_1707_list__2pre__induct,axiom,
% 2.39/2.74 ! [P2: list_nat > list_P8527749157015355191n_assn > $o,W1: list_nat,W2: list_P8527749157015355191n_assn] :
% 2.39/2.74 ( ( P2 @ nil_nat @ nil_Pr5671120429643327159n_assn )
% 2.39/2.74 => ( ! [E: nat,W12: list_nat,W22: list_P8527749157015355191n_assn] :
% 2.39/2.74 ( ( P2 @ W12 @ W22 )
% 2.39/2.74 => ( P2 @ ( cons_nat @ E @ W12 ) @ W22 ) )
% 2.39/2.74 => ( ! [E: produc6575502325842934193n_assn,W13: list_nat,W23: list_P8527749157015355191n_assn] :
% 2.39/2.74 ( ( P2 @ W13 @ W23 )
% 2.39/2.74 => ( P2 @ W13 @ ( cons_P2971678138204555879n_assn @ E @ W23 ) ) )
% 2.39/2.74 => ( P2 @ W1 @ W2 ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % list_2pre_induct
% 2.39/2.74 thf(fact_1708_list__2pre__induct,axiom,
% 2.39/2.74 ! [P2: list_nat > list_int > $o,W1: list_nat,W2: list_int] :
% 2.39/2.74 ( ( P2 @ nil_nat @ nil_int )
% 2.39/2.74 => ( ! [E: nat,W12: list_nat,W22: list_int] :
% 2.39/2.74 ( ( P2 @ W12 @ W22 )
% 2.39/2.74 => ( P2 @ ( cons_nat @ E @ W12 ) @ W22 ) )
% 2.39/2.74 => ( ! [E: int,W13: list_nat,W23: list_int] :
% 2.39/2.74 ( ( P2 @ W13 @ W23 )
% 2.39/2.74 => ( P2 @ W13 @ ( cons_int @ E @ W23 ) ) )
% 2.39/2.74 => ( P2 @ W1 @ W2 ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % list_2pre_induct
% 2.39/2.74 thf(fact_1709_list__2pre__induct,axiom,
% 2.39/2.74 ! [P2: list_nat > list_nat > $o,W1: list_nat,W2: list_nat] :
% 2.39/2.74 ( ( P2 @ nil_nat @ nil_nat )
% 2.39/2.74 => ( ! [E: nat,W12: list_nat,W22: list_nat] :
% 2.39/2.74 ( ( P2 @ W12 @ W22 )
% 2.39/2.74 => ( P2 @ ( cons_nat @ E @ W12 ) @ W22 ) )
% 2.39/2.74 => ( ! [E: nat,W13: list_nat,W23: list_nat] :
% 2.39/2.74 ( ( P2 @ W13 @ W23 )
% 2.39/2.74 => ( P2 @ W13 @ ( cons_nat @ E @ W23 ) ) )
% 2.39/2.74 => ( P2 @ W1 @ W2 ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % list_2pre_induct
% 2.39/2.74 thf(fact_1710_list__induct__first2,axiom,
% 2.39/2.74 ! [P2: list_P8527749157015355191n_assn > $o,Xs: list_P8527749157015355191n_assn] :
% 2.39/2.74 ( ( P2 @ nil_Pr5671120429643327159n_assn )
% 2.39/2.74 => ( ! [X3: produc6575502325842934193n_assn] : ( P2 @ ( cons_P2971678138204555879n_assn @ X3 @ nil_Pr5671120429643327159n_assn ) )
% 2.39/2.74 => ( ! [X1: produc6575502325842934193n_assn,X23: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn] :
% 2.39/2.74 ( ( P2 @ Xs2 )
% 2.39/2.74 => ( P2 @ ( cons_P2971678138204555879n_assn @ X1 @ ( cons_P2971678138204555879n_assn @ X23 @ Xs2 ) ) ) )
% 2.39/2.74 => ( P2 @ Xs ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % list_induct_first2
% 2.39/2.74 thf(fact_1711_list__induct__first2,axiom,
% 2.39/2.74 ! [P2: list_int > $o,Xs: list_int] :
% 2.39/2.74 ( ( P2 @ nil_int )
% 2.39/2.74 => ( ! [X3: int] : ( P2 @ ( cons_int @ X3 @ nil_int ) )
% 2.39/2.74 => ( ! [X1: int,X23: int,Xs2: list_int] :
% 2.39/2.74 ( ( P2 @ Xs2 )
% 2.39/2.74 => ( P2 @ ( cons_int @ X1 @ ( cons_int @ X23 @ Xs2 ) ) ) )
% 2.39/2.74 => ( P2 @ Xs ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % list_induct_first2
% 2.39/2.74 thf(fact_1712_list__induct__first2,axiom,
% 2.39/2.74 ! [P2: list_nat > $o,Xs: list_nat] :
% 2.39/2.74 ( ( P2 @ nil_nat )
% 2.39/2.74 => ( ! [X3: nat] : ( P2 @ ( cons_nat @ X3 @ nil_nat ) )
% 2.39/2.74 => ( ! [X1: nat,X23: nat,Xs2: list_nat] :
% 2.39/2.74 ( ( P2 @ Xs2 )
% 2.39/2.74 => ( P2 @ ( cons_nat @ X1 @ ( cons_nat @ X23 @ Xs2 ) ) ) )
% 2.39/2.74 => ( P2 @ Xs ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % list_induct_first2
% 2.39/2.74 thf(fact_1713_mergesort__by__rel__merge__induct,axiom,
% 2.39/2.74 ! [P2: list_P8527749157015355191n_assn > list_P8527749157015355191n_assn > $o,R: produc6575502325842934193n_assn > produc6575502325842934193n_assn > $o,Xs: list_P8527749157015355191n_assn,Ys: list_P8527749157015355191n_assn] :
% 2.39/2.74 ( ! [Xs2: list_P8527749157015355191n_assn] : ( P2 @ Xs2 @ nil_Pr5671120429643327159n_assn )
% 2.39/2.74 => ( ! [X_1: list_P8527749157015355191n_assn] : ( P2 @ nil_Pr5671120429643327159n_assn @ X_1 )
% 2.39/2.74 => ( ! [X3: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn,Y3: produc6575502325842934193n_assn,Ys3: list_P8527749157015355191n_assn] :
% 2.39/2.74 ( ( R @ X3 @ Y3 )
% 2.39/2.74 => ( ( P2 @ Xs2 @ ( cons_P2971678138204555879n_assn @ Y3 @ Ys3 ) )
% 2.39/2.74 => ( P2 @ ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) @ ( cons_P2971678138204555879n_assn @ Y3 @ Ys3 ) ) ) )
% 2.39/2.74 => ( ! [X3: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn,Y3: produc6575502325842934193n_assn,Ys3: list_P8527749157015355191n_assn] :
% 2.39/2.74 ( ~ ( R @ X3 @ Y3 )
% 2.39/2.74 => ( ( P2 @ ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) @ Ys3 )
% 2.39/2.74 => ( P2 @ ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) @ ( cons_P2971678138204555879n_assn @ Y3 @ Ys3 ) ) ) )
% 2.39/2.74 => ( P2 @ Xs @ Ys ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % mergesort_by_rel_merge_induct
% 2.39/2.74 thf(fact_1714_mergesort__by__rel__merge__induct,axiom,
% 2.39/2.74 ! [P2: list_int > list_P8527749157015355191n_assn > $o,R: int > produc6575502325842934193n_assn > $o,Xs: list_int,Ys: list_P8527749157015355191n_assn] :
% 2.39/2.74 ( ! [Xs2: list_int] : ( P2 @ Xs2 @ nil_Pr5671120429643327159n_assn )
% 2.39/2.74 => ( ! [X_1: list_P8527749157015355191n_assn] : ( P2 @ nil_int @ X_1 )
% 2.39/2.74 => ( ! [X3: int,Xs2: list_int,Y3: produc6575502325842934193n_assn,Ys3: list_P8527749157015355191n_assn] :
% 2.39/2.74 ( ( R @ X3 @ Y3 )
% 2.39/2.74 => ( ( P2 @ Xs2 @ ( cons_P2971678138204555879n_assn @ Y3 @ Ys3 ) )
% 2.39/2.74 => ( P2 @ ( cons_int @ X3 @ Xs2 ) @ ( cons_P2971678138204555879n_assn @ Y3 @ Ys3 ) ) ) )
% 2.39/2.74 => ( ! [X3: int,Xs2: list_int,Y3: produc6575502325842934193n_assn,Ys3: list_P8527749157015355191n_assn] :
% 2.39/2.74 ( ~ ( R @ X3 @ Y3 )
% 2.39/2.74 => ( ( P2 @ ( cons_int @ X3 @ Xs2 ) @ Ys3 )
% 2.39/2.74 => ( P2 @ ( cons_int @ X3 @ Xs2 ) @ ( cons_P2971678138204555879n_assn @ Y3 @ Ys3 ) ) ) )
% 2.39/2.74 => ( P2 @ Xs @ Ys ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % mergesort_by_rel_merge_induct
% 2.39/2.74 thf(fact_1715_mergesort__by__rel__merge__induct,axiom,
% 2.39/2.74 ! [P2: list_nat > list_P8527749157015355191n_assn > $o,R: nat > produc6575502325842934193n_assn > $o,Xs: list_nat,Ys: list_P8527749157015355191n_assn] :
% 2.39/2.74 ( ! [Xs2: list_nat] : ( P2 @ Xs2 @ nil_Pr5671120429643327159n_assn )
% 2.39/2.74 => ( ! [X_1: list_P8527749157015355191n_assn] : ( P2 @ nil_nat @ X_1 )
% 2.39/2.74 => ( ! [X3: nat,Xs2: list_nat,Y3: produc6575502325842934193n_assn,Ys3: list_P8527749157015355191n_assn] :
% 2.39/2.74 ( ( R @ X3 @ Y3 )
% 2.39/2.74 => ( ( P2 @ Xs2 @ ( cons_P2971678138204555879n_assn @ Y3 @ Ys3 ) )
% 2.39/2.74 => ( P2 @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_P2971678138204555879n_assn @ Y3 @ Ys3 ) ) ) )
% 2.39/2.74 => ( ! [X3: nat,Xs2: list_nat,Y3: produc6575502325842934193n_assn,Ys3: list_P8527749157015355191n_assn] :
% 2.39/2.74 ( ~ ( R @ X3 @ Y3 )
% 2.39/2.74 => ( ( P2 @ ( cons_nat @ X3 @ Xs2 ) @ Ys3 )
% 2.39/2.74 => ( P2 @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_P2971678138204555879n_assn @ Y3 @ Ys3 ) ) ) )
% 2.39/2.74 => ( P2 @ Xs @ Ys ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % mergesort_by_rel_merge_induct
% 2.39/2.74 thf(fact_1716_mergesort__by__rel__merge__induct,axiom,
% 2.39/2.74 ! [P2: list_P8527749157015355191n_assn > list_int > $o,R: produc6575502325842934193n_assn > int > $o,Xs: list_P8527749157015355191n_assn,Ys: list_int] :
% 2.39/2.74 ( ! [Xs2: list_P8527749157015355191n_assn] : ( P2 @ Xs2 @ nil_int )
% 2.39/2.74 => ( ! [X_1: list_int] : ( P2 @ nil_Pr5671120429643327159n_assn @ X_1 )
% 2.39/2.74 => ( ! [X3: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn,Y3: int,Ys3: list_int] :
% 2.39/2.74 ( ( R @ X3 @ Y3 )
% 2.39/2.74 => ( ( P2 @ Xs2 @ ( cons_int @ Y3 @ Ys3 ) )
% 2.39/2.74 => ( P2 @ ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) @ ( cons_int @ Y3 @ Ys3 ) ) ) )
% 2.39/2.74 => ( ! [X3: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn,Y3: int,Ys3: list_int] :
% 2.39/2.74 ( ~ ( R @ X3 @ Y3 )
% 2.39/2.74 => ( ( P2 @ ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) @ Ys3 )
% 2.39/2.74 => ( P2 @ ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) @ ( cons_int @ Y3 @ Ys3 ) ) ) )
% 2.39/2.74 => ( P2 @ Xs @ Ys ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % mergesort_by_rel_merge_induct
% 2.39/2.74 thf(fact_1717_mergesort__by__rel__merge__induct,axiom,
% 2.39/2.74 ! [P2: list_int > list_int > $o,R: int > int > $o,Xs: list_int,Ys: list_int] :
% 2.39/2.74 ( ! [Xs2: list_int] : ( P2 @ Xs2 @ nil_int )
% 2.39/2.74 => ( ! [X_1: list_int] : ( P2 @ nil_int @ X_1 )
% 2.39/2.74 => ( ! [X3: int,Xs2: list_int,Y3: int,Ys3: list_int] :
% 2.39/2.74 ( ( R @ X3 @ Y3 )
% 2.39/2.74 => ( ( P2 @ Xs2 @ ( cons_int @ Y3 @ Ys3 ) )
% 2.39/2.74 => ( P2 @ ( cons_int @ X3 @ Xs2 ) @ ( cons_int @ Y3 @ Ys3 ) ) ) )
% 2.39/2.74 => ( ! [X3: int,Xs2: list_int,Y3: int,Ys3: list_int] :
% 2.39/2.74 ( ~ ( R @ X3 @ Y3 )
% 2.39/2.74 => ( ( P2 @ ( cons_int @ X3 @ Xs2 ) @ Ys3 )
% 2.39/2.74 => ( P2 @ ( cons_int @ X3 @ Xs2 ) @ ( cons_int @ Y3 @ Ys3 ) ) ) )
% 2.39/2.74 => ( P2 @ Xs @ Ys ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % mergesort_by_rel_merge_induct
% 2.39/2.74 thf(fact_1718_mergesort__by__rel__merge__induct,axiom,
% 2.39/2.74 ! [P2: list_nat > list_int > $o,R: nat > int > $o,Xs: list_nat,Ys: list_int] :
% 2.39/2.74 ( ! [Xs2: list_nat] : ( P2 @ Xs2 @ nil_int )
% 2.39/2.74 => ( ! [X_1: list_int] : ( P2 @ nil_nat @ X_1 )
% 2.39/2.74 => ( ! [X3: nat,Xs2: list_nat,Y3: int,Ys3: list_int] :
% 2.39/2.74 ( ( R @ X3 @ Y3 )
% 2.39/2.74 => ( ( P2 @ Xs2 @ ( cons_int @ Y3 @ Ys3 ) )
% 2.39/2.74 => ( P2 @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_int @ Y3 @ Ys3 ) ) ) )
% 2.39/2.74 => ( ! [X3: nat,Xs2: list_nat,Y3: int,Ys3: list_int] :
% 2.39/2.74 ( ~ ( R @ X3 @ Y3 )
% 2.39/2.74 => ( ( P2 @ ( cons_nat @ X3 @ Xs2 ) @ Ys3 )
% 2.39/2.74 => ( P2 @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_int @ Y3 @ Ys3 ) ) ) )
% 2.39/2.74 => ( P2 @ Xs @ Ys ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % mergesort_by_rel_merge_induct
% 2.39/2.74 thf(fact_1719_mergesort__by__rel__merge__induct,axiom,
% 2.39/2.74 ! [P2: list_P8527749157015355191n_assn > list_nat > $o,R: produc6575502325842934193n_assn > nat > $o,Xs: list_P8527749157015355191n_assn,Ys: list_nat] :
% 2.39/2.74 ( ! [Xs2: list_P8527749157015355191n_assn] : ( P2 @ Xs2 @ nil_nat )
% 2.39/2.74 => ( ! [X_1: list_nat] : ( P2 @ nil_Pr5671120429643327159n_assn @ X_1 )
% 2.39/2.74 => ( ! [X3: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn,Y3: nat,Ys3: list_nat] :
% 2.39/2.74 ( ( R @ X3 @ Y3 )
% 2.39/2.74 => ( ( P2 @ Xs2 @ ( cons_nat @ Y3 @ Ys3 ) )
% 2.39/2.74 => ( P2 @ ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) ) ) )
% 2.39/2.74 => ( ! [X3: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn,Y3: nat,Ys3: list_nat] :
% 2.39/2.74 ( ~ ( R @ X3 @ Y3 )
% 2.39/2.74 => ( ( P2 @ ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) @ Ys3 )
% 2.39/2.74 => ( P2 @ ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) ) ) )
% 2.39/2.74 => ( P2 @ Xs @ Ys ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % mergesort_by_rel_merge_induct
% 2.39/2.74 thf(fact_1720_mergesort__by__rel__merge__induct,axiom,
% 2.39/2.74 ! [P2: list_int > list_nat > $o,R: int > nat > $o,Xs: list_int,Ys: list_nat] :
% 2.39/2.74 ( ! [Xs2: list_int] : ( P2 @ Xs2 @ nil_nat )
% 2.39/2.74 => ( ! [X_1: list_nat] : ( P2 @ nil_int @ X_1 )
% 2.39/2.74 => ( ! [X3: int,Xs2: list_int,Y3: nat,Ys3: list_nat] :
% 2.39/2.74 ( ( R @ X3 @ Y3 )
% 2.39/2.74 => ( ( P2 @ Xs2 @ ( cons_nat @ Y3 @ Ys3 ) )
% 2.39/2.74 => ( P2 @ ( cons_int @ X3 @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) ) ) )
% 2.39/2.74 => ( ! [X3: int,Xs2: list_int,Y3: nat,Ys3: list_nat] :
% 2.39/2.74 ( ~ ( R @ X3 @ Y3 )
% 2.39/2.74 => ( ( P2 @ ( cons_int @ X3 @ Xs2 ) @ Ys3 )
% 2.39/2.74 => ( P2 @ ( cons_int @ X3 @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) ) ) )
% 2.39/2.74 => ( P2 @ Xs @ Ys ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % mergesort_by_rel_merge_induct
% 2.39/2.74 thf(fact_1721_mergesort__by__rel__merge__induct,axiom,
% 2.39/2.74 ! [P2: list_nat > list_nat > $o,R: nat > nat > $o,Xs: list_nat,Ys: list_nat] :
% 2.39/2.74 ( ! [Xs2: list_nat] : ( P2 @ Xs2 @ nil_nat )
% 2.39/2.74 => ( ! [X_1: list_nat] : ( P2 @ nil_nat @ X_1 )
% 2.39/2.74 => ( ! [X3: nat,Xs2: list_nat,Y3: nat,Ys3: list_nat] :
% 2.39/2.74 ( ( R @ X3 @ Y3 )
% 2.39/2.74 => ( ( P2 @ Xs2 @ ( cons_nat @ Y3 @ Ys3 ) )
% 2.39/2.74 => ( P2 @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) ) ) )
% 2.39/2.74 => ( ! [X3: nat,Xs2: list_nat,Y3: nat,Ys3: list_nat] :
% 2.39/2.74 ( ~ ( R @ X3 @ Y3 )
% 2.39/2.74 => ( ( P2 @ ( cons_nat @ X3 @ Xs2 ) @ Ys3 )
% 2.39/2.74 => ( P2 @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) ) ) )
% 2.39/2.74 => ( P2 @ Xs @ Ys ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % mergesort_by_rel_merge_induct
% 2.39/2.74 thf(fact_1722_list_Odistinct_I1_J,axiom,
% 2.39/2.74 ! [X21: produc6575502325842934193n_assn,X22: list_P8527749157015355191n_assn] :
% 2.39/2.74 ( nil_Pr5671120429643327159n_assn
% 2.39/2.74 != ( cons_P2971678138204555879n_assn @ X21 @ X22 ) ) ).
% 2.39/2.74
% 2.39/2.74 % list.distinct(1)
% 2.39/2.74 thf(fact_1723_list_Odistinct_I1_J,axiom,
% 2.39/2.74 ! [X21: int,X22: list_int] :
% 2.39/2.74 ( nil_int
% 2.39/2.74 != ( cons_int @ X21 @ X22 ) ) ).
% 2.39/2.74
% 2.39/2.74 % list.distinct(1)
% 2.39/2.74 thf(fact_1724_list_Odistinct_I1_J,axiom,
% 2.39/2.74 ! [X21: nat,X22: list_nat] :
% 2.39/2.74 ( nil_nat
% 2.39/2.74 != ( cons_nat @ X21 @ X22 ) ) ).
% 2.39/2.74
% 2.39/2.74 % list.distinct(1)
% 2.39/2.74 thf(fact_1725_list_OdiscI,axiom,
% 2.39/2.74 ! [List: list_P8527749157015355191n_assn,X21: produc6575502325842934193n_assn,X22: list_P8527749157015355191n_assn] :
% 2.39/2.74 ( ( List
% 2.39/2.74 = ( cons_P2971678138204555879n_assn @ X21 @ X22 ) )
% 2.39/2.74 => ( List != nil_Pr5671120429643327159n_assn ) ) ).
% 2.39/2.74
% 2.39/2.74 % list.discI
% 2.39/2.74 thf(fact_1726_list_OdiscI,axiom,
% 2.39/2.74 ! [List: list_int,X21: int,X22: list_int] :
% 2.39/2.74 ( ( List
% 2.39/2.74 = ( cons_int @ X21 @ X22 ) )
% 2.39/2.74 => ( List != nil_int ) ) ).
% 2.39/2.74
% 2.39/2.74 % list.discI
% 2.39/2.74 thf(fact_1727_list_OdiscI,axiom,
% 2.39/2.74 ! [List: list_nat,X21: nat,X22: list_nat] :
% 2.39/2.74 ( ( List
% 2.39/2.74 = ( cons_nat @ X21 @ X22 ) )
% 2.39/2.74 => ( List != nil_nat ) ) ).
% 2.39/2.74
% 2.39/2.74 % list.discI
% 2.39/2.74 thf(fact_1728_list_Oexhaust,axiom,
% 2.39/2.74 ! [Y: list_P8527749157015355191n_assn] :
% 2.39/2.74 ( ( Y != nil_Pr5671120429643327159n_assn )
% 2.39/2.74 => ~ ! [X212: produc6575502325842934193n_assn,X222: list_P8527749157015355191n_assn] :
% 2.39/2.74 ( Y
% 2.39/2.74 != ( cons_P2971678138204555879n_assn @ X212 @ X222 ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % list.exhaust
% 2.39/2.74 thf(fact_1729_list_Oexhaust,axiom,
% 2.39/2.74 ! [Y: list_int] :
% 2.39/2.74 ( ( Y != nil_int )
% 2.39/2.74 => ~ ! [X212: int,X222: list_int] :
% 2.39/2.74 ( Y
% 2.39/2.74 != ( cons_int @ X212 @ X222 ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % list.exhaust
% 2.39/2.74 thf(fact_1730_list_Oexhaust,axiom,
% 2.39/2.74 ! [Y: list_nat] :
% 2.39/2.74 ( ( Y != nil_nat )
% 2.39/2.74 => ~ ! [X212: nat,X222: list_nat] :
% 2.39/2.74 ( Y
% 2.39/2.74 != ( cons_nat @ X212 @ X222 ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % list.exhaust
% 2.39/2.74 thf(fact_1731_min__list_Ocases,axiom,
% 2.39/2.74 ! [X: list_int] :
% 2.39/2.74 ( ! [X3: int,Xs2: list_int] :
% 2.39/2.74 ( X
% 2.39/2.74 != ( cons_int @ X3 @ Xs2 ) )
% 2.39/2.74 => ( X = nil_int ) ) ).
% 2.39/2.74
% 2.39/2.74 % min_list.cases
% 2.39/2.74 thf(fact_1732_min__list_Ocases,axiom,
% 2.39/2.74 ! [X: list_nat] :
% 2.39/2.74 ( ! [X3: nat,Xs2: list_nat] :
% 2.39/2.74 ( X
% 2.39/2.74 != ( cons_nat @ X3 @ Xs2 ) )
% 2.39/2.74 => ( X = nil_nat ) ) ).
% 2.39/2.74
% 2.39/2.74 % min_list.cases
% 2.39/2.74 thf(fact_1733_remdups__adj_Ocases,axiom,
% 2.39/2.74 ! [X: list_P8527749157015355191n_assn] :
% 2.39/2.74 ( ( X != nil_Pr5671120429643327159n_assn )
% 2.39/2.74 => ( ! [X3: produc6575502325842934193n_assn] :
% 2.39/2.74 ( X
% 2.39/2.74 != ( cons_P2971678138204555879n_assn @ X3 @ nil_Pr5671120429643327159n_assn ) )
% 2.39/2.74 => ~ ! [X3: produc6575502325842934193n_assn,Y3: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn] :
% 2.39/2.74 ( X
% 2.39/2.74 != ( cons_P2971678138204555879n_assn @ X3 @ ( cons_P2971678138204555879n_assn @ Y3 @ Xs2 ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % remdups_adj.cases
% 2.39/2.74 thf(fact_1734_remdups__adj_Ocases,axiom,
% 2.39/2.74 ! [X: list_int] :
% 2.39/2.74 ( ( X != nil_int )
% 2.39/2.74 => ( ! [X3: int] :
% 2.39/2.74 ( X
% 2.39/2.74 != ( cons_int @ X3 @ nil_int ) )
% 2.39/2.74 => ~ ! [X3: int,Y3: int,Xs2: list_int] :
% 2.39/2.74 ( X
% 2.39/2.74 != ( cons_int @ X3 @ ( cons_int @ Y3 @ Xs2 ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % remdups_adj.cases
% 2.39/2.74 thf(fact_1735_remdups__adj_Ocases,axiom,
% 2.39/2.74 ! [X: list_nat] :
% 2.39/2.74 ( ( X != nil_nat )
% 2.39/2.74 => ( ! [X3: nat] :
% 2.39/2.74 ( X
% 2.39/2.74 != ( cons_nat @ X3 @ nil_nat ) )
% 2.39/2.74 => ~ ! [X3: nat,Y3: nat,Xs2: list_nat] :
% 2.39/2.74 ( X
% 2.39/2.74 != ( cons_nat @ X3 @ ( cons_nat @ Y3 @ Xs2 ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % remdups_adj.cases
% 2.39/2.74 thf(fact_1736_neq__Nil__conv,axiom,
% 2.39/2.74 ! [Xs: list_P8527749157015355191n_assn] :
% 2.39/2.74 ( ( Xs != nil_Pr5671120429643327159n_assn )
% 2.39/2.74 = ( ? [Y2: produc6575502325842934193n_assn,Ys4: list_P8527749157015355191n_assn] :
% 2.39/2.74 ( Xs
% 2.39/2.74 = ( cons_P2971678138204555879n_assn @ Y2 @ Ys4 ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % neq_Nil_conv
% 2.39/2.74 thf(fact_1737_neq__Nil__conv,axiom,
% 2.39/2.74 ! [Xs: list_int] :
% 2.39/2.74 ( ( Xs != nil_int )
% 2.39/2.74 = ( ? [Y2: int,Ys4: list_int] :
% 2.39/2.74 ( Xs
% 2.39/2.74 = ( cons_int @ Y2 @ Ys4 ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % neq_Nil_conv
% 2.39/2.74 thf(fact_1738_neq__Nil__conv,axiom,
% 2.39/2.74 ! [Xs: list_nat] :
% 2.39/2.74 ( ( Xs != nil_nat )
% 2.39/2.74 = ( ? [Y2: nat,Ys4: list_nat] :
% 2.39/2.74 ( Xs
% 2.39/2.74 = ( cons_nat @ Y2 @ Ys4 ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % neq_Nil_conv
% 2.39/2.74 thf(fact_1739_list__induct2_H,axiom,
% 2.39/2.74 ! [P2: list_P8527749157015355191n_assn > list_P8527749157015355191n_assn > $o,Xs: list_P8527749157015355191n_assn,Ys: list_P8527749157015355191n_assn] :
% 2.39/2.74 ( ( P2 @ nil_Pr5671120429643327159n_assn @ nil_Pr5671120429643327159n_assn )
% 2.39/2.74 => ( ! [X3: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn] : ( P2 @ ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) @ nil_Pr5671120429643327159n_assn )
% 2.39/2.74 => ( ! [Y3: produc6575502325842934193n_assn,Ys3: list_P8527749157015355191n_assn] : ( P2 @ nil_Pr5671120429643327159n_assn @ ( cons_P2971678138204555879n_assn @ Y3 @ Ys3 ) )
% 2.39/2.74 => ( ! [X3: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn,Y3: produc6575502325842934193n_assn,Ys3: list_P8527749157015355191n_assn] :
% 2.39/2.74 ( ( P2 @ Xs2 @ Ys3 )
% 2.39/2.74 => ( P2 @ ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) @ ( cons_P2971678138204555879n_assn @ Y3 @ Ys3 ) ) )
% 2.39/2.74 => ( P2 @ Xs @ Ys ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % list_induct2'
% 2.39/2.74 thf(fact_1740_list__induct2_H,axiom,
% 2.39/2.74 ! [P2: list_P8527749157015355191n_assn > list_int > $o,Xs: list_P8527749157015355191n_assn,Ys: list_int] :
% 2.39/2.74 ( ( P2 @ nil_Pr5671120429643327159n_assn @ nil_int )
% 2.39/2.74 => ( ! [X3: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn] : ( P2 @ ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) @ nil_int )
% 2.39/2.74 => ( ! [Y3: int,Ys3: list_int] : ( P2 @ nil_Pr5671120429643327159n_assn @ ( cons_int @ Y3 @ Ys3 ) )
% 2.39/2.74 => ( ! [X3: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn,Y3: int,Ys3: list_int] :
% 2.39/2.74 ( ( P2 @ Xs2 @ Ys3 )
% 2.39/2.74 => ( P2 @ ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) @ ( cons_int @ Y3 @ Ys3 ) ) )
% 2.39/2.74 => ( P2 @ Xs @ Ys ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % list_induct2'
% 2.39/2.74 thf(fact_1741_list__induct2_H,axiom,
% 2.39/2.74 ! [P2: list_P8527749157015355191n_assn > list_nat > $o,Xs: list_P8527749157015355191n_assn,Ys: list_nat] :
% 2.39/2.74 ( ( P2 @ nil_Pr5671120429643327159n_assn @ nil_nat )
% 2.39/2.74 => ( ! [X3: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn] : ( P2 @ ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) @ nil_nat )
% 2.39/2.74 => ( ! [Y3: nat,Ys3: list_nat] : ( P2 @ nil_Pr5671120429643327159n_assn @ ( cons_nat @ Y3 @ Ys3 ) )
% 2.39/2.74 => ( ! [X3: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn,Y3: nat,Ys3: list_nat] :
% 2.39/2.74 ( ( P2 @ Xs2 @ Ys3 )
% 2.39/2.74 => ( P2 @ ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) ) )
% 2.39/2.74 => ( P2 @ Xs @ Ys ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % list_induct2'
% 2.39/2.74 thf(fact_1742_list__induct2_H,axiom,
% 2.39/2.74 ! [P2: list_int > list_P8527749157015355191n_assn > $o,Xs: list_int,Ys: list_P8527749157015355191n_assn] :
% 2.39/2.74 ( ( P2 @ nil_int @ nil_Pr5671120429643327159n_assn )
% 2.39/2.74 => ( ! [X3: int,Xs2: list_int] : ( P2 @ ( cons_int @ X3 @ Xs2 ) @ nil_Pr5671120429643327159n_assn )
% 2.39/2.74 => ( ! [Y3: produc6575502325842934193n_assn,Ys3: list_P8527749157015355191n_assn] : ( P2 @ nil_int @ ( cons_P2971678138204555879n_assn @ Y3 @ Ys3 ) )
% 2.39/2.74 => ( ! [X3: int,Xs2: list_int,Y3: produc6575502325842934193n_assn,Ys3: list_P8527749157015355191n_assn] :
% 2.39/2.74 ( ( P2 @ Xs2 @ Ys3 )
% 2.39/2.74 => ( P2 @ ( cons_int @ X3 @ Xs2 ) @ ( cons_P2971678138204555879n_assn @ Y3 @ Ys3 ) ) )
% 2.39/2.74 => ( P2 @ Xs @ Ys ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % list_induct2'
% 2.39/2.74 thf(fact_1743_list__induct2_H,axiom,
% 2.39/2.74 ! [P2: list_int > list_int > $o,Xs: list_int,Ys: list_int] :
% 2.39/2.74 ( ( P2 @ nil_int @ nil_int )
% 2.39/2.74 => ( ! [X3: int,Xs2: list_int] : ( P2 @ ( cons_int @ X3 @ Xs2 ) @ nil_int )
% 2.39/2.74 => ( ! [Y3: int,Ys3: list_int] : ( P2 @ nil_int @ ( cons_int @ Y3 @ Ys3 ) )
% 2.39/2.74 => ( ! [X3: int,Xs2: list_int,Y3: int,Ys3: list_int] :
% 2.39/2.74 ( ( P2 @ Xs2 @ Ys3 )
% 2.39/2.74 => ( P2 @ ( cons_int @ X3 @ Xs2 ) @ ( cons_int @ Y3 @ Ys3 ) ) )
% 2.39/2.74 => ( P2 @ Xs @ Ys ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % list_induct2'
% 2.39/2.74 thf(fact_1744_list__induct2_H,axiom,
% 2.39/2.74 ! [P2: list_int > list_nat > $o,Xs: list_int,Ys: list_nat] :
% 2.39/2.74 ( ( P2 @ nil_int @ nil_nat )
% 2.39/2.74 => ( ! [X3: int,Xs2: list_int] : ( P2 @ ( cons_int @ X3 @ Xs2 ) @ nil_nat )
% 2.39/2.74 => ( ! [Y3: nat,Ys3: list_nat] : ( P2 @ nil_int @ ( cons_nat @ Y3 @ Ys3 ) )
% 2.39/2.74 => ( ! [X3: int,Xs2: list_int,Y3: nat,Ys3: list_nat] :
% 2.39/2.74 ( ( P2 @ Xs2 @ Ys3 )
% 2.39/2.74 => ( P2 @ ( cons_int @ X3 @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) ) )
% 2.39/2.74 => ( P2 @ Xs @ Ys ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % list_induct2'
% 2.39/2.74 thf(fact_1745_list__induct2_H,axiom,
% 2.39/2.74 ! [P2: list_nat > list_P8527749157015355191n_assn > $o,Xs: list_nat,Ys: list_P8527749157015355191n_assn] :
% 2.39/2.74 ( ( P2 @ nil_nat @ nil_Pr5671120429643327159n_assn )
% 2.39/2.74 => ( ! [X3: nat,Xs2: list_nat] : ( P2 @ ( cons_nat @ X3 @ Xs2 ) @ nil_Pr5671120429643327159n_assn )
% 2.39/2.74 => ( ! [Y3: produc6575502325842934193n_assn,Ys3: list_P8527749157015355191n_assn] : ( P2 @ nil_nat @ ( cons_P2971678138204555879n_assn @ Y3 @ Ys3 ) )
% 2.39/2.74 => ( ! [X3: nat,Xs2: list_nat,Y3: produc6575502325842934193n_assn,Ys3: list_P8527749157015355191n_assn] :
% 2.39/2.74 ( ( P2 @ Xs2 @ Ys3 )
% 2.39/2.74 => ( P2 @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_P2971678138204555879n_assn @ Y3 @ Ys3 ) ) )
% 2.39/2.74 => ( P2 @ Xs @ Ys ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % list_induct2'
% 2.39/2.74 thf(fact_1746_list__induct2_H,axiom,
% 2.39/2.74 ! [P2: list_nat > list_int > $o,Xs: list_nat,Ys: list_int] :
% 2.39/2.74 ( ( P2 @ nil_nat @ nil_int )
% 2.39/2.74 => ( ! [X3: nat,Xs2: list_nat] : ( P2 @ ( cons_nat @ X3 @ Xs2 ) @ nil_int )
% 2.39/2.74 => ( ! [Y3: int,Ys3: list_int] : ( P2 @ nil_nat @ ( cons_int @ Y3 @ Ys3 ) )
% 2.39/2.74 => ( ! [X3: nat,Xs2: list_nat,Y3: int,Ys3: list_int] :
% 2.39/2.74 ( ( P2 @ Xs2 @ Ys3 )
% 2.39/2.74 => ( P2 @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_int @ Y3 @ Ys3 ) ) )
% 2.39/2.74 => ( P2 @ Xs @ Ys ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % list_induct2'
% 2.39/2.74 thf(fact_1747_list__induct2_H,axiom,
% 2.39/2.74 ! [P2: list_nat > list_nat > $o,Xs: list_nat,Ys: list_nat] :
% 2.39/2.74 ( ( P2 @ nil_nat @ nil_nat )
% 2.39/2.74 => ( ! [X3: nat,Xs2: list_nat] : ( P2 @ ( cons_nat @ X3 @ Xs2 ) @ nil_nat )
% 2.39/2.74 => ( ! [Y3: nat,Ys3: list_nat] : ( P2 @ nil_nat @ ( cons_nat @ Y3 @ Ys3 ) )
% 2.39/2.74 => ( ! [X3: nat,Xs2: list_nat,Y3: nat,Ys3: list_nat] :
% 2.39/2.74 ( ( P2 @ Xs2 @ Ys3 )
% 2.39/2.74 => ( P2 @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) ) )
% 2.39/2.74 => ( P2 @ Xs @ Ys ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % list_induct2'
% 2.39/2.74 thf(fact_1748_list__nonempty__induct,axiom,
% 2.39/2.74 ! [Xs: list_P8527749157015355191n_assn,P2: list_P8527749157015355191n_assn > $o] :
% 2.39/2.74 ( ( Xs != nil_Pr5671120429643327159n_assn )
% 2.39/2.74 => ( ! [X3: produc6575502325842934193n_assn] : ( P2 @ ( cons_P2971678138204555879n_assn @ X3 @ nil_Pr5671120429643327159n_assn ) )
% 2.39/2.74 => ( ! [X3: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn] :
% 2.39/2.74 ( ( Xs2 != nil_Pr5671120429643327159n_assn )
% 2.39/2.74 => ( ( P2 @ Xs2 )
% 2.39/2.74 => ( P2 @ ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) ) ) )
% 2.39/2.74 => ( P2 @ Xs ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % list_nonempty_induct
% 2.39/2.74 thf(fact_1749_list__nonempty__induct,axiom,
% 2.39/2.74 ! [Xs: list_int,P2: list_int > $o] :
% 2.39/2.74 ( ( Xs != nil_int )
% 2.39/2.74 => ( ! [X3: int] : ( P2 @ ( cons_int @ X3 @ nil_int ) )
% 2.39/2.74 => ( ! [X3: int,Xs2: list_int] :
% 2.39/2.74 ( ( Xs2 != nil_int )
% 2.39/2.74 => ( ( P2 @ Xs2 )
% 2.39/2.74 => ( P2 @ ( cons_int @ X3 @ Xs2 ) ) ) )
% 2.39/2.74 => ( P2 @ Xs ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % list_nonempty_induct
% 2.39/2.74 thf(fact_1750_list__nonempty__induct,axiom,
% 2.39/2.74 ! [Xs: list_nat,P2: list_nat > $o] :
% 2.39/2.74 ( ( Xs != nil_nat )
% 2.39/2.74 => ( ! [X3: nat] : ( P2 @ ( cons_nat @ X3 @ nil_nat ) )
% 2.39/2.74 => ( ! [X3: nat,Xs2: list_nat] :
% 2.39/2.74 ( ( Xs2 != nil_nat )
% 2.39/2.74 => ( ( P2 @ Xs2 )
% 2.39/2.74 => ( P2 @ ( cons_nat @ X3 @ Xs2 ) ) ) )
% 2.39/2.74 => ( P2 @ Xs ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % list_nonempty_induct
% 2.39/2.74 thf(fact_1751_merge_Ocases,axiom,
% 2.39/2.74 ! [X: produc1186641810826059865st_int] :
% 2.39/2.74 ( ! [L2: list_int] :
% 2.39/2.74 ( X
% 2.39/2.74 != ( produc364263696895485585st_int @ nil_int @ L2 ) )
% 2.39/2.74 => ( ! [V: int,Va: list_int] :
% 2.39/2.74 ( X
% 2.39/2.74 != ( produc364263696895485585st_int @ ( cons_int @ V @ Va ) @ nil_int ) )
% 2.39/2.74 => ~ ! [X1: int,L1: list_int,X23: int,L2: list_int] :
% 2.39/2.74 ( X
% 2.39/2.74 != ( produc364263696895485585st_int @ ( cons_int @ X1 @ L1 ) @ ( cons_int @ X23 @ L2 ) ) ) ) ) ).
% 2.39/2.74
% 2.39/2.74 % merge.cases
% 2.39/2.74 thf(fact_1752_merge_Ocases,axiom,
% 2.39/2.75 ! [X: produc1828647624359046049st_nat] :
% 2.39/2.75 ( ! [L2: list_nat] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc2694037385005941721st_nat @ nil_nat @ L2 ) )
% 2.39/2.75 => ( ! [V: nat,Va: list_nat] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc2694037385005941721st_nat @ ( cons_nat @ V @ Va ) @ nil_nat ) )
% 2.39/2.75 => ~ ! [X1: nat,L1: list_nat,X23: nat,L2: list_nat] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc2694037385005941721st_nat @ ( cons_nat @ X1 @ L1 ) @ ( cons_nat @ X23 @ L2 ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % merge.cases
% 2.39/2.75 thf(fact_1753_shuffles_Ocases,axiom,
% 2.39/2.75 ! [X: produc337509097454979815n_assn] :
% 2.39/2.75 ( ! [Ys3: list_P8527749157015355191n_assn] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc3014731801419794263n_assn @ nil_Pr5671120429643327159n_assn @ Ys3 ) )
% 2.39/2.75 => ( ! [Xs2: list_P8527749157015355191n_assn] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc3014731801419794263n_assn @ Xs2 @ nil_Pr5671120429643327159n_assn ) )
% 2.39/2.75 => ~ ! [X3: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn,Y3: produc6575502325842934193n_assn,Ys3: list_P8527749157015355191n_assn] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc3014731801419794263n_assn @ ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) @ ( cons_P2971678138204555879n_assn @ Y3 @ Ys3 ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % shuffles.cases
% 2.39/2.75 thf(fact_1754_shuffles_Ocases,axiom,
% 2.39/2.75 ! [X: produc1186641810826059865st_int] :
% 2.39/2.75 ( ! [Ys3: list_int] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc364263696895485585st_int @ nil_int @ Ys3 ) )
% 2.39/2.75 => ( ! [Xs2: list_int] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc364263696895485585st_int @ Xs2 @ nil_int ) )
% 2.39/2.75 => ~ ! [X3: int,Xs2: list_int,Y3: int,Ys3: list_int] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc364263696895485585st_int @ ( cons_int @ X3 @ Xs2 ) @ ( cons_int @ Y3 @ Ys3 ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % shuffles.cases
% 2.39/2.75 thf(fact_1755_shuffles_Ocases,axiom,
% 2.39/2.75 ! [X: produc1828647624359046049st_nat] :
% 2.39/2.75 ( ! [Ys3: list_nat] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc2694037385005941721st_nat @ nil_nat @ Ys3 ) )
% 2.39/2.75 => ( ! [Xs2: list_nat] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc2694037385005941721st_nat @ Xs2 @ nil_nat ) )
% 2.39/2.75 => ~ ! [X3: nat,Xs2: list_nat,Y3: nat,Ys3: list_nat] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc2694037385005941721st_nat @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % shuffles.cases
% 2.39/2.75 thf(fact_1756_successively_Ocases,axiom,
% 2.39/2.75 ! [X: produc4530688714081574576n_assn] :
% 2.39/2.75 ( ! [P4: produc6575502325842934193n_assn > produc6575502325842934193n_assn > $o] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc6115016301897879072n_assn @ P4 @ nil_Pr5671120429643327159n_assn ) )
% 2.39/2.75 => ( ! [P4: produc6575502325842934193n_assn > produc6575502325842934193n_assn > $o,X3: produc6575502325842934193n_assn] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc6115016301897879072n_assn @ P4 @ ( cons_P2971678138204555879n_assn @ X3 @ nil_Pr5671120429643327159n_assn ) ) )
% 2.39/2.75 => ~ ! [P4: produc6575502325842934193n_assn > produc6575502325842934193n_assn > $o,X3: produc6575502325842934193n_assn,Y3: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc6115016301897879072n_assn @ P4 @ ( cons_P2971678138204555879n_assn @ X3 @ ( cons_P2971678138204555879n_assn @ Y3 @ Xs2 ) ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % successively.cases
% 2.39/2.75 thf(fact_1757_successively_Ocases,axiom,
% 2.39/2.75 ! [X: produc5834231552977413017st_int] :
% 2.39/2.75 ( ! [P4: int > int > $o] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc8618682346314911123st_int @ P4 @ nil_int ) )
% 2.39/2.75 => ( ! [P4: int > int > $o,X3: int] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc8618682346314911123st_int @ P4 @ ( cons_int @ X3 @ nil_int ) ) )
% 2.39/2.75 => ~ ! [P4: int > int > $o,X3: int,Y3: int,Xs2: list_int] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc8618682346314911123st_int @ P4 @ ( cons_int @ X3 @ ( cons_int @ Y3 @ Xs2 ) ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % successively.cases
% 2.39/2.75 thf(fact_1758_successively_Ocases,axiom,
% 2.39/2.75 ! [X: produc254973753779126261st_nat] :
% 2.39/2.75 ( ! [P4: nat > nat > $o] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc4727192421694094319st_nat @ P4 @ nil_nat ) )
% 2.39/2.75 => ( ! [P4: nat > nat > $o,X3: nat] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc4727192421694094319st_nat @ P4 @ ( cons_nat @ X3 @ nil_nat ) ) )
% 2.39/2.75 => ~ ! [P4: nat > nat > $o,X3: nat,Y3: nat,Xs2: list_nat] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc4727192421694094319st_nat @ P4 @ ( cons_nat @ X3 @ ( cons_nat @ Y3 @ Xs2 ) ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % successively.cases
% 2.39/2.75 thf(fact_1759_sorted__wrt_Ocases,axiom,
% 2.39/2.75 ! [X: produc4530688714081574576n_assn] :
% 2.39/2.75 ( ! [P4: produc6575502325842934193n_assn > produc6575502325842934193n_assn > $o] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc6115016301897879072n_assn @ P4 @ nil_Pr5671120429643327159n_assn ) )
% 2.39/2.75 => ~ ! [P4: produc6575502325842934193n_assn > produc6575502325842934193n_assn > $o,X3: produc6575502325842934193n_assn,Ys3: list_P8527749157015355191n_assn] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc6115016301897879072n_assn @ P4 @ ( cons_P2971678138204555879n_assn @ X3 @ Ys3 ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % sorted_wrt.cases
% 2.39/2.75 thf(fact_1760_sorted__wrt_Ocases,axiom,
% 2.39/2.75 ! [X: produc5834231552977413017st_int] :
% 2.39/2.75 ( ! [P4: int > int > $o] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc8618682346314911123st_int @ P4 @ nil_int ) )
% 2.39/2.75 => ~ ! [P4: int > int > $o,X3: int,Ys3: list_int] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc8618682346314911123st_int @ P4 @ ( cons_int @ X3 @ Ys3 ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % sorted_wrt.cases
% 2.39/2.75 thf(fact_1761_sorted__wrt_Ocases,axiom,
% 2.39/2.75 ! [X: produc254973753779126261st_nat] :
% 2.39/2.75 ( ! [P4: nat > nat > $o] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc4727192421694094319st_nat @ P4 @ nil_nat ) )
% 2.39/2.75 => ~ ! [P4: nat > nat > $o,X3: nat,Ys3: list_nat] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc4727192421694094319st_nat @ P4 @ ( cons_nat @ X3 @ Ys3 ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % sorted_wrt.cases
% 2.39/2.75 thf(fact_1762_mergesort__by__rel__split_Ocases,axiom,
% 2.39/2.75 ! [X: produc858023921370090807n_assn] :
% 2.39/2.75 ( ! [Xs1: list_P8527749157015355191n_assn,Xs22: list_P8527749157015355191n_assn] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc7497315745449715623n_assn @ ( produc3014731801419794263n_assn @ Xs1 @ Xs22 ) @ nil_Pr5671120429643327159n_assn ) )
% 2.39/2.75 => ( ! [Xs1: list_P8527749157015355191n_assn,Xs22: list_P8527749157015355191n_assn,X3: produc6575502325842934193n_assn] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc7497315745449715623n_assn @ ( produc3014731801419794263n_assn @ Xs1 @ Xs22 ) @ ( cons_P2971678138204555879n_assn @ X3 @ nil_Pr5671120429643327159n_assn ) ) )
% 2.39/2.75 => ~ ! [Xs1: list_P8527749157015355191n_assn,Xs22: list_P8527749157015355191n_assn,X1: produc6575502325842934193n_assn,X23: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc7497315745449715623n_assn @ ( produc3014731801419794263n_assn @ Xs1 @ Xs22 ) @ ( cons_P2971678138204555879n_assn @ X1 @ ( cons_P2971678138204555879n_assn @ X23 @ Xs2 ) ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mergesort_by_rel_split.cases
% 2.39/2.75 thf(fact_1763_mergesort__by__rel__split_Ocases,axiom,
% 2.39/2.75 ! [X: produc5625914783551145028st_int] :
% 2.39/2.75 ( ! [Xs1: list_int,Xs22: list_int] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc6571967182415643454st_int @ ( produc364263696895485585st_int @ Xs1 @ Xs22 ) @ nil_int ) )
% 2.39/2.75 => ( ! [Xs1: list_int,Xs22: list_int,X3: int] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc6571967182415643454st_int @ ( produc364263696895485585st_int @ Xs1 @ Xs22 ) @ ( cons_int @ X3 @ nil_int ) ) )
% 2.39/2.75 => ~ ! [Xs1: list_int,Xs22: list_int,X1: int,X23: int,Xs2: list_int] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc6571967182415643454st_int @ ( produc364263696895485585st_int @ Xs1 @ Xs22 ) @ ( cons_int @ X1 @ ( cons_int @ X23 @ Xs2 ) ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mergesort_by_rel_split.cases
% 2.39/2.75 thf(fact_1764_mergesort__by__rel__split_Ocases,axiom,
% 2.39/2.75 ! [X: produc8368264342088597808st_nat] :
% 2.39/2.75 ( ! [Xs1: list_nat,Xs22: list_nat] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc1778712578675790378st_nat @ ( produc2694037385005941721st_nat @ Xs1 @ Xs22 ) @ nil_nat ) )
% 2.39/2.75 => ( ! [Xs1: list_nat,Xs22: list_nat,X3: nat] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc1778712578675790378st_nat @ ( produc2694037385005941721st_nat @ Xs1 @ Xs22 ) @ ( cons_nat @ X3 @ nil_nat ) ) )
% 2.39/2.75 => ~ ! [Xs1: list_nat,Xs22: list_nat,X1: nat,X23: nat,Xs2: list_nat] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc1778712578675790378st_nat @ ( produc2694037385005941721st_nat @ Xs1 @ Xs22 ) @ ( cons_nat @ X1 @ ( cons_nat @ X23 @ Xs2 ) ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mergesort_by_rel_split.cases
% 2.39/2.75 thf(fact_1765_mergesort__by__rel__merge_Ocases,axiom,
% 2.39/2.75 ! [X: produc6691681559177096800n_assn] :
% 2.39/2.75 ( ! [R3: produc6575502325842934193n_assn > produc6575502325842934193n_assn > $o,X3: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn,Y3: produc6575502325842934193n_assn,Ys3: list_P8527749157015355191n_assn] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc218933061472242640n_assn @ R3 @ ( produc3014731801419794263n_assn @ ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) @ ( cons_P2971678138204555879n_assn @ Y3 @ Ys3 ) ) ) )
% 2.39/2.75 => ( ! [R3: produc6575502325842934193n_assn > produc6575502325842934193n_assn > $o,Xs2: list_P8527749157015355191n_assn] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc218933061472242640n_assn @ R3 @ ( produc3014731801419794263n_assn @ Xs2 @ nil_Pr5671120429643327159n_assn ) ) )
% 2.39/2.75 => ~ ! [R3: produc6575502325842934193n_assn > produc6575502325842934193n_assn > $o,V: produc6575502325842934193n_assn,Va: list_P8527749157015355191n_assn] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc218933061472242640n_assn @ R3 @ ( produc3014731801419794263n_assn @ nil_Pr5671120429643327159n_assn @ ( cons_P2971678138204555879n_assn @ V @ Va ) ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mergesort_by_rel_merge.cases
% 2.39/2.75 thf(fact_1766_mergesort__by__rel__merge_Ocases,axiom,
% 2.39/2.75 ! [X: produc6134427711877206866st_int] :
% 2.39/2.75 ( ! [R3: int > int > $o,X3: int,Xs2: list_int,Y3: int,Ys3: list_int] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc6519019827157805250st_int @ R3 @ ( produc364263696895485585st_int @ ( cons_int @ X3 @ Xs2 ) @ ( cons_int @ Y3 @ Ys3 ) ) ) )
% 2.39/2.75 => ( ! [R3: int > int > $o,Xs2: list_int] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc6519019827157805250st_int @ R3 @ ( produc364263696895485585st_int @ Xs2 @ nil_int ) ) )
% 2.39/2.75 => ~ ! [R3: int > int > $o,V: int,Va: list_int] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc6519019827157805250st_int @ R3 @ ( produc364263696895485585st_int @ nil_int @ ( cons_int @ V @ Va ) ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mergesort_by_rel_merge.cases
% 2.39/2.75 thf(fact_1767_mergesort__by__rel__merge_Ocases,axiom,
% 2.39/2.75 ! [X: produc4787317212837456354st_nat] :
% 2.39/2.75 ( ! [R3: nat > nat > $o,X3: nat,Xs2: list_nat,Y3: nat,Ys3: list_nat] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc3127733452865184594st_nat @ R3 @ ( produc2694037385005941721st_nat @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) ) ) )
% 2.39/2.75 => ( ! [R3: nat > nat > $o,Xs2: list_nat] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc3127733452865184594st_nat @ R3 @ ( produc2694037385005941721st_nat @ Xs2 @ nil_nat ) ) )
% 2.39/2.75 => ~ ! [R3: nat > nat > $o,V: nat,Va: list_nat] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc3127733452865184594st_nat @ R3 @ ( produc2694037385005941721st_nat @ nil_nat @ ( cons_nat @ V @ Va ) ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mergesort_by_rel_merge.cases
% 2.39/2.75 thf(fact_1768_quicksort__by__rel_Ocases,axiom,
% 2.39/2.75 ! [X: produc6691681559177096800n_assn] :
% 2.39/2.75 ( ! [R3: produc6575502325842934193n_assn > produc6575502325842934193n_assn > $o,Sl: list_P8527749157015355191n_assn] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc218933061472242640n_assn @ R3 @ ( produc3014731801419794263n_assn @ Sl @ nil_Pr5671120429643327159n_assn ) ) )
% 2.39/2.75 => ~ ! [R3: produc6575502325842934193n_assn > produc6575502325842934193n_assn > $o,Sl: list_P8527749157015355191n_assn,X3: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc218933061472242640n_assn @ R3 @ ( produc3014731801419794263n_assn @ Sl @ ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % quicksort_by_rel.cases
% 2.39/2.75 thf(fact_1769_quicksort__by__rel_Ocases,axiom,
% 2.39/2.75 ! [X: produc6134427711877206866st_int] :
% 2.39/2.75 ( ! [R3: int > int > $o,Sl: list_int] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc6519019827157805250st_int @ R3 @ ( produc364263696895485585st_int @ Sl @ nil_int ) ) )
% 2.39/2.75 => ~ ! [R3: int > int > $o,Sl: list_int,X3: int,Xs2: list_int] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc6519019827157805250st_int @ R3 @ ( produc364263696895485585st_int @ Sl @ ( cons_int @ X3 @ Xs2 ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % quicksort_by_rel.cases
% 2.39/2.75 thf(fact_1770_quicksort__by__rel_Ocases,axiom,
% 2.39/2.75 ! [X: produc4787317212837456354st_nat] :
% 2.39/2.75 ( ! [R3: nat > nat > $o,Sl: list_nat] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc3127733452865184594st_nat @ R3 @ ( produc2694037385005941721st_nat @ Sl @ nil_nat ) ) )
% 2.39/2.75 => ~ ! [R3: nat > nat > $o,Sl: list_nat,X3: nat,Xs2: list_nat] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc3127733452865184594st_nat @ R3 @ ( produc2694037385005941721st_nat @ Sl @ ( cons_nat @ X3 @ Xs2 ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % quicksort_by_rel.cases
% 2.39/2.75 thf(fact_1771_partition__rev_Ocases,axiom,
% 2.39/2.75 ! [X: produc3251403909973641504n_assn] :
% 2.39/2.75 ( ! [P4: produc6575502325842934193n_assn > $o,Yes: list_P8527749157015355191n_assn,No: list_P8527749157015355191n_assn] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc7995034776595945426n_assn @ P4 @ ( produc7497315745449715623n_assn @ ( produc3014731801419794263n_assn @ Yes @ No ) @ nil_Pr5671120429643327159n_assn ) ) )
% 2.39/2.75 => ~ ! [P4: produc6575502325842934193n_assn > $o,Yes: list_P8527749157015355191n_assn,No: list_P8527749157015355191n_assn,X3: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc7995034776595945426n_assn @ P4 @ ( produc7497315745449715623n_assn @ ( produc3014731801419794263n_assn @ Yes @ No ) @ ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % partition_rev.cases
% 2.39/2.75 thf(fact_1772_partition__rev_Ocases,axiom,
% 2.39/2.75 ! [X: produc141556263843406102st_int] :
% 2.39/2.75 ( ! [P4: int > $o,Yes: list_int,No: list_int] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc3116401902672145424st_int @ P4 @ ( produc6571967182415643454st_int @ ( produc364263696895485585st_int @ Yes @ No ) @ nil_int ) ) )
% 2.39/2.75 => ~ ! [P4: int > $o,Yes: list_int,No: list_int,X3: int,Xs2: list_int] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc3116401902672145424st_int @ P4 @ ( produc6571967182415643454st_int @ ( produc364263696895485585st_int @ Yes @ No ) @ ( cons_int @ X3 @ Xs2 ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % partition_rev.cases
% 2.39/2.75 thf(fact_1773_partition__rev_Ocases,axiom,
% 2.39/2.75 ! [X: produc6155704871766690142st_nat] :
% 2.39/2.75 ( ! [P4: nat > $o,Yes: list_nat,No: list_nat] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc2404789219858123352st_nat @ P4 @ ( produc1778712578675790378st_nat @ ( produc2694037385005941721st_nat @ Yes @ No ) @ nil_nat ) ) )
% 2.39/2.75 => ~ ! [P4: nat > $o,Yes: list_nat,No: list_nat,X3: nat,Xs2: list_nat] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc2404789219858123352st_nat @ P4 @ ( produc1778712578675790378st_nat @ ( produc2694037385005941721st_nat @ Yes @ No ) @ ( cons_nat @ X3 @ Xs2 ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % partition_rev.cases
% 2.39/2.75 thf(fact_1774_list__all__zip_Ocases,axiom,
% 2.39/2.75 ! [X: produc6691681559177096800n_assn] :
% 2.39/2.75 ( ! [P4: produc6575502325842934193n_assn > produc6575502325842934193n_assn > $o] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc218933061472242640n_assn @ P4 @ ( produc3014731801419794263n_assn @ nil_Pr5671120429643327159n_assn @ nil_Pr5671120429643327159n_assn ) ) )
% 2.39/2.75 => ( ! [P4: produc6575502325842934193n_assn > produc6575502325842934193n_assn > $o,A6: produc6575502325842934193n_assn,As: list_P8527749157015355191n_assn,B5: produc6575502325842934193n_assn,Bs2: list_P8527749157015355191n_assn] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc218933061472242640n_assn @ P4 @ ( produc3014731801419794263n_assn @ ( cons_P2971678138204555879n_assn @ A6 @ As ) @ ( cons_P2971678138204555879n_assn @ B5 @ Bs2 ) ) ) )
% 2.39/2.75 => ( ! [P4: produc6575502325842934193n_assn > produc6575502325842934193n_assn > $o,V: produc6575502325842934193n_assn,Va: list_P8527749157015355191n_assn] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc218933061472242640n_assn @ P4 @ ( produc3014731801419794263n_assn @ ( cons_P2971678138204555879n_assn @ V @ Va ) @ nil_Pr5671120429643327159n_assn ) ) )
% 2.39/2.75 => ~ ! [P4: produc6575502325842934193n_assn > produc6575502325842934193n_assn > $o,V: produc6575502325842934193n_assn,Va: list_P8527749157015355191n_assn] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc218933061472242640n_assn @ P4 @ ( produc3014731801419794263n_assn @ nil_Pr5671120429643327159n_assn @ ( cons_P2971678138204555879n_assn @ V @ Va ) ) ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % list_all_zip.cases
% 2.39/2.75 thf(fact_1775_list__all__zip_Ocases,axiom,
% 2.39/2.75 ! [X: produc4920635200459206554st_int] :
% 2.39/2.75 ( ! [P4: produc6575502325842934193n_assn > int > $o] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc7143791561355829714st_int @ P4 @ ( produc1996262876970182428st_int @ nil_Pr5671120429643327159n_assn @ nil_int ) ) )
% 2.39/2.75 => ( ! [P4: produc6575502325842934193n_assn > int > $o,A6: produc6575502325842934193n_assn,As: list_P8527749157015355191n_assn,B5: int,Bs2: list_int] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc7143791561355829714st_int @ P4 @ ( produc1996262876970182428st_int @ ( cons_P2971678138204555879n_assn @ A6 @ As ) @ ( cons_int @ B5 @ Bs2 ) ) ) )
% 2.39/2.75 => ( ! [P4: produc6575502325842934193n_assn > int > $o,V: produc6575502325842934193n_assn,Va: list_P8527749157015355191n_assn] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc7143791561355829714st_int @ P4 @ ( produc1996262876970182428st_int @ ( cons_P2971678138204555879n_assn @ V @ Va ) @ nil_int ) ) )
% 2.39/2.75 => ~ ! [P4: produc6575502325842934193n_assn > int > $o,V: int,Va: list_int] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc7143791561355829714st_int @ P4 @ ( produc1996262876970182428st_int @ nil_Pr5671120429643327159n_assn @ ( cons_int @ V @ Va ) ) ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % list_all_zip.cases
% 2.39/2.75 thf(fact_1776_list__all__zip_Ocases,axiom,
% 2.39/2.75 ! [X: produc6280221377895650458st_nat] :
% 2.39/2.75 ( ! [P4: produc6575502325842934193n_assn > nat > $o] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc6179912464936081618st_nat @ P4 @ ( produc6174113896479379136st_nat @ nil_Pr5671120429643327159n_assn @ nil_nat ) ) )
% 2.39/2.75 => ( ! [P4: produc6575502325842934193n_assn > nat > $o,A6: produc6575502325842934193n_assn,As: list_P8527749157015355191n_assn,B5: nat,Bs2: list_nat] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc6179912464936081618st_nat @ P4 @ ( produc6174113896479379136st_nat @ ( cons_P2971678138204555879n_assn @ A6 @ As ) @ ( cons_nat @ B5 @ Bs2 ) ) ) )
% 2.39/2.75 => ( ! [P4: produc6575502325842934193n_assn > nat > $o,V: produc6575502325842934193n_assn,Va: list_P8527749157015355191n_assn] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc6179912464936081618st_nat @ P4 @ ( produc6174113896479379136st_nat @ ( cons_P2971678138204555879n_assn @ V @ Va ) @ nil_nat ) ) )
% 2.39/2.75 => ~ ! [P4: produc6575502325842934193n_assn > nat > $o,V: nat,Va: list_nat] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc6179912464936081618st_nat @ P4 @ ( produc6174113896479379136st_nat @ nil_Pr5671120429643327159n_assn @ ( cons_nat @ V @ Va ) ) ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % list_all_zip.cases
% 2.39/2.75 thf(fact_1777_list__all__zip_Ocases,axiom,
% 2.39/2.75 ! [X: produc4944321512348556200n_assn] :
% 2.39/2.75 ( ! [P4: int > produc6575502325842934193n_assn > $o] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc3092413063583913184n_assn @ P4 @ ( produc4510294837168919970n_assn @ nil_int @ nil_Pr5671120429643327159n_assn ) ) )
% 2.39/2.75 => ( ! [P4: int > produc6575502325842934193n_assn > $o,A6: int,As: list_int,B5: produc6575502325842934193n_assn,Bs2: list_P8527749157015355191n_assn] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc3092413063583913184n_assn @ P4 @ ( produc4510294837168919970n_assn @ ( cons_int @ A6 @ As ) @ ( cons_P2971678138204555879n_assn @ B5 @ Bs2 ) ) ) )
% 2.39/2.75 => ( ! [P4: int > produc6575502325842934193n_assn > $o,V: int,Va: list_int] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc3092413063583913184n_assn @ P4 @ ( produc4510294837168919970n_assn @ ( cons_int @ V @ Va ) @ nil_Pr5671120429643327159n_assn ) ) )
% 2.39/2.75 => ~ ! [P4: int > produc6575502325842934193n_assn > $o,V: produc6575502325842934193n_assn,Va: list_P8527749157015355191n_assn] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc3092413063583913184n_assn @ P4 @ ( produc4510294837168919970n_assn @ nil_int @ ( cons_P2971678138204555879n_assn @ V @ Va ) ) ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % list_all_zip.cases
% 2.39/2.75 thf(fact_1778_list__all__zip_Ocases,axiom,
% 2.39/2.75 ! [X: produc6134427711877206866st_int] :
% 2.39/2.75 ( ! [P4: int > int > $o] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc6519019827157805250st_int @ P4 @ ( produc364263696895485585st_int @ nil_int @ nil_int ) ) )
% 2.39/2.75 => ( ! [P4: int > int > $o,A6: int,As: list_int,B5: int,Bs2: list_int] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc6519019827157805250st_int @ P4 @ ( produc364263696895485585st_int @ ( cons_int @ A6 @ As ) @ ( cons_int @ B5 @ Bs2 ) ) ) )
% 2.39/2.75 => ( ! [P4: int > int > $o,V: int,Va: list_int] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc6519019827157805250st_int @ P4 @ ( produc364263696895485585st_int @ ( cons_int @ V @ Va ) @ nil_int ) ) )
% 2.39/2.75 => ~ ! [P4: int > int > $o,V: int,Va: list_int] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc6519019827157805250st_int @ P4 @ ( produc364263696895485585st_int @ nil_int @ ( cons_int @ V @ Va ) ) ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % list_all_zip.cases
% 2.39/2.75 thf(fact_1779_list__all__zip_Ocases,axiom,
% 2.39/2.75 ! [X: produc5074578776457504922st_nat] :
% 2.39/2.75 ( ! [P4: int > nat > $o] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc3135705617881911306st_nat @ P4 @ ( produc4542114716404682293st_nat @ nil_int @ nil_nat ) ) )
% 2.39/2.75 => ( ! [P4: int > nat > $o,A6: int,As: list_int,B5: nat,Bs2: list_nat] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc3135705617881911306st_nat @ P4 @ ( produc4542114716404682293st_nat @ ( cons_int @ A6 @ As ) @ ( cons_nat @ B5 @ Bs2 ) ) ) )
% 2.39/2.75 => ( ! [P4: int > nat > $o,V: int,Va: list_int] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc3135705617881911306st_nat @ P4 @ ( produc4542114716404682293st_nat @ ( cons_int @ V @ Va ) @ nil_nat ) ) )
% 2.39/2.75 => ~ ! [P4: int > nat > $o,V: nat,Va: list_nat] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc3135705617881911306st_nat @ P4 @ ( produc4542114716404682293st_nat @ nil_int @ ( cons_nat @ V @ Va ) ) ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % list_all_zip.cases
% 2.39/2.75 thf(fact_1780_list__all__zip_Ocases,axiom,
% 2.39/2.75 ! [X: produc3272579373640082088n_assn] :
% 2.39/2.75 ( ! [P4: nat > produc6575502325842934193n_assn > $o] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc1692222275734866400n_assn @ P4 @ ( produc7706768604797473534n_assn @ nil_nat @ nil_Pr5671120429643327159n_assn ) ) )
% 2.39/2.75 => ( ! [P4: nat > produc6575502325842934193n_assn > $o,A6: nat,As: list_nat,B5: produc6575502325842934193n_assn,Bs2: list_P8527749157015355191n_assn] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc1692222275734866400n_assn @ P4 @ ( produc7706768604797473534n_assn @ ( cons_nat @ A6 @ As ) @ ( cons_P2971678138204555879n_assn @ B5 @ Bs2 ) ) ) )
% 2.39/2.75 => ( ! [P4: nat > produc6575502325842934193n_assn > $o,V: nat,Va: list_nat] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc1692222275734866400n_assn @ P4 @ ( produc7706768604797473534n_assn @ ( cons_nat @ V @ Va ) @ nil_Pr5671120429643327159n_assn ) ) )
% 2.39/2.75 => ~ ! [P4: nat > produc6575502325842934193n_assn > $o,V: produc6575502325842934193n_assn,Va: list_P8527749157015355191n_assn] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc1692222275734866400n_assn @ P4 @ ( produc7706768604797473534n_assn @ nil_nat @ ( cons_P2971678138204555879n_assn @ V @ Va ) ) ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % list_all_zip.cases
% 2.39/2.75 thf(fact_1781_list__all__zip_Ocases,axiom,
% 2.39/2.75 ! [X: produc5847166148257158298st_int] :
% 2.39/2.75 ( ! [P4: nat > int > $o] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc6511047662141078538st_int @ P4 @ ( produc7739558402351520821st_int @ nil_nat @ nil_int ) ) )
% 2.39/2.75 => ( ! [P4: nat > int > $o,A6: nat,As: list_nat,B5: int,Bs2: list_int] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc6511047662141078538st_int @ P4 @ ( produc7739558402351520821st_int @ ( cons_nat @ A6 @ As ) @ ( cons_int @ B5 @ Bs2 ) ) ) )
% 2.39/2.75 => ( ! [P4: nat > int > $o,V: nat,Va: list_nat] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc6511047662141078538st_int @ P4 @ ( produc7739558402351520821st_int @ ( cons_nat @ V @ Va ) @ nil_int ) ) )
% 2.39/2.75 => ~ ! [P4: nat > int > $o,V: int,Va: list_int] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc6511047662141078538st_int @ P4 @ ( produc7739558402351520821st_int @ nil_nat @ ( cons_int @ V @ Va ) ) ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % list_all_zip.cases
% 2.39/2.75 thf(fact_1782_list__all__zip_Ocases,axiom,
% 2.39/2.75 ! [X: produc4787317212837456354st_nat] :
% 2.39/2.75 ( ! [P4: nat > nat > $o] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc3127733452865184594st_nat @ P4 @ ( produc2694037385005941721st_nat @ nil_nat @ nil_nat ) ) )
% 2.39/2.75 => ( ! [P4: nat > nat > $o,A6: nat,As: list_nat,B5: nat,Bs2: list_nat] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc3127733452865184594st_nat @ P4 @ ( produc2694037385005941721st_nat @ ( cons_nat @ A6 @ As ) @ ( cons_nat @ B5 @ Bs2 ) ) ) )
% 2.39/2.75 => ( ! [P4: nat > nat > $o,V: nat,Va: list_nat] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc3127733452865184594st_nat @ P4 @ ( produc2694037385005941721st_nat @ ( cons_nat @ V @ Va ) @ nil_nat ) ) )
% 2.39/2.75 => ~ ! [P4: nat > nat > $o,V: nat,Va: list_nat] :
% 2.39/2.75 ( X
% 2.39/2.75 != ( produc3127733452865184594st_nat @ P4 @ ( produc2694037385005941721st_nat @ nil_nat @ ( cons_nat @ V @ Va ) ) ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % list_all_zip.cases
% 2.39/2.75 thf(fact_1783_minus__less__iff,axiom,
% 2.39/2.75 ! [A: int,B: int] :
% 2.39/2.75 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
% 2.39/2.75 = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 2.39/2.75
% 2.39/2.75 % minus_less_iff
% 2.39/2.75 thf(fact_1784_minus__less__iff,axiom,
% 2.39/2.75 ! [A: rat,B: rat] :
% 2.39/2.75 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B )
% 2.39/2.75 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 2.39/2.75
% 2.39/2.75 % minus_less_iff
% 2.39/2.75 thf(fact_1785_minus__less__iff,axiom,
% 2.39/2.75 ! [A: code_integer,B: code_integer] :
% 2.39/2.75 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 2.39/2.75 = ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 2.39/2.75
% 2.39/2.75 % minus_less_iff
% 2.39/2.75 thf(fact_1786_less__minus__iff,axiom,
% 2.39/2.75 ! [A: int,B: int] :
% 2.39/2.75 ( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
% 2.39/2.75 = ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % less_minus_iff
% 2.39/2.75 thf(fact_1787_less__minus__iff,axiom,
% 2.39/2.75 ! [A: rat,B: rat] :
% 2.39/2.75 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ B ) )
% 2.39/2.75 = ( ord_less_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % less_minus_iff
% 2.39/2.75 thf(fact_1788_less__minus__iff,axiom,
% 2.39/2.75 ! [A: code_integer,B: code_integer] :
% 2.39/2.75 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 2.39/2.75 = ( ord_le6747313008572928689nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % less_minus_iff
% 2.39/2.75 thf(fact_1789_measures__less,axiom,
% 2.39/2.75 ! [F2: nat > nat,X: nat,Y: nat,Fs: list_nat_nat] :
% 2.39/2.75 ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 2.39/2.75 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( measures_nat @ ( cons_nat_nat @ F2 @ Fs ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % measures_less
% 2.39/2.75 thf(fact_1790_measures__less,axiom,
% 2.39/2.75 ! [F2: int > nat,X: int,Y: int,Fs: list_int_nat] :
% 2.39/2.75 ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 2.39/2.75 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( measures_int @ ( cons_int_nat @ F2 @ Fs ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % measures_less
% 2.39/2.75 thf(fact_1791_less__infI1,axiom,
% 2.39/2.75 ! [A: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.39/2.75 ( ( ord_le7866589430770878221at_nat @ A @ X )
% 2.39/2.75 => ( ord_le7866589430770878221at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ X ) ) ).
% 2.39/2.75
% 2.39/2.75 % less_infI1
% 2.39/2.75 thf(fact_1792_less__infI1,axiom,
% 2.39/2.75 ! [A: set_nat,X: set_nat,B: set_nat] :
% 2.39/2.75 ( ( ord_less_set_nat @ A @ X )
% 2.39/2.75 => ( ord_less_set_nat @ ( inf_inf_set_nat @ A @ B ) @ X ) ) ).
% 2.39/2.75
% 2.39/2.75 % less_infI1
% 2.39/2.75 thf(fact_1793_less__infI1,axiom,
% 2.39/2.75 ! [A: product_prod_int_int > $o,X: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 2.39/2.75 ( ( ord_le8213806771718485336_int_o @ A @ X )
% 2.39/2.75 => ( ord_le8213806771718485336_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ X ) ) ).
% 2.39/2.75
% 2.39/2.75 % less_infI1
% 2.39/2.75 thf(fact_1794_less__infI1,axiom,
% 2.39/2.75 ! [A: assn,X: assn,B: assn] :
% 2.39/2.75 ( ( ord_less_assn @ A @ X )
% 2.39/2.75 => ( ord_less_assn @ ( inf_inf_assn @ A @ B ) @ X ) ) ).
% 2.39/2.75
% 2.39/2.75 % less_infI1
% 2.39/2.75 thf(fact_1795_less__infI1,axiom,
% 2.39/2.75 ! [A: rat,X: rat,B: rat] :
% 2.39/2.75 ( ( ord_less_rat @ A @ X )
% 2.39/2.75 => ( ord_less_rat @ ( inf_inf_rat @ A @ B ) @ X ) ) ).
% 2.39/2.75
% 2.39/2.75 % less_infI1
% 2.39/2.75 thf(fact_1796_less__infI1,axiom,
% 2.39/2.75 ! [A: nat,X: nat,B: nat] :
% 2.39/2.75 ( ( ord_less_nat @ A @ X )
% 2.39/2.75 => ( ord_less_nat @ ( inf_inf_nat @ A @ B ) @ X ) ) ).
% 2.39/2.75
% 2.39/2.75 % less_infI1
% 2.39/2.75 thf(fact_1797_less__infI1,axiom,
% 2.39/2.75 ! [A: int,X: int,B: int] :
% 2.39/2.75 ( ( ord_less_int @ A @ X )
% 2.39/2.75 => ( ord_less_int @ ( inf_inf_int @ A @ B ) @ X ) ) ).
% 2.39/2.75
% 2.39/2.75 % less_infI1
% 2.39/2.75 thf(fact_1798_less__infI2,axiom,
% 2.39/2.75 ! [B: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 2.39/2.75 ( ( ord_le7866589430770878221at_nat @ B @ X )
% 2.39/2.75 => ( ord_le7866589430770878221at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ X ) ) ).
% 2.39/2.75
% 2.39/2.75 % less_infI2
% 2.39/2.75 thf(fact_1799_less__infI2,axiom,
% 2.39/2.75 ! [B: set_nat,X: set_nat,A: set_nat] :
% 2.39/2.75 ( ( ord_less_set_nat @ B @ X )
% 2.39/2.75 => ( ord_less_set_nat @ ( inf_inf_set_nat @ A @ B ) @ X ) ) ).
% 2.39/2.75
% 2.39/2.75 % less_infI2
% 2.39/2.75 thf(fact_1800_less__infI2,axiom,
% 2.39/2.75 ! [B: product_prod_int_int > $o,X: product_prod_int_int > $o,A: product_prod_int_int > $o] :
% 2.39/2.75 ( ( ord_le8213806771718485336_int_o @ B @ X )
% 2.39/2.75 => ( ord_le8213806771718485336_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ X ) ) ).
% 2.39/2.75
% 2.39/2.75 % less_infI2
% 2.39/2.75 thf(fact_1801_less__infI2,axiom,
% 2.39/2.75 ! [B: assn,X: assn,A: assn] :
% 2.39/2.75 ( ( ord_less_assn @ B @ X )
% 2.39/2.75 => ( ord_less_assn @ ( inf_inf_assn @ A @ B ) @ X ) ) ).
% 2.39/2.75
% 2.39/2.75 % less_infI2
% 2.39/2.75 thf(fact_1802_less__infI2,axiom,
% 2.39/2.75 ! [B: rat,X: rat,A: rat] :
% 2.39/2.75 ( ( ord_less_rat @ B @ X )
% 2.39/2.75 => ( ord_less_rat @ ( inf_inf_rat @ A @ B ) @ X ) ) ).
% 2.39/2.75
% 2.39/2.75 % less_infI2
% 2.39/2.75 thf(fact_1803_less__infI2,axiom,
% 2.39/2.75 ! [B: nat,X: nat,A: nat] :
% 2.39/2.75 ( ( ord_less_nat @ B @ X )
% 2.39/2.75 => ( ord_less_nat @ ( inf_inf_nat @ A @ B ) @ X ) ) ).
% 2.39/2.75
% 2.39/2.75 % less_infI2
% 2.39/2.75 thf(fact_1804_less__infI2,axiom,
% 2.39/2.75 ! [B: int,X: int,A: int] :
% 2.39/2.75 ( ( ord_less_int @ B @ X )
% 2.39/2.75 => ( ord_less_int @ ( inf_inf_int @ A @ B ) @ X ) ) ).
% 2.39/2.75
% 2.39/2.75 % less_infI2
% 2.39/2.75 thf(fact_1805_inf_Oabsorb3,axiom,
% 2.39/2.75 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.39/2.75 ( ( ord_le7866589430770878221at_nat @ A @ B )
% 2.39/2.75 => ( ( inf_in2572325071724192079at_nat @ A @ B )
% 2.39/2.75 = A ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.absorb3
% 2.39/2.75 thf(fact_1806_inf_Oabsorb3,axiom,
% 2.39/2.75 ! [A: set_nat,B: set_nat] :
% 2.39/2.75 ( ( ord_less_set_nat @ A @ B )
% 2.39/2.75 => ( ( inf_inf_set_nat @ A @ B )
% 2.39/2.75 = A ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.absorb3
% 2.39/2.75 thf(fact_1807_inf_Oabsorb3,axiom,
% 2.39/2.75 ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 2.39/2.75 ( ( ord_le8213806771718485336_int_o @ A @ B )
% 2.39/2.75 => ( ( inf_in3604695632404883862_int_o @ A @ B )
% 2.39/2.75 = A ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.absorb3
% 2.39/2.75 thf(fact_1808_inf_Oabsorb3,axiom,
% 2.39/2.75 ! [A: assn,B: assn] :
% 2.39/2.75 ( ( ord_less_assn @ A @ B )
% 2.39/2.75 => ( ( inf_inf_assn @ A @ B )
% 2.39/2.75 = A ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.absorb3
% 2.39/2.75 thf(fact_1809_inf_Oabsorb3,axiom,
% 2.39/2.75 ! [A: rat,B: rat] :
% 2.39/2.75 ( ( ord_less_rat @ A @ B )
% 2.39/2.75 => ( ( inf_inf_rat @ A @ B )
% 2.39/2.75 = A ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.absorb3
% 2.39/2.75 thf(fact_1810_inf_Oabsorb3,axiom,
% 2.39/2.75 ! [A: nat,B: nat] :
% 2.39/2.75 ( ( ord_less_nat @ A @ B )
% 2.39/2.75 => ( ( inf_inf_nat @ A @ B )
% 2.39/2.75 = A ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.absorb3
% 2.39/2.75 thf(fact_1811_inf_Oabsorb3,axiom,
% 2.39/2.75 ! [A: int,B: int] :
% 2.39/2.75 ( ( ord_less_int @ A @ B )
% 2.39/2.75 => ( ( inf_inf_int @ A @ B )
% 2.39/2.75 = A ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.absorb3
% 2.39/2.75 thf(fact_1812_inf_Oabsorb4,axiom,
% 2.39/2.75 ! [B: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 2.39/2.75 ( ( ord_le7866589430770878221at_nat @ B @ A )
% 2.39/2.75 => ( ( inf_in2572325071724192079at_nat @ A @ B )
% 2.39/2.75 = B ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.absorb4
% 2.39/2.75 thf(fact_1813_inf_Oabsorb4,axiom,
% 2.39/2.75 ! [B: set_nat,A: set_nat] :
% 2.39/2.75 ( ( ord_less_set_nat @ B @ A )
% 2.39/2.75 => ( ( inf_inf_set_nat @ A @ B )
% 2.39/2.75 = B ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.absorb4
% 2.39/2.75 thf(fact_1814_inf_Oabsorb4,axiom,
% 2.39/2.75 ! [B: product_prod_int_int > $o,A: product_prod_int_int > $o] :
% 2.39/2.75 ( ( ord_le8213806771718485336_int_o @ B @ A )
% 2.39/2.75 => ( ( inf_in3604695632404883862_int_o @ A @ B )
% 2.39/2.75 = B ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.absorb4
% 2.39/2.75 thf(fact_1815_inf_Oabsorb4,axiom,
% 2.39/2.75 ! [B: assn,A: assn] :
% 2.39/2.75 ( ( ord_less_assn @ B @ A )
% 2.39/2.75 => ( ( inf_inf_assn @ A @ B )
% 2.39/2.75 = B ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.absorb4
% 2.39/2.75 thf(fact_1816_inf_Oabsorb4,axiom,
% 2.39/2.75 ! [B: rat,A: rat] :
% 2.39/2.75 ( ( ord_less_rat @ B @ A )
% 2.39/2.75 => ( ( inf_inf_rat @ A @ B )
% 2.39/2.75 = B ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.absorb4
% 2.39/2.75 thf(fact_1817_inf_Oabsorb4,axiom,
% 2.39/2.75 ! [B: nat,A: nat] :
% 2.39/2.75 ( ( ord_less_nat @ B @ A )
% 2.39/2.75 => ( ( inf_inf_nat @ A @ B )
% 2.39/2.75 = B ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.absorb4
% 2.39/2.75 thf(fact_1818_inf_Oabsorb4,axiom,
% 2.39/2.75 ! [B: int,A: int] :
% 2.39/2.75 ( ( ord_less_int @ B @ A )
% 2.39/2.75 => ( ( inf_inf_int @ A @ B )
% 2.39/2.75 = B ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.absorb4
% 2.39/2.75 thf(fact_1819_inf_Ostrict__boundedE,axiom,
% 2.39/2.75 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat] :
% 2.39/2.75 ( ( ord_le7866589430770878221at_nat @ A @ ( inf_in2572325071724192079at_nat @ B @ C ) )
% 2.39/2.75 => ~ ( ( ord_le7866589430770878221at_nat @ A @ B )
% 2.39/2.75 => ~ ( ord_le7866589430770878221at_nat @ A @ C ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.strict_boundedE
% 2.39/2.75 thf(fact_1820_inf_Ostrict__boundedE,axiom,
% 2.39/2.75 ! [A: set_nat,B: set_nat,C: set_nat] :
% 2.39/2.75 ( ( ord_less_set_nat @ A @ ( inf_inf_set_nat @ B @ C ) )
% 2.39/2.75 => ~ ( ( ord_less_set_nat @ A @ B )
% 2.39/2.75 => ~ ( ord_less_set_nat @ A @ C ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.strict_boundedE
% 2.39/2.75 thf(fact_1821_inf_Ostrict__boundedE,axiom,
% 2.39/2.75 ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o,C: product_prod_int_int > $o] :
% 2.39/2.75 ( ( ord_le8213806771718485336_int_o @ A @ ( inf_in3604695632404883862_int_o @ B @ C ) )
% 2.39/2.75 => ~ ( ( ord_le8213806771718485336_int_o @ A @ B )
% 2.39/2.75 => ~ ( ord_le8213806771718485336_int_o @ A @ C ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.strict_boundedE
% 2.39/2.75 thf(fact_1822_inf_Ostrict__boundedE,axiom,
% 2.39/2.75 ! [A: assn,B: assn,C: assn] :
% 2.39/2.75 ( ( ord_less_assn @ A @ ( inf_inf_assn @ B @ C ) )
% 2.39/2.75 => ~ ( ( ord_less_assn @ A @ B )
% 2.39/2.75 => ~ ( ord_less_assn @ A @ C ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.strict_boundedE
% 2.39/2.75 thf(fact_1823_inf_Ostrict__boundedE,axiom,
% 2.39/2.75 ! [A: rat,B: rat,C: rat] :
% 2.39/2.75 ( ( ord_less_rat @ A @ ( inf_inf_rat @ B @ C ) )
% 2.39/2.75 => ~ ( ( ord_less_rat @ A @ B )
% 2.39/2.75 => ~ ( ord_less_rat @ A @ C ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.strict_boundedE
% 2.39/2.75 thf(fact_1824_inf_Ostrict__boundedE,axiom,
% 2.39/2.75 ! [A: nat,B: nat,C: nat] :
% 2.39/2.75 ( ( ord_less_nat @ A @ ( inf_inf_nat @ B @ C ) )
% 2.39/2.75 => ~ ( ( ord_less_nat @ A @ B )
% 2.39/2.75 => ~ ( ord_less_nat @ A @ C ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.strict_boundedE
% 2.39/2.75 thf(fact_1825_inf_Ostrict__boundedE,axiom,
% 2.39/2.75 ! [A: int,B: int,C: int] :
% 2.39/2.75 ( ( ord_less_int @ A @ ( inf_inf_int @ B @ C ) )
% 2.39/2.75 => ~ ( ( ord_less_int @ A @ B )
% 2.39/2.75 => ~ ( ord_less_int @ A @ C ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.strict_boundedE
% 2.39/2.75 thf(fact_1826_inf_Ostrict__order__iff,axiom,
% 2.39/2.75 ( ord_le7866589430770878221at_nat
% 2.39/2.75 = ( ^ [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 2.39/2.75 ( ( A2
% 2.39/2.75 = ( inf_in2572325071724192079at_nat @ A2 @ B2 ) )
% 2.39/2.75 & ( A2 != B2 ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.strict_order_iff
% 2.39/2.75 thf(fact_1827_inf_Ostrict__order__iff,axiom,
% 2.39/2.75 ( ord_less_set_nat
% 2.39/2.75 = ( ^ [A2: set_nat,B2: set_nat] :
% 2.39/2.75 ( ( A2
% 2.39/2.75 = ( inf_inf_set_nat @ A2 @ B2 ) )
% 2.39/2.75 & ( A2 != B2 ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.strict_order_iff
% 2.39/2.75 thf(fact_1828_inf_Ostrict__order__iff,axiom,
% 2.39/2.75 ( ord_le8213806771718485336_int_o
% 2.39/2.75 = ( ^ [A2: product_prod_int_int > $o,B2: product_prod_int_int > $o] :
% 2.39/2.75 ( ( A2
% 2.39/2.75 = ( inf_in3604695632404883862_int_o @ A2 @ B2 ) )
% 2.39/2.75 & ( A2 != B2 ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.strict_order_iff
% 2.39/2.75 thf(fact_1829_inf_Ostrict__order__iff,axiom,
% 2.39/2.75 ( ord_less_assn
% 2.39/2.75 = ( ^ [A2: assn,B2: assn] :
% 2.39/2.75 ( ( A2
% 2.39/2.75 = ( inf_inf_assn @ A2 @ B2 ) )
% 2.39/2.75 & ( A2 != B2 ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.strict_order_iff
% 2.39/2.75 thf(fact_1830_inf_Ostrict__order__iff,axiom,
% 2.39/2.75 ( ord_less_rat
% 2.39/2.75 = ( ^ [A2: rat,B2: rat] :
% 2.39/2.75 ( ( A2
% 2.39/2.75 = ( inf_inf_rat @ A2 @ B2 ) )
% 2.39/2.75 & ( A2 != B2 ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.strict_order_iff
% 2.39/2.75 thf(fact_1831_inf_Ostrict__order__iff,axiom,
% 2.39/2.75 ( ord_less_nat
% 2.39/2.75 = ( ^ [A2: nat,B2: nat] :
% 2.39/2.75 ( ( A2
% 2.39/2.75 = ( inf_inf_nat @ A2 @ B2 ) )
% 2.39/2.75 & ( A2 != B2 ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.strict_order_iff
% 2.39/2.75 thf(fact_1832_inf_Ostrict__order__iff,axiom,
% 2.39/2.75 ( ord_less_int
% 2.39/2.75 = ( ^ [A2: int,B2: int] :
% 2.39/2.75 ( ( A2
% 2.39/2.75 = ( inf_inf_int @ A2 @ B2 ) )
% 2.39/2.75 & ( A2 != B2 ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.strict_order_iff
% 2.39/2.75 thf(fact_1833_inf_Ostrict__coboundedI1,axiom,
% 2.39/2.75 ! [A: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 2.39/2.75 ( ( ord_le7866589430770878221at_nat @ A @ C )
% 2.39/2.75 => ( ord_le7866589430770878221at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ C ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.strict_coboundedI1
% 2.39/2.75 thf(fact_1834_inf_Ostrict__coboundedI1,axiom,
% 2.39/2.75 ! [A: set_nat,C: set_nat,B: set_nat] :
% 2.39/2.75 ( ( ord_less_set_nat @ A @ C )
% 2.39/2.75 => ( ord_less_set_nat @ ( inf_inf_set_nat @ A @ B ) @ C ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.strict_coboundedI1
% 2.39/2.75 thf(fact_1835_inf_Ostrict__coboundedI1,axiom,
% 2.39/2.75 ! [A: product_prod_int_int > $o,C: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 2.39/2.75 ( ( ord_le8213806771718485336_int_o @ A @ C )
% 2.39/2.75 => ( ord_le8213806771718485336_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ C ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.strict_coboundedI1
% 2.39/2.75 thf(fact_1836_inf_Ostrict__coboundedI1,axiom,
% 2.39/2.75 ! [A: assn,C: assn,B: assn] :
% 2.39/2.75 ( ( ord_less_assn @ A @ C )
% 2.39/2.75 => ( ord_less_assn @ ( inf_inf_assn @ A @ B ) @ C ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.strict_coboundedI1
% 2.39/2.75 thf(fact_1837_inf_Ostrict__coboundedI1,axiom,
% 2.39/2.75 ! [A: rat,C: rat,B: rat] :
% 2.39/2.75 ( ( ord_less_rat @ A @ C )
% 2.39/2.75 => ( ord_less_rat @ ( inf_inf_rat @ A @ B ) @ C ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.strict_coboundedI1
% 2.39/2.75 thf(fact_1838_inf_Ostrict__coboundedI1,axiom,
% 2.39/2.75 ! [A: nat,C: nat,B: nat] :
% 2.39/2.75 ( ( ord_less_nat @ A @ C )
% 2.39/2.75 => ( ord_less_nat @ ( inf_inf_nat @ A @ B ) @ C ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.strict_coboundedI1
% 2.39/2.75 thf(fact_1839_inf_Ostrict__coboundedI1,axiom,
% 2.39/2.75 ! [A: int,C: int,B: int] :
% 2.39/2.75 ( ( ord_less_int @ A @ C )
% 2.39/2.75 => ( ord_less_int @ ( inf_inf_int @ A @ B ) @ C ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.strict_coboundedI1
% 2.39/2.75 thf(fact_1840_inf_Ostrict__coboundedI2,axiom,
% 2.39/2.75 ! [B: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 2.39/2.75 ( ( ord_le7866589430770878221at_nat @ B @ C )
% 2.39/2.75 => ( ord_le7866589430770878221at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ C ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.strict_coboundedI2
% 2.39/2.75 thf(fact_1841_inf_Ostrict__coboundedI2,axiom,
% 2.39/2.75 ! [B: set_nat,C: set_nat,A: set_nat] :
% 2.39/2.75 ( ( ord_less_set_nat @ B @ C )
% 2.39/2.75 => ( ord_less_set_nat @ ( inf_inf_set_nat @ A @ B ) @ C ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.strict_coboundedI2
% 2.39/2.75 thf(fact_1842_inf_Ostrict__coboundedI2,axiom,
% 2.39/2.75 ! [B: product_prod_int_int > $o,C: product_prod_int_int > $o,A: product_prod_int_int > $o] :
% 2.39/2.75 ( ( ord_le8213806771718485336_int_o @ B @ C )
% 2.39/2.75 => ( ord_le8213806771718485336_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ C ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.strict_coboundedI2
% 2.39/2.75 thf(fact_1843_inf_Ostrict__coboundedI2,axiom,
% 2.39/2.75 ! [B: assn,C: assn,A: assn] :
% 2.39/2.75 ( ( ord_less_assn @ B @ C )
% 2.39/2.75 => ( ord_less_assn @ ( inf_inf_assn @ A @ B ) @ C ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.strict_coboundedI2
% 2.39/2.75 thf(fact_1844_inf_Ostrict__coboundedI2,axiom,
% 2.39/2.75 ! [B: rat,C: rat,A: rat] :
% 2.39/2.75 ( ( ord_less_rat @ B @ C )
% 2.39/2.75 => ( ord_less_rat @ ( inf_inf_rat @ A @ B ) @ C ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.strict_coboundedI2
% 2.39/2.75 thf(fact_1845_inf_Ostrict__coboundedI2,axiom,
% 2.39/2.75 ! [B: nat,C: nat,A: nat] :
% 2.39/2.75 ( ( ord_less_nat @ B @ C )
% 2.39/2.75 => ( ord_less_nat @ ( inf_inf_nat @ A @ B ) @ C ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.strict_coboundedI2
% 2.39/2.75 thf(fact_1846_inf_Ostrict__coboundedI2,axiom,
% 2.39/2.75 ! [B: int,C: int,A: int] :
% 2.39/2.75 ( ( ord_less_int @ B @ C )
% 2.39/2.75 => ( ord_less_int @ ( inf_inf_int @ A @ B ) @ C ) ) ).
% 2.39/2.75
% 2.39/2.75 % inf.strict_coboundedI2
% 2.39/2.75 thf(fact_1847_sup_Ostrict__coboundedI2,axiom,
% 2.39/2.75 ! [C: set_nat,B: set_nat,A: set_nat] :
% 2.39/2.75 ( ( ord_less_set_nat @ C @ B )
% 2.39/2.75 => ( ord_less_set_nat @ C @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % sup.strict_coboundedI2
% 2.39/2.75 thf(fact_1848_sup_Ostrict__coboundedI2,axiom,
% 2.39/2.75 ! [C: assn,B: assn,A: assn] :
% 2.39/2.75 ( ( ord_less_assn @ C @ B )
% 2.39/2.75 => ( ord_less_assn @ C @ ( sup_sup_assn @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % sup.strict_coboundedI2
% 2.39/2.75 thf(fact_1849_sup_Ostrict__coboundedI2,axiom,
% 2.39/2.75 ! [C: rat,B: rat,A: rat] :
% 2.39/2.75 ( ( ord_less_rat @ C @ B )
% 2.39/2.75 => ( ord_less_rat @ C @ ( sup_sup_rat @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % sup.strict_coboundedI2
% 2.39/2.75 thf(fact_1850_sup_Ostrict__coboundedI2,axiom,
% 2.39/2.75 ! [C: nat,B: nat,A: nat] :
% 2.39/2.75 ( ( ord_less_nat @ C @ B )
% 2.39/2.75 => ( ord_less_nat @ C @ ( sup_sup_nat @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % sup.strict_coboundedI2
% 2.39/2.75 thf(fact_1851_sup_Ostrict__coboundedI2,axiom,
% 2.39/2.75 ! [C: int,B: int,A: int] :
% 2.39/2.75 ( ( ord_less_int @ C @ B )
% 2.39/2.75 => ( ord_less_int @ C @ ( sup_sup_int @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % sup.strict_coboundedI2
% 2.39/2.75 thf(fact_1852_sup_Ostrict__coboundedI1,axiom,
% 2.39/2.75 ! [C: set_nat,A: set_nat,B: set_nat] :
% 2.39/2.75 ( ( ord_less_set_nat @ C @ A )
% 2.39/2.75 => ( ord_less_set_nat @ C @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % sup.strict_coboundedI1
% 2.39/2.75 thf(fact_1853_sup_Ostrict__coboundedI1,axiom,
% 2.39/2.75 ! [C: assn,A: assn,B: assn] :
% 2.39/2.75 ( ( ord_less_assn @ C @ A )
% 2.39/2.75 => ( ord_less_assn @ C @ ( sup_sup_assn @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % sup.strict_coboundedI1
% 2.39/2.75 thf(fact_1854_sup_Ostrict__coboundedI1,axiom,
% 2.39/2.75 ! [C: rat,A: rat,B: rat] :
% 2.39/2.75 ( ( ord_less_rat @ C @ A )
% 2.39/2.75 => ( ord_less_rat @ C @ ( sup_sup_rat @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % sup.strict_coboundedI1
% 2.39/2.75 thf(fact_1855_sup_Ostrict__coboundedI1,axiom,
% 2.39/2.75 ! [C: nat,A: nat,B: nat] :
% 2.39/2.75 ( ( ord_less_nat @ C @ A )
% 2.39/2.75 => ( ord_less_nat @ C @ ( sup_sup_nat @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % sup.strict_coboundedI1
% 2.39/2.75 thf(fact_1856_sup_Ostrict__coboundedI1,axiom,
% 2.39/2.75 ! [C: int,A: int,B: int] :
% 2.39/2.75 ( ( ord_less_int @ C @ A )
% 2.39/2.75 => ( ord_less_int @ C @ ( sup_sup_int @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % sup.strict_coboundedI1
% 2.39/2.75 thf(fact_1857_sup_Ostrict__order__iff,axiom,
% 2.39/2.75 ( ord_less_set_nat
% 2.39/2.75 = ( ^ [B2: set_nat,A2: set_nat] :
% 2.39/2.75 ( ( A2
% 2.39/2.75 = ( sup_sup_set_nat @ A2 @ B2 ) )
% 2.39/2.75 & ( A2 != B2 ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % sup.strict_order_iff
% 2.39/2.75 thf(fact_1858_sup_Ostrict__order__iff,axiom,
% 2.39/2.75 ( ord_less_assn
% 2.39/2.75 = ( ^ [B2: assn,A2: assn] :
% 2.39/2.75 ( ( A2
% 2.39/2.75 = ( sup_sup_assn @ A2 @ B2 ) )
% 2.39/2.75 & ( A2 != B2 ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % sup.strict_order_iff
% 2.39/2.75 thf(fact_1859_sup_Ostrict__order__iff,axiom,
% 2.39/2.75 ( ord_less_rat
% 2.39/2.75 = ( ^ [B2: rat,A2: rat] :
% 2.39/2.75 ( ( A2
% 2.39/2.75 = ( sup_sup_rat @ A2 @ B2 ) )
% 2.39/2.75 & ( A2 != B2 ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % sup.strict_order_iff
% 2.39/2.75 thf(fact_1860_sup_Ostrict__order__iff,axiom,
% 2.39/2.75 ( ord_less_nat
% 2.39/2.75 = ( ^ [B2: nat,A2: nat] :
% 2.39/2.75 ( ( A2
% 2.39/2.75 = ( sup_sup_nat @ A2 @ B2 ) )
% 2.39/2.75 & ( A2 != B2 ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % sup.strict_order_iff
% 2.39/2.75 thf(fact_1861_sup_Ostrict__order__iff,axiom,
% 2.39/2.75 ( ord_less_int
% 2.39/2.75 = ( ^ [B2: int,A2: int] :
% 2.39/2.75 ( ( A2
% 2.39/2.75 = ( sup_sup_int @ A2 @ B2 ) )
% 2.39/2.75 & ( A2 != B2 ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % sup.strict_order_iff
% 2.39/2.75 thf(fact_1862_sup_Ostrict__boundedE,axiom,
% 2.39/2.75 ! [B: set_nat,C: set_nat,A: set_nat] :
% 2.39/2.75 ( ( ord_less_set_nat @ ( sup_sup_set_nat @ B @ C ) @ A )
% 2.39/2.75 => ~ ( ( ord_less_set_nat @ B @ A )
% 2.39/2.75 => ~ ( ord_less_set_nat @ C @ A ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % sup.strict_boundedE
% 2.39/2.75 thf(fact_1863_sup_Ostrict__boundedE,axiom,
% 2.39/2.75 ! [B: assn,C: assn,A: assn] :
% 2.39/2.75 ( ( ord_less_assn @ ( sup_sup_assn @ B @ C ) @ A )
% 2.39/2.75 => ~ ( ( ord_less_assn @ B @ A )
% 2.39/2.75 => ~ ( ord_less_assn @ C @ A ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % sup.strict_boundedE
% 2.39/2.75 thf(fact_1864_sup_Ostrict__boundedE,axiom,
% 2.39/2.75 ! [B: rat,C: rat,A: rat] :
% 2.39/2.75 ( ( ord_less_rat @ ( sup_sup_rat @ B @ C ) @ A )
% 2.39/2.75 => ~ ( ( ord_less_rat @ B @ A )
% 2.39/2.75 => ~ ( ord_less_rat @ C @ A ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % sup.strict_boundedE
% 2.39/2.75 thf(fact_1865_sup_Ostrict__boundedE,axiom,
% 2.39/2.75 ! [B: nat,C: nat,A: nat] :
% 2.39/2.75 ( ( ord_less_nat @ ( sup_sup_nat @ B @ C ) @ A )
% 2.39/2.75 => ~ ( ( ord_less_nat @ B @ A )
% 2.39/2.75 => ~ ( ord_less_nat @ C @ A ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % sup.strict_boundedE
% 2.39/2.75 thf(fact_1866_sup_Ostrict__boundedE,axiom,
% 2.39/2.75 ! [B: int,C: int,A: int] :
% 2.39/2.75 ( ( ord_less_int @ ( sup_sup_int @ B @ C ) @ A )
% 2.39/2.75 => ~ ( ( ord_less_int @ B @ A )
% 2.39/2.75 => ~ ( ord_less_int @ C @ A ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % sup.strict_boundedE
% 2.39/2.75 thf(fact_1867_sup_Oabsorb4,axiom,
% 2.39/2.75 ! [A: set_nat,B: set_nat] :
% 2.39/2.75 ( ( ord_less_set_nat @ A @ B )
% 2.39/2.75 => ( ( sup_sup_set_nat @ A @ B )
% 2.39/2.75 = B ) ) ).
% 2.39/2.75
% 2.39/2.75 % sup.absorb4
% 2.39/2.75 thf(fact_1868_sup_Oabsorb4,axiom,
% 2.39/2.75 ! [A: assn,B: assn] :
% 2.39/2.75 ( ( ord_less_assn @ A @ B )
% 2.39/2.75 => ( ( sup_sup_assn @ A @ B )
% 2.39/2.75 = B ) ) ).
% 2.39/2.75
% 2.39/2.75 % sup.absorb4
% 2.39/2.75 thf(fact_1869_sup_Oabsorb4,axiom,
% 2.39/2.75 ! [A: rat,B: rat] :
% 2.39/2.75 ( ( ord_less_rat @ A @ B )
% 2.39/2.75 => ( ( sup_sup_rat @ A @ B )
% 2.39/2.75 = B ) ) ).
% 2.39/2.75
% 2.39/2.75 % sup.absorb4
% 2.39/2.75 thf(fact_1870_sup_Oabsorb4,axiom,
% 2.39/2.75 ! [A: nat,B: nat] :
% 2.39/2.75 ( ( ord_less_nat @ A @ B )
% 2.39/2.75 => ( ( sup_sup_nat @ A @ B )
% 2.39/2.75 = B ) ) ).
% 2.39/2.75
% 2.39/2.75 % sup.absorb4
% 2.39/2.75 thf(fact_1871_sup_Oabsorb4,axiom,
% 2.39/2.75 ! [A: int,B: int] :
% 2.39/2.75 ( ( ord_less_int @ A @ B )
% 2.39/2.75 => ( ( sup_sup_int @ A @ B )
% 2.39/2.75 = B ) ) ).
% 2.39/2.75
% 2.39/2.75 % sup.absorb4
% 2.39/2.75 thf(fact_1872_sup_Oabsorb3,axiom,
% 2.39/2.75 ! [B: set_nat,A: set_nat] :
% 2.39/2.75 ( ( ord_less_set_nat @ B @ A )
% 2.39/2.75 => ( ( sup_sup_set_nat @ A @ B )
% 2.39/2.75 = A ) ) ).
% 2.39/2.75
% 2.39/2.75 % sup.absorb3
% 2.39/2.75 thf(fact_1873_sup_Oabsorb3,axiom,
% 2.39/2.75 ! [B: assn,A: assn] :
% 2.39/2.75 ( ( ord_less_assn @ B @ A )
% 2.39/2.75 => ( ( sup_sup_assn @ A @ B )
% 2.39/2.75 = A ) ) ).
% 2.39/2.75
% 2.39/2.75 % sup.absorb3
% 2.39/2.75 thf(fact_1874_sup_Oabsorb3,axiom,
% 2.39/2.75 ! [B: rat,A: rat] :
% 2.39/2.75 ( ( ord_less_rat @ B @ A )
% 2.39/2.75 => ( ( sup_sup_rat @ A @ B )
% 2.39/2.75 = A ) ) ).
% 2.39/2.75
% 2.39/2.75 % sup.absorb3
% 2.39/2.75 thf(fact_1875_sup_Oabsorb3,axiom,
% 2.39/2.75 ! [B: nat,A: nat] :
% 2.39/2.75 ( ( ord_less_nat @ B @ A )
% 2.39/2.75 => ( ( sup_sup_nat @ A @ B )
% 2.39/2.75 = A ) ) ).
% 2.39/2.75
% 2.39/2.75 % sup.absorb3
% 2.39/2.75 thf(fact_1876_sup_Oabsorb3,axiom,
% 2.39/2.75 ! [B: int,A: int] :
% 2.39/2.75 ( ( ord_less_int @ B @ A )
% 2.39/2.75 => ( ( sup_sup_int @ A @ B )
% 2.39/2.75 = A ) ) ).
% 2.39/2.75
% 2.39/2.75 % sup.absorb3
% 2.39/2.75 thf(fact_1877_less__supI2,axiom,
% 2.39/2.75 ! [X: set_nat,B: set_nat,A: set_nat] :
% 2.39/2.75 ( ( ord_less_set_nat @ X @ B )
% 2.39/2.75 => ( ord_less_set_nat @ X @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % less_supI2
% 2.39/2.75 thf(fact_1878_less__supI2,axiom,
% 2.39/2.75 ! [X: assn,B: assn,A: assn] :
% 2.39/2.75 ( ( ord_less_assn @ X @ B )
% 2.39/2.75 => ( ord_less_assn @ X @ ( sup_sup_assn @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % less_supI2
% 2.39/2.75 thf(fact_1879_less__supI2,axiom,
% 2.39/2.75 ! [X: rat,B: rat,A: rat] :
% 2.39/2.75 ( ( ord_less_rat @ X @ B )
% 2.39/2.75 => ( ord_less_rat @ X @ ( sup_sup_rat @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % less_supI2
% 2.39/2.75 thf(fact_1880_less__supI2,axiom,
% 2.39/2.75 ! [X: nat,B: nat,A: nat] :
% 2.39/2.75 ( ( ord_less_nat @ X @ B )
% 2.39/2.75 => ( ord_less_nat @ X @ ( sup_sup_nat @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % less_supI2
% 2.39/2.75 thf(fact_1881_less__supI2,axiom,
% 2.39/2.75 ! [X: int,B: int,A: int] :
% 2.39/2.75 ( ( ord_less_int @ X @ B )
% 2.39/2.75 => ( ord_less_int @ X @ ( sup_sup_int @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % less_supI2
% 2.39/2.75 thf(fact_1882_less__supI1,axiom,
% 2.39/2.75 ! [X: set_nat,A: set_nat,B: set_nat] :
% 2.39/2.75 ( ( ord_less_set_nat @ X @ A )
% 2.39/2.75 => ( ord_less_set_nat @ X @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % less_supI1
% 2.39/2.75 thf(fact_1883_less__supI1,axiom,
% 2.39/2.75 ! [X: assn,A: assn,B: assn] :
% 2.39/2.75 ( ( ord_less_assn @ X @ A )
% 2.39/2.75 => ( ord_less_assn @ X @ ( sup_sup_assn @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % less_supI1
% 2.39/2.75 thf(fact_1884_less__supI1,axiom,
% 2.39/2.75 ! [X: rat,A: rat,B: rat] :
% 2.39/2.75 ( ( ord_less_rat @ X @ A )
% 2.39/2.75 => ( ord_less_rat @ X @ ( sup_sup_rat @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % less_supI1
% 2.39/2.75 thf(fact_1885_less__supI1,axiom,
% 2.39/2.75 ! [X: nat,A: nat,B: nat] :
% 2.39/2.75 ( ( ord_less_nat @ X @ A )
% 2.39/2.75 => ( ord_less_nat @ X @ ( sup_sup_nat @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % less_supI1
% 2.39/2.75 thf(fact_1886_less__supI1,axiom,
% 2.39/2.75 ! [X: int,A: int,B: int] :
% 2.39/2.75 ( ( ord_less_int @ X @ A )
% 2.39/2.75 => ( ord_less_int @ X @ ( sup_sup_int @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % less_supI1
% 2.39/2.75 thf(fact_1887_map__eq__Cons__conv,axiom,
% 2.39/2.75 ! [F2: produc6575502325842934193n_assn > assn,Xs: list_P8527749157015355191n_assn,Y: assn,Ys: list_assn] :
% 2.39/2.75 ( ( ( map_Pr8991440229025900053n_assn @ F2 @ Xs )
% 2.39/2.75 = ( cons_assn @ Y @ Ys ) )
% 2.39/2.75 = ( ? [Z3: produc6575502325842934193n_assn,Zs2: list_P8527749157015355191n_assn] :
% 2.39/2.75 ( ( Xs
% 2.39/2.75 = ( cons_P2971678138204555879n_assn @ Z3 @ Zs2 ) )
% 2.39/2.75 & ( ( F2 @ Z3 )
% 2.39/2.75 = Y )
% 2.39/2.75 & ( ( map_Pr8991440229025900053n_assn @ F2 @ Zs2 )
% 2.39/2.75 = Ys ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % map_eq_Cons_conv
% 2.39/2.75 thf(fact_1888_map__eq__Cons__conv,axiom,
% 2.39/2.75 ! [F2: int > int,Xs: list_int,Y: int,Ys: list_int] :
% 2.39/2.75 ( ( ( map_int_int @ F2 @ Xs )
% 2.39/2.75 = ( cons_int @ Y @ Ys ) )
% 2.39/2.75 = ( ? [Z3: int,Zs2: list_int] :
% 2.39/2.75 ( ( Xs
% 2.39/2.75 = ( cons_int @ Z3 @ Zs2 ) )
% 2.39/2.75 & ( ( F2 @ Z3 )
% 2.39/2.75 = Y )
% 2.39/2.75 & ( ( map_int_int @ F2 @ Zs2 )
% 2.39/2.75 = Ys ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % map_eq_Cons_conv
% 2.39/2.75 thf(fact_1889_map__eq__Cons__conv,axiom,
% 2.39/2.75 ! [F2: nat > int,Xs: list_nat,Y: int,Ys: list_int] :
% 2.39/2.75 ( ( ( map_nat_int @ F2 @ Xs )
% 2.39/2.75 = ( cons_int @ Y @ Ys ) )
% 2.39/2.75 = ( ? [Z3: nat,Zs2: list_nat] :
% 2.39/2.75 ( ( Xs
% 2.39/2.75 = ( cons_nat @ Z3 @ Zs2 ) )
% 2.39/2.75 & ( ( F2 @ Z3 )
% 2.39/2.75 = Y )
% 2.39/2.75 & ( ( map_nat_int @ F2 @ Zs2 )
% 2.39/2.75 = Ys ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % map_eq_Cons_conv
% 2.39/2.75 thf(fact_1890_map__eq__Cons__conv,axiom,
% 2.39/2.75 ! [F2: int > nat,Xs: list_int,Y: nat,Ys: list_nat] :
% 2.39/2.75 ( ( ( map_int_nat @ F2 @ Xs )
% 2.39/2.75 = ( cons_nat @ Y @ Ys ) )
% 2.39/2.75 = ( ? [Z3: int,Zs2: list_int] :
% 2.39/2.75 ( ( Xs
% 2.39/2.75 = ( cons_int @ Z3 @ Zs2 ) )
% 2.39/2.75 & ( ( F2 @ Z3 )
% 2.39/2.75 = Y )
% 2.39/2.75 & ( ( map_int_nat @ F2 @ Zs2 )
% 2.39/2.75 = Ys ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % map_eq_Cons_conv
% 2.39/2.75 thf(fact_1891_map__eq__Cons__conv,axiom,
% 2.39/2.75 ! [F2: nat > nat,Xs: list_nat,Y: nat,Ys: list_nat] :
% 2.39/2.75 ( ( ( map_nat_nat @ F2 @ Xs )
% 2.39/2.75 = ( cons_nat @ Y @ Ys ) )
% 2.39/2.75 = ( ? [Z3: nat,Zs2: list_nat] :
% 2.39/2.75 ( ( Xs
% 2.39/2.75 = ( cons_nat @ Z3 @ Zs2 ) )
% 2.39/2.75 & ( ( F2 @ Z3 )
% 2.39/2.75 = Y )
% 2.39/2.75 & ( ( map_nat_nat @ F2 @ Zs2 )
% 2.39/2.75 = Ys ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % map_eq_Cons_conv
% 2.39/2.75 thf(fact_1892_Cons__eq__map__conv,axiom,
% 2.39/2.75 ! [X: assn,Xs: list_assn,F2: produc6575502325842934193n_assn > assn,Ys: list_P8527749157015355191n_assn] :
% 2.39/2.75 ( ( ( cons_assn @ X @ Xs )
% 2.39/2.75 = ( map_Pr8991440229025900053n_assn @ F2 @ Ys ) )
% 2.39/2.75 = ( ? [Z3: produc6575502325842934193n_assn,Zs2: list_P8527749157015355191n_assn] :
% 2.39/2.75 ( ( Ys
% 2.39/2.75 = ( cons_P2971678138204555879n_assn @ Z3 @ Zs2 ) )
% 2.39/2.75 & ( X
% 2.39/2.75 = ( F2 @ Z3 ) )
% 2.39/2.75 & ( Xs
% 2.39/2.75 = ( map_Pr8991440229025900053n_assn @ F2 @ Zs2 ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % Cons_eq_map_conv
% 2.39/2.75 thf(fact_1893_Cons__eq__map__conv,axiom,
% 2.39/2.75 ! [X: int,Xs: list_int,F2: int > int,Ys: list_int] :
% 2.39/2.75 ( ( ( cons_int @ X @ Xs )
% 2.39/2.75 = ( map_int_int @ F2 @ Ys ) )
% 2.39/2.75 = ( ? [Z3: int,Zs2: list_int] :
% 2.39/2.75 ( ( Ys
% 2.39/2.75 = ( cons_int @ Z3 @ Zs2 ) )
% 2.39/2.75 & ( X
% 2.39/2.75 = ( F2 @ Z3 ) )
% 2.39/2.75 & ( Xs
% 2.39/2.75 = ( map_int_int @ F2 @ Zs2 ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % Cons_eq_map_conv
% 2.39/2.75 thf(fact_1894_Cons__eq__map__conv,axiom,
% 2.39/2.75 ! [X: int,Xs: list_int,F2: nat > int,Ys: list_nat] :
% 2.39/2.75 ( ( ( cons_int @ X @ Xs )
% 2.39/2.75 = ( map_nat_int @ F2 @ Ys ) )
% 2.39/2.75 = ( ? [Z3: nat,Zs2: list_nat] :
% 2.39/2.75 ( ( Ys
% 2.39/2.75 = ( cons_nat @ Z3 @ Zs2 ) )
% 2.39/2.75 & ( X
% 2.39/2.75 = ( F2 @ Z3 ) )
% 2.39/2.75 & ( Xs
% 2.39/2.75 = ( map_nat_int @ F2 @ Zs2 ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % Cons_eq_map_conv
% 2.39/2.75 thf(fact_1895_Cons__eq__map__conv,axiom,
% 2.39/2.75 ! [X: nat,Xs: list_nat,F2: int > nat,Ys: list_int] :
% 2.39/2.75 ( ( ( cons_nat @ X @ Xs )
% 2.39/2.75 = ( map_int_nat @ F2 @ Ys ) )
% 2.39/2.75 = ( ? [Z3: int,Zs2: list_int] :
% 2.39/2.75 ( ( Ys
% 2.39/2.75 = ( cons_int @ Z3 @ Zs2 ) )
% 2.39/2.75 & ( X
% 2.39/2.75 = ( F2 @ Z3 ) )
% 2.39/2.75 & ( Xs
% 2.39/2.75 = ( map_int_nat @ F2 @ Zs2 ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % Cons_eq_map_conv
% 2.39/2.75 thf(fact_1896_Cons__eq__map__conv,axiom,
% 2.39/2.75 ! [X: nat,Xs: list_nat,F2: nat > nat,Ys: list_nat] :
% 2.39/2.75 ( ( ( cons_nat @ X @ Xs )
% 2.39/2.75 = ( map_nat_nat @ F2 @ Ys ) )
% 2.39/2.75 = ( ? [Z3: nat,Zs2: list_nat] :
% 2.39/2.75 ( ( Ys
% 2.39/2.75 = ( cons_nat @ Z3 @ Zs2 ) )
% 2.39/2.75 & ( X
% 2.39/2.75 = ( F2 @ Z3 ) )
% 2.39/2.75 & ( Xs
% 2.39/2.75 = ( map_nat_nat @ F2 @ Zs2 ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % Cons_eq_map_conv
% 2.39/2.75 thf(fact_1897_map__eq__Cons__D,axiom,
% 2.39/2.75 ! [F2: produc6575502325842934193n_assn > assn,Xs: list_P8527749157015355191n_assn,Y: assn,Ys: list_assn] :
% 2.39/2.75 ( ( ( map_Pr8991440229025900053n_assn @ F2 @ Xs )
% 2.39/2.75 = ( cons_assn @ Y @ Ys ) )
% 2.39/2.75 => ? [Z2: produc6575502325842934193n_assn,Zs3: list_P8527749157015355191n_assn] :
% 2.39/2.75 ( ( Xs
% 2.39/2.75 = ( cons_P2971678138204555879n_assn @ Z2 @ Zs3 ) )
% 2.39/2.75 & ( ( F2 @ Z2 )
% 2.39/2.75 = Y )
% 2.39/2.75 & ( ( map_Pr8991440229025900053n_assn @ F2 @ Zs3 )
% 2.39/2.75 = Ys ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % map_eq_Cons_D
% 2.39/2.75 thf(fact_1898_map__eq__Cons__D,axiom,
% 2.39/2.75 ! [F2: int > int,Xs: list_int,Y: int,Ys: list_int] :
% 2.39/2.75 ( ( ( map_int_int @ F2 @ Xs )
% 2.39/2.75 = ( cons_int @ Y @ Ys ) )
% 2.39/2.75 => ? [Z2: int,Zs3: list_int] :
% 2.39/2.75 ( ( Xs
% 2.39/2.75 = ( cons_int @ Z2 @ Zs3 ) )
% 2.39/2.75 & ( ( F2 @ Z2 )
% 2.39/2.75 = Y )
% 2.39/2.75 & ( ( map_int_int @ F2 @ Zs3 )
% 2.39/2.75 = Ys ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % map_eq_Cons_D
% 2.39/2.75 thf(fact_1899_map__eq__Cons__D,axiom,
% 2.39/2.75 ! [F2: nat > int,Xs: list_nat,Y: int,Ys: list_int] :
% 2.39/2.75 ( ( ( map_nat_int @ F2 @ Xs )
% 2.39/2.75 = ( cons_int @ Y @ Ys ) )
% 2.39/2.75 => ? [Z2: nat,Zs3: list_nat] :
% 2.39/2.75 ( ( Xs
% 2.39/2.75 = ( cons_nat @ Z2 @ Zs3 ) )
% 2.39/2.75 & ( ( F2 @ Z2 )
% 2.39/2.75 = Y )
% 2.39/2.75 & ( ( map_nat_int @ F2 @ Zs3 )
% 2.39/2.75 = Ys ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % map_eq_Cons_D
% 2.39/2.75 thf(fact_1900_map__eq__Cons__D,axiom,
% 2.39/2.75 ! [F2: int > nat,Xs: list_int,Y: nat,Ys: list_nat] :
% 2.39/2.75 ( ( ( map_int_nat @ F2 @ Xs )
% 2.39/2.75 = ( cons_nat @ Y @ Ys ) )
% 2.39/2.75 => ? [Z2: int,Zs3: list_int] :
% 2.39/2.75 ( ( Xs
% 2.39/2.75 = ( cons_int @ Z2 @ Zs3 ) )
% 2.39/2.75 & ( ( F2 @ Z2 )
% 2.39/2.75 = Y )
% 2.39/2.75 & ( ( map_int_nat @ F2 @ Zs3 )
% 2.39/2.75 = Ys ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % map_eq_Cons_D
% 2.39/2.75 thf(fact_1901_map__eq__Cons__D,axiom,
% 2.39/2.75 ! [F2: nat > nat,Xs: list_nat,Y: nat,Ys: list_nat] :
% 2.39/2.75 ( ( ( map_nat_nat @ F2 @ Xs )
% 2.39/2.75 = ( cons_nat @ Y @ Ys ) )
% 2.39/2.75 => ? [Z2: nat,Zs3: list_nat] :
% 2.39/2.75 ( ( Xs
% 2.39/2.75 = ( cons_nat @ Z2 @ Zs3 ) )
% 2.39/2.75 & ( ( F2 @ Z2 )
% 2.39/2.75 = Y )
% 2.39/2.75 & ( ( map_nat_nat @ F2 @ Zs3 )
% 2.39/2.75 = Ys ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % map_eq_Cons_D
% 2.39/2.75 thf(fact_1902_Cons__eq__map__D,axiom,
% 2.39/2.75 ! [X: assn,Xs: list_assn,F2: produc6575502325842934193n_assn > assn,Ys: list_P8527749157015355191n_assn] :
% 2.39/2.75 ( ( ( cons_assn @ X @ Xs )
% 2.39/2.75 = ( map_Pr8991440229025900053n_assn @ F2 @ Ys ) )
% 2.39/2.75 => ? [Z2: produc6575502325842934193n_assn,Zs3: list_P8527749157015355191n_assn] :
% 2.39/2.75 ( ( Ys
% 2.39/2.75 = ( cons_P2971678138204555879n_assn @ Z2 @ Zs3 ) )
% 2.39/2.75 & ( X
% 2.39/2.75 = ( F2 @ Z2 ) )
% 2.39/2.75 & ( Xs
% 2.39/2.75 = ( map_Pr8991440229025900053n_assn @ F2 @ Zs3 ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % Cons_eq_map_D
% 2.39/2.75 thf(fact_1903_Cons__eq__map__D,axiom,
% 2.39/2.75 ! [X: int,Xs: list_int,F2: int > int,Ys: list_int] :
% 2.39/2.75 ( ( ( cons_int @ X @ Xs )
% 2.39/2.75 = ( map_int_int @ F2 @ Ys ) )
% 2.39/2.75 => ? [Z2: int,Zs3: list_int] :
% 2.39/2.75 ( ( Ys
% 2.39/2.75 = ( cons_int @ Z2 @ Zs3 ) )
% 2.39/2.75 & ( X
% 2.39/2.75 = ( F2 @ Z2 ) )
% 2.39/2.75 & ( Xs
% 2.39/2.75 = ( map_int_int @ F2 @ Zs3 ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % Cons_eq_map_D
% 2.39/2.75 thf(fact_1904_Cons__eq__map__D,axiom,
% 2.39/2.75 ! [X: int,Xs: list_int,F2: nat > int,Ys: list_nat] :
% 2.39/2.75 ( ( ( cons_int @ X @ Xs )
% 2.39/2.75 = ( map_nat_int @ F2 @ Ys ) )
% 2.39/2.75 => ? [Z2: nat,Zs3: list_nat] :
% 2.39/2.75 ( ( Ys
% 2.39/2.75 = ( cons_nat @ Z2 @ Zs3 ) )
% 2.39/2.75 & ( X
% 2.39/2.75 = ( F2 @ Z2 ) )
% 2.39/2.75 & ( Xs
% 2.39/2.75 = ( map_nat_int @ F2 @ Zs3 ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % Cons_eq_map_D
% 2.39/2.75 thf(fact_1905_Cons__eq__map__D,axiom,
% 2.39/2.75 ! [X: nat,Xs: list_nat,F2: int > nat,Ys: list_int] :
% 2.39/2.75 ( ( ( cons_nat @ X @ Xs )
% 2.39/2.75 = ( map_int_nat @ F2 @ Ys ) )
% 2.39/2.75 => ? [Z2: int,Zs3: list_int] :
% 2.39/2.75 ( ( Ys
% 2.39/2.75 = ( cons_int @ Z2 @ Zs3 ) )
% 2.39/2.75 & ( X
% 2.39/2.75 = ( F2 @ Z2 ) )
% 2.39/2.75 & ( Xs
% 2.39/2.75 = ( map_int_nat @ F2 @ Zs3 ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % Cons_eq_map_D
% 2.39/2.75 thf(fact_1906_Cons__eq__map__D,axiom,
% 2.39/2.75 ! [X: nat,Xs: list_nat,F2: nat > nat,Ys: list_nat] :
% 2.39/2.75 ( ( ( cons_nat @ X @ Xs )
% 2.39/2.75 = ( map_nat_nat @ F2 @ Ys ) )
% 2.39/2.75 => ? [Z2: nat,Zs3: list_nat] :
% 2.39/2.75 ( ( Ys
% 2.39/2.75 = ( cons_nat @ Z2 @ Zs3 ) )
% 2.39/2.75 & ( X
% 2.39/2.75 = ( F2 @ Z2 ) )
% 2.39/2.75 & ( Xs
% 2.39/2.75 = ( map_nat_nat @ F2 @ Zs3 ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % Cons_eq_map_D
% 2.39/2.75 thf(fact_1907_list_Osimps_I9_J,axiom,
% 2.39/2.75 ! [F2: produc6575502325842934193n_assn > assn,X21: produc6575502325842934193n_assn,X22: list_P8527749157015355191n_assn] :
% 2.39/2.75 ( ( map_Pr8991440229025900053n_assn @ F2 @ ( cons_P2971678138204555879n_assn @ X21 @ X22 ) )
% 2.39/2.75 = ( cons_assn @ ( F2 @ X21 ) @ ( map_Pr8991440229025900053n_assn @ F2 @ X22 ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % list.simps(9)
% 2.39/2.75 thf(fact_1908_list_Osimps_I9_J,axiom,
% 2.39/2.75 ! [F2: int > int,X21: int,X22: list_int] :
% 2.39/2.75 ( ( map_int_int @ F2 @ ( cons_int @ X21 @ X22 ) )
% 2.39/2.75 = ( cons_int @ ( F2 @ X21 ) @ ( map_int_int @ F2 @ X22 ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % list.simps(9)
% 2.39/2.75 thf(fact_1909_list_Osimps_I9_J,axiom,
% 2.39/2.75 ! [F2: int > nat,X21: int,X22: list_int] :
% 2.39/2.75 ( ( map_int_nat @ F2 @ ( cons_int @ X21 @ X22 ) )
% 2.39/2.75 = ( cons_nat @ ( F2 @ X21 ) @ ( map_int_nat @ F2 @ X22 ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % list.simps(9)
% 2.39/2.75 thf(fact_1910_list_Osimps_I9_J,axiom,
% 2.39/2.75 ! [F2: nat > int,X21: nat,X22: list_nat] :
% 2.39/2.75 ( ( map_nat_int @ F2 @ ( cons_nat @ X21 @ X22 ) )
% 2.39/2.75 = ( cons_int @ ( F2 @ X21 ) @ ( map_nat_int @ F2 @ X22 ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % list.simps(9)
% 2.39/2.75 thf(fact_1911_list_Osimps_I9_J,axiom,
% 2.39/2.75 ! [F2: nat > nat,X21: nat,X22: list_nat] :
% 2.39/2.75 ( ( map_nat_nat @ F2 @ ( cons_nat @ X21 @ X22 ) )
% 2.39/2.75 = ( cons_nat @ ( F2 @ X21 ) @ ( map_nat_nat @ F2 @ X22 ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % list.simps(9)
% 2.39/2.75 thf(fact_1912_splice_Osimps_I2_J,axiom,
% 2.39/2.75 ! [X: int,Xs: list_int,Ys: list_int] :
% 2.39/2.75 ( ( splice_int @ ( cons_int @ X @ Xs ) @ Ys )
% 2.39/2.75 = ( cons_int @ X @ ( splice_int @ Ys @ Xs ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % splice.simps(2)
% 2.39/2.75 thf(fact_1913_splice_Osimps_I2_J,axiom,
% 2.39/2.75 ! [X: nat,Xs: list_nat,Ys: list_nat] :
% 2.39/2.75 ( ( splice_nat @ ( cons_nat @ X @ Xs ) @ Ys )
% 2.39/2.75 = ( cons_nat @ X @ ( splice_nat @ Ys @ Xs ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % splice.simps(2)
% 2.39/2.75 thf(fact_1914_null__rec_I1_J,axiom,
% 2.39/2.75 ! [X: int,Xs: list_int] :
% 2.39/2.75 ~ ( null_int @ ( cons_int @ X @ Xs ) ) ).
% 2.39/2.75
% 2.39/2.75 % null_rec(1)
% 2.39/2.75 thf(fact_1915_null__rec_I1_J,axiom,
% 2.39/2.75 ! [X: nat,Xs: list_nat] :
% 2.39/2.75 ~ ( null_nat @ ( cons_nat @ X @ Xs ) ) ).
% 2.39/2.75
% 2.39/2.75 % null_rec(1)
% 2.39/2.75 thf(fact_1916_member__rec_I1_J,axiom,
% 2.39/2.75 ! [X: int,Xs: list_int,Y: int] :
% 2.39/2.75 ( ( member_int @ ( cons_int @ X @ Xs ) @ Y )
% 2.39/2.75 = ( ( X = Y )
% 2.39/2.75 | ( member_int @ Xs @ Y ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % member_rec(1)
% 2.39/2.75 thf(fact_1917_member__rec_I1_J,axiom,
% 2.39/2.75 ! [X: nat,Xs: list_nat,Y: nat] :
% 2.39/2.75 ( ( member_nat @ ( cons_nat @ X @ Xs ) @ Y )
% 2.39/2.75 = ( ( X = Y )
% 2.39/2.75 | ( member_nat @ Xs @ Y ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % member_rec(1)
% 2.39/2.75 thf(fact_1918_mult__neg__neg,axiom,
% 2.39/2.75 ! [A: code_integer,B: code_integer] :
% 2.39/2.75 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 2.39/2.75 => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 2.39/2.75 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_neg_neg
% 2.39/2.75 thf(fact_1919_mult__neg__neg,axiom,
% 2.39/2.75 ! [A: rat,B: rat] :
% 2.39/2.75 ( ( ord_less_rat @ A @ zero_zero_rat )
% 2.39/2.75 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 2.39/2.75 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_neg_neg
% 2.39/2.75 thf(fact_1920_mult__neg__neg,axiom,
% 2.39/2.75 ! [A: int,B: int] :
% 2.39/2.75 ( ( ord_less_int @ A @ zero_zero_int )
% 2.39/2.75 => ( ( ord_less_int @ B @ zero_zero_int )
% 2.39/2.75 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_neg_neg
% 2.39/2.75 thf(fact_1921_not__square__less__zero,axiom,
% 2.39/2.75 ! [A: code_integer] :
% 2.39/2.75 ~ ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ A ) @ zero_z3403309356797280102nteger ) ).
% 2.39/2.75
% 2.39/2.75 % not_square_less_zero
% 2.39/2.75 thf(fact_1922_not__square__less__zero,axiom,
% 2.39/2.75 ! [A: rat] :
% 2.39/2.75 ~ ( ord_less_rat @ ( times_times_rat @ A @ A ) @ zero_zero_rat ) ).
% 2.39/2.75
% 2.39/2.75 % not_square_less_zero
% 2.39/2.75 thf(fact_1923_not__square__less__zero,axiom,
% 2.39/2.75 ! [A: int] :
% 2.39/2.75 ~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ) ).
% 2.39/2.75
% 2.39/2.75 % not_square_less_zero
% 2.39/2.75 thf(fact_1924_mult__less__0__iff,axiom,
% 2.39/2.75 ! [A: code_integer,B: code_integer] :
% 2.39/2.75 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger )
% 2.39/2.75 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.75 & ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger ) )
% 2.39/2.75 | ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 2.39/2.75 & ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_less_0_iff
% 2.39/2.75 thf(fact_1925_mult__less__0__iff,axiom,
% 2.39/2.75 ! [A: rat,B: rat] :
% 2.39/2.75 ( ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 2.39/2.75 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 2.39/2.75 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 2.39/2.75 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 2.39/2.75 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_less_0_iff
% 2.39/2.75 thf(fact_1926_mult__less__0__iff,axiom,
% 2.39/2.75 ! [A: int,B: int] :
% 2.39/2.75 ( ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 2.39/2.75 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 2.39/2.75 & ( ord_less_int @ B @ zero_zero_int ) )
% 2.39/2.75 | ( ( ord_less_int @ A @ zero_zero_int )
% 2.39/2.75 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_less_0_iff
% 2.39/2.75 thf(fact_1927_mult__neg__pos,axiom,
% 2.39/2.75 ! [A: code_natural,B: code_natural] :
% 2.39/2.75 ( ( ord_le5570908160329646204atural @ A @ zero_z2226904508553997617atural )
% 2.39/2.75 => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ B )
% 2.39/2.75 => ( ord_le5570908160329646204atural @ ( times_2397367101498566445atural @ A @ B ) @ zero_z2226904508553997617atural ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_neg_pos
% 2.39/2.75 thf(fact_1928_mult__neg__pos,axiom,
% 2.39/2.75 ! [A: code_integer,B: code_integer] :
% 2.39/2.75 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 2.39/2.75 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 2.39/2.75 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_neg_pos
% 2.39/2.75 thf(fact_1929_mult__neg__pos,axiom,
% 2.39/2.75 ! [A: rat,B: rat] :
% 2.39/2.75 ( ( ord_less_rat @ A @ zero_zero_rat )
% 2.39/2.75 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 2.39/2.75 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_neg_pos
% 2.39/2.75 thf(fact_1930_mult__neg__pos,axiom,
% 2.39/2.75 ! [A: nat,B: nat] :
% 2.39/2.75 ( ( ord_less_nat @ A @ zero_zero_nat )
% 2.39/2.75 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 2.39/2.75 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_neg_pos
% 2.39/2.75 thf(fact_1931_mult__neg__pos,axiom,
% 2.39/2.75 ! [A: int,B: int] :
% 2.39/2.75 ( ( ord_less_int @ A @ zero_zero_int )
% 2.39/2.75 => ( ( ord_less_int @ zero_zero_int @ B )
% 2.39/2.75 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_neg_pos
% 2.39/2.75 thf(fact_1932_mult__pos__neg,axiom,
% 2.39/2.75 ! [A: code_natural,B: code_natural] :
% 2.39/2.75 ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A )
% 2.39/2.75 => ( ( ord_le5570908160329646204atural @ B @ zero_z2226904508553997617atural )
% 2.39/2.75 => ( ord_le5570908160329646204atural @ ( times_2397367101498566445atural @ A @ B ) @ zero_z2226904508553997617atural ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_pos_neg
% 2.39/2.75 thf(fact_1933_mult__pos__neg,axiom,
% 2.39/2.75 ! [A: code_integer,B: code_integer] :
% 2.39/2.75 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.75 => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 2.39/2.75 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_pos_neg
% 2.39/2.75 thf(fact_1934_mult__pos__neg,axiom,
% 2.39/2.75 ! [A: rat,B: rat] :
% 2.39/2.75 ( ( ord_less_rat @ zero_zero_rat @ A )
% 2.39/2.75 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 2.39/2.75 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_pos_neg
% 2.39/2.75 thf(fact_1935_mult__pos__neg,axiom,
% 2.39/2.75 ! [A: nat,B: nat] :
% 2.39/2.75 ( ( ord_less_nat @ zero_zero_nat @ A )
% 2.39/2.75 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 2.39/2.75 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_pos_neg
% 2.39/2.75 thf(fact_1936_mult__pos__neg,axiom,
% 2.39/2.75 ! [A: int,B: int] :
% 2.39/2.75 ( ( ord_less_int @ zero_zero_int @ A )
% 2.39/2.75 => ( ( ord_less_int @ B @ zero_zero_int )
% 2.39/2.75 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_pos_neg
% 2.39/2.75 thf(fact_1937_mult__pos__pos,axiom,
% 2.39/2.75 ! [A: code_natural,B: code_natural] :
% 2.39/2.75 ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A )
% 2.39/2.75 => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ B )
% 2.39/2.75 => ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ ( times_2397367101498566445atural @ A @ B ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_pos_pos
% 2.39/2.75 thf(fact_1938_mult__pos__pos,axiom,
% 2.39/2.75 ! [A: code_integer,B: code_integer] :
% 2.39/2.75 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.75 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 2.39/2.75 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_pos_pos
% 2.39/2.75 thf(fact_1939_mult__pos__pos,axiom,
% 2.39/2.75 ! [A: rat,B: rat] :
% 2.39/2.75 ( ( ord_less_rat @ zero_zero_rat @ A )
% 2.39/2.75 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 2.39/2.75 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_pos_pos
% 2.39/2.75 thf(fact_1940_mult__pos__pos,axiom,
% 2.39/2.75 ! [A: nat,B: nat] :
% 2.39/2.75 ( ( ord_less_nat @ zero_zero_nat @ A )
% 2.39/2.75 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 2.39/2.75 => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_pos_pos
% 2.39/2.75 thf(fact_1941_mult__pos__pos,axiom,
% 2.39/2.75 ! [A: int,B: int] :
% 2.39/2.75 ( ( ord_less_int @ zero_zero_int @ A )
% 2.39/2.75 => ( ( ord_less_int @ zero_zero_int @ B )
% 2.39/2.75 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_pos_pos
% 2.39/2.75 thf(fact_1942_mult__pos__neg2,axiom,
% 2.39/2.75 ! [A: code_natural,B: code_natural] :
% 2.39/2.75 ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A )
% 2.39/2.75 => ( ( ord_le5570908160329646204atural @ B @ zero_z2226904508553997617atural )
% 2.39/2.75 => ( ord_le5570908160329646204atural @ ( times_2397367101498566445atural @ B @ A ) @ zero_z2226904508553997617atural ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_pos_neg2
% 2.39/2.75 thf(fact_1943_mult__pos__neg2,axiom,
% 2.39/2.75 ! [A: code_integer,B: code_integer] :
% 2.39/2.75 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.75 => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 2.39/2.75 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ B @ A ) @ zero_z3403309356797280102nteger ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_pos_neg2
% 2.39/2.75 thf(fact_1944_mult__pos__neg2,axiom,
% 2.39/2.75 ! [A: rat,B: rat] :
% 2.39/2.75 ( ( ord_less_rat @ zero_zero_rat @ A )
% 2.39/2.75 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 2.39/2.75 => ( ord_less_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_pos_neg2
% 2.39/2.75 thf(fact_1945_mult__pos__neg2,axiom,
% 2.39/2.75 ! [A: nat,B: nat] :
% 2.39/2.75 ( ( ord_less_nat @ zero_zero_nat @ A )
% 2.39/2.75 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 2.39/2.75 => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_pos_neg2
% 2.39/2.75 thf(fact_1946_mult__pos__neg2,axiom,
% 2.39/2.75 ! [A: int,B: int] :
% 2.39/2.75 ( ( ord_less_int @ zero_zero_int @ A )
% 2.39/2.75 => ( ( ord_less_int @ B @ zero_zero_int )
% 2.39/2.75 => ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_pos_neg2
% 2.39/2.75 thf(fact_1947_zero__less__mult__iff,axiom,
% 2.39/2.75 ! [A: code_integer,B: code_integer] :
% 2.39/2.75 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) )
% 2.39/2.75 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.75 & ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) )
% 2.39/2.75 | ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 2.39/2.75 & ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % zero_less_mult_iff
% 2.39/2.75 thf(fact_1948_zero__less__mult__iff,axiom,
% 2.39/2.75 ! [A: rat,B: rat] :
% 2.39/2.75 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 2.39/2.75 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 2.39/2.75 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 2.39/2.75 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 2.39/2.75 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % zero_less_mult_iff
% 2.39/2.75 thf(fact_1949_zero__less__mult__iff,axiom,
% 2.39/2.75 ! [A: int,B: int] :
% 2.39/2.75 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 2.39/2.75 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 2.39/2.75 & ( ord_less_int @ zero_zero_int @ B ) )
% 2.39/2.75 | ( ( ord_less_int @ A @ zero_zero_int )
% 2.39/2.75 & ( ord_less_int @ B @ zero_zero_int ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % zero_less_mult_iff
% 2.39/2.75 thf(fact_1950_zero__less__mult__pos,axiom,
% 2.39/2.75 ! [A: code_natural,B: code_natural] :
% 2.39/2.75 ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ ( times_2397367101498566445atural @ A @ B ) )
% 2.39/2.75 => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A )
% 2.39/2.75 => ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % zero_less_mult_pos
% 2.39/2.75 thf(fact_1951_zero__less__mult__pos,axiom,
% 2.39/2.75 ! [A: code_integer,B: code_integer] :
% 2.39/2.75 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) )
% 2.39/2.75 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.75 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % zero_less_mult_pos
% 2.39/2.75 thf(fact_1952_zero__less__mult__pos,axiom,
% 2.39/2.75 ! [A: rat,B: rat] :
% 2.39/2.75 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 2.39/2.75 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 2.39/2.75 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % zero_less_mult_pos
% 2.39/2.75 thf(fact_1953_zero__less__mult__pos,axiom,
% 2.39/2.75 ! [A: nat,B: nat] :
% 2.39/2.75 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 2.39/2.75 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 2.39/2.75 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % zero_less_mult_pos
% 2.39/2.75 thf(fact_1954_zero__less__mult__pos,axiom,
% 2.39/2.75 ! [A: int,B: int] :
% 2.39/2.75 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 2.39/2.75 => ( ( ord_less_int @ zero_zero_int @ A )
% 2.39/2.75 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % zero_less_mult_pos
% 2.39/2.75 thf(fact_1955_zero__less__mult__pos2,axiom,
% 2.39/2.75 ! [B: code_natural,A: code_natural] :
% 2.39/2.75 ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ ( times_2397367101498566445atural @ B @ A ) )
% 2.39/2.75 => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A )
% 2.39/2.75 => ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % zero_less_mult_pos2
% 2.39/2.75 thf(fact_1956_zero__less__mult__pos2,axiom,
% 2.39/2.75 ! [B: code_integer,A: code_integer] :
% 2.39/2.75 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ B @ A ) )
% 2.39/2.75 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.75 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % zero_less_mult_pos2
% 2.39/2.75 thf(fact_1957_zero__less__mult__pos2,axiom,
% 2.39/2.75 ! [B: rat,A: rat] :
% 2.39/2.75 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B @ A ) )
% 2.39/2.75 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 2.39/2.75 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % zero_less_mult_pos2
% 2.39/2.75 thf(fact_1958_zero__less__mult__pos2,axiom,
% 2.39/2.75 ! [B: nat,A: nat] :
% 2.39/2.75 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 2.39/2.75 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 2.39/2.75 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % zero_less_mult_pos2
% 2.39/2.75 thf(fact_1959_zero__less__mult__pos2,axiom,
% 2.39/2.75 ! [B: int,A: int] :
% 2.39/2.75 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
% 2.39/2.75 => ( ( ord_less_int @ zero_zero_int @ A )
% 2.39/2.75 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % zero_less_mult_pos2
% 2.39/2.75 thf(fact_1960_mult__less__cancel__left__neg,axiom,
% 2.39/2.75 ! [C: code_integer,A: code_integer,B: code_integer] :
% 2.39/2.75 ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 2.39/2.75 => ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 2.39/2.75 = ( ord_le6747313008572928689nteger @ B @ A ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_less_cancel_left_neg
% 2.39/2.75 thf(fact_1961_mult__less__cancel__left__neg,axiom,
% 2.39/2.75 ! [C: rat,A: rat,B: rat] :
% 2.39/2.75 ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.75 => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 2.39/2.75 = ( ord_less_rat @ B @ A ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_less_cancel_left_neg
% 2.39/2.75 thf(fact_1962_mult__less__cancel__left__neg,axiom,
% 2.39/2.75 ! [C: int,A: int,B: int] :
% 2.39/2.75 ( ( ord_less_int @ C @ zero_zero_int )
% 2.39/2.75 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 2.39/2.75 = ( ord_less_int @ B @ A ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_less_cancel_left_neg
% 2.39/2.75 thf(fact_1963_mult__less__cancel__left__pos,axiom,
% 2.39/2.75 ! [C: code_integer,A: code_integer,B: code_integer] :
% 2.39/2.75 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 2.39/2.75 => ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 2.39/2.75 = ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_less_cancel_left_pos
% 2.39/2.75 thf(fact_1964_mult__less__cancel__left__pos,axiom,
% 2.39/2.75 ! [C: rat,A: rat,B: rat] :
% 2.39/2.75 ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.75 => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 2.39/2.75 = ( ord_less_rat @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_less_cancel_left_pos
% 2.39/2.75 thf(fact_1965_mult__less__cancel__left__pos,axiom,
% 2.39/2.75 ! [C: int,A: int,B: int] :
% 2.39/2.75 ( ( ord_less_int @ zero_zero_int @ C )
% 2.39/2.75 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 2.39/2.75 = ( ord_less_int @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_less_cancel_left_pos
% 2.39/2.75 thf(fact_1966_mult__strict__left__mono__neg,axiom,
% 2.39/2.75 ! [B: code_integer,A: code_integer,C: code_integer] :
% 2.39/2.75 ( ( ord_le6747313008572928689nteger @ B @ A )
% 2.39/2.75 => ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 2.39/2.75 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_strict_left_mono_neg
% 2.39/2.75 thf(fact_1967_mult__strict__left__mono__neg,axiom,
% 2.39/2.75 ! [B: rat,A: rat,C: rat] :
% 2.39/2.75 ( ( ord_less_rat @ B @ A )
% 2.39/2.75 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.75 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_strict_left_mono_neg
% 2.39/2.75 thf(fact_1968_mult__strict__left__mono__neg,axiom,
% 2.39/2.75 ! [B: int,A: int,C: int] :
% 2.39/2.75 ( ( ord_less_int @ B @ A )
% 2.39/2.75 => ( ( ord_less_int @ C @ zero_zero_int )
% 2.39/2.75 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_strict_left_mono_neg
% 2.39/2.75 thf(fact_1969_mult__strict__left__mono,axiom,
% 2.39/2.75 ! [A: code_natural,B: code_natural,C: code_natural] :
% 2.39/2.75 ( ( ord_le5570908160329646204atural @ A @ B )
% 2.39/2.75 => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ C )
% 2.39/2.75 => ( ord_le5570908160329646204atural @ ( times_2397367101498566445atural @ C @ A ) @ ( times_2397367101498566445atural @ C @ B ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_strict_left_mono
% 2.39/2.75 thf(fact_1970_mult__strict__left__mono,axiom,
% 2.39/2.75 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.75 ( ( ord_le6747313008572928689nteger @ A @ B )
% 2.39/2.75 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 2.39/2.75 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_strict_left_mono
% 2.39/2.75 thf(fact_1971_mult__strict__left__mono,axiom,
% 2.39/2.75 ! [A: rat,B: rat,C: rat] :
% 2.39/2.75 ( ( ord_less_rat @ A @ B )
% 2.39/2.75 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.75 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_strict_left_mono
% 2.39/2.75 thf(fact_1972_mult__strict__left__mono,axiom,
% 2.39/2.75 ! [A: nat,B: nat,C: nat] :
% 2.39/2.75 ( ( ord_less_nat @ A @ B )
% 2.39/2.75 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 2.39/2.75 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_strict_left_mono
% 2.39/2.75 thf(fact_1973_mult__strict__left__mono,axiom,
% 2.39/2.75 ! [A: int,B: int,C: int] :
% 2.39/2.75 ( ( ord_less_int @ A @ B )
% 2.39/2.75 => ( ( ord_less_int @ zero_zero_int @ C )
% 2.39/2.75 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_strict_left_mono
% 2.39/2.75 thf(fact_1974_mult__less__cancel__left__disj,axiom,
% 2.39/2.75 ! [C: code_integer,A: code_integer,B: code_integer] :
% 2.39/2.75 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 2.39/2.75 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 2.39/2.75 & ( ord_le6747313008572928689nteger @ A @ B ) )
% 2.39/2.75 | ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 2.39/2.75 & ( ord_le6747313008572928689nteger @ B @ A ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_less_cancel_left_disj
% 2.39/2.75 thf(fact_1975_mult__less__cancel__left__disj,axiom,
% 2.39/2.75 ! [C: rat,A: rat,B: rat] :
% 2.39/2.75 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 2.39/2.75 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.75 & ( ord_less_rat @ A @ B ) )
% 2.39/2.75 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.75 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_less_cancel_left_disj
% 2.39/2.75 thf(fact_1976_mult__less__cancel__left__disj,axiom,
% 2.39/2.75 ! [C: int,A: int,B: int] :
% 2.39/2.75 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 2.39/2.75 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 2.39/2.75 & ( ord_less_int @ A @ B ) )
% 2.39/2.75 | ( ( ord_less_int @ C @ zero_zero_int )
% 2.39/2.75 & ( ord_less_int @ B @ A ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_less_cancel_left_disj
% 2.39/2.75 thf(fact_1977_mult__strict__right__mono__neg,axiom,
% 2.39/2.75 ! [B: code_integer,A: code_integer,C: code_integer] :
% 2.39/2.75 ( ( ord_le6747313008572928689nteger @ B @ A )
% 2.39/2.75 => ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 2.39/2.75 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_strict_right_mono_neg
% 2.39/2.75 thf(fact_1978_mult__strict__right__mono__neg,axiom,
% 2.39/2.75 ! [B: rat,A: rat,C: rat] :
% 2.39/2.75 ( ( ord_less_rat @ B @ A )
% 2.39/2.75 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.75 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_strict_right_mono_neg
% 2.39/2.75 thf(fact_1979_mult__strict__right__mono__neg,axiom,
% 2.39/2.75 ! [B: int,A: int,C: int] :
% 2.39/2.75 ( ( ord_less_int @ B @ A )
% 2.39/2.75 => ( ( ord_less_int @ C @ zero_zero_int )
% 2.39/2.75 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_strict_right_mono_neg
% 2.39/2.75 thf(fact_1980_mult__strict__right__mono,axiom,
% 2.39/2.75 ! [A: code_natural,B: code_natural,C: code_natural] :
% 2.39/2.75 ( ( ord_le5570908160329646204atural @ A @ B )
% 2.39/2.75 => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ C )
% 2.39/2.75 => ( ord_le5570908160329646204atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ C ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_strict_right_mono
% 2.39/2.75 thf(fact_1981_mult__strict__right__mono,axiom,
% 2.39/2.75 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.75 ( ( ord_le6747313008572928689nteger @ A @ B )
% 2.39/2.75 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 2.39/2.75 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_strict_right_mono
% 2.39/2.75 thf(fact_1982_mult__strict__right__mono,axiom,
% 2.39/2.75 ! [A: rat,B: rat,C: rat] :
% 2.39/2.75 ( ( ord_less_rat @ A @ B )
% 2.39/2.75 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.75 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_strict_right_mono
% 2.39/2.75 thf(fact_1983_mult__strict__right__mono,axiom,
% 2.39/2.75 ! [A: nat,B: nat,C: nat] :
% 2.39/2.75 ( ( ord_less_nat @ A @ B )
% 2.39/2.75 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 2.39/2.75 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_strict_right_mono
% 2.39/2.75 thf(fact_1984_mult__strict__right__mono,axiom,
% 2.39/2.75 ! [A: int,B: int,C: int] :
% 2.39/2.75 ( ( ord_less_int @ A @ B )
% 2.39/2.75 => ( ( ord_less_int @ zero_zero_int @ C )
% 2.39/2.75 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_strict_right_mono
% 2.39/2.75 thf(fact_1985_mult__less__cancel__right__disj,axiom,
% 2.39/2.75 ! [A: code_integer,C: code_integer,B: code_integer] :
% 2.39/2.75 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 2.39/2.75 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 2.39/2.75 & ( ord_le6747313008572928689nteger @ A @ B ) )
% 2.39/2.75 | ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 2.39/2.75 & ( ord_le6747313008572928689nteger @ B @ A ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_less_cancel_right_disj
% 2.39/2.75 thf(fact_1986_mult__less__cancel__right__disj,axiom,
% 2.39/2.75 ! [A: rat,C: rat,B: rat] :
% 2.39/2.75 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 2.39/2.75 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.75 & ( ord_less_rat @ A @ B ) )
% 2.39/2.75 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.75 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_less_cancel_right_disj
% 2.39/2.75 thf(fact_1987_mult__less__cancel__right__disj,axiom,
% 2.39/2.75 ! [A: int,C: int,B: int] :
% 2.39/2.75 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 2.39/2.75 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 2.39/2.75 & ( ord_less_int @ A @ B ) )
% 2.39/2.75 | ( ( ord_less_int @ C @ zero_zero_int )
% 2.39/2.75 & ( ord_less_int @ B @ A ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_less_cancel_right_disj
% 2.39/2.75 thf(fact_1988_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 2.39/2.75 ! [A: code_natural,B: code_natural,C: code_natural] :
% 2.39/2.75 ( ( ord_le5570908160329646204atural @ A @ B )
% 2.39/2.75 => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ C )
% 2.39/2.75 => ( ord_le5570908160329646204atural @ ( times_2397367101498566445atural @ C @ A ) @ ( times_2397367101498566445atural @ C @ B ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 2.39/2.75 thf(fact_1989_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 2.39/2.75 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.75 ( ( ord_le6747313008572928689nteger @ A @ B )
% 2.39/2.75 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 2.39/2.75 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 2.39/2.75 thf(fact_1990_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 2.39/2.75 ! [A: rat,B: rat,C: rat] :
% 2.39/2.75 ( ( ord_less_rat @ A @ B )
% 2.39/2.75 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.75 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 2.39/2.75 thf(fact_1991_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 2.39/2.75 ! [A: nat,B: nat,C: nat] :
% 2.39/2.75 ( ( ord_less_nat @ A @ B )
% 2.39/2.75 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 2.39/2.75 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 2.39/2.75 thf(fact_1992_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 2.39/2.75 ! [A: int,B: int,C: int] :
% 2.39/2.75 ( ( ord_less_int @ A @ B )
% 2.39/2.75 => ( ( ord_less_int @ zero_zero_int @ C )
% 2.39/2.75 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 2.39/2.75 thf(fact_1993_less__numeral__extra_I1_J,axiom,
% 2.39/2.75 ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ one_one_Code_natural ).
% 2.39/2.75
% 2.39/2.75 % less_numeral_extra(1)
% 2.39/2.75 thf(fact_1994_less__numeral__extra_I1_J,axiom,
% 2.39/2.75 ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 2.39/2.75
% 2.39/2.75 % less_numeral_extra(1)
% 2.39/2.75 thf(fact_1995_less__numeral__extra_I1_J,axiom,
% 2.39/2.75 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 2.39/2.75
% 2.39/2.75 % less_numeral_extra(1)
% 2.39/2.75 thf(fact_1996_less__numeral__extra_I1_J,axiom,
% 2.39/2.75 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 2.39/2.75
% 2.39/2.75 % less_numeral_extra(1)
% 2.39/2.75 thf(fact_1997_less__numeral__extra_I1_J,axiom,
% 2.39/2.75 ord_less_int @ zero_zero_int @ one_one_int ).
% 2.39/2.75
% 2.39/2.75 % less_numeral_extra(1)
% 2.39/2.75 thf(fact_1998_zero__less__one,axiom,
% 2.39/2.75 ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ one_one_Code_natural ).
% 2.39/2.75
% 2.39/2.75 % zero_less_one
% 2.39/2.75 thf(fact_1999_zero__less__one,axiom,
% 2.39/2.75 ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 2.39/2.75
% 2.39/2.75 % zero_less_one
% 2.39/2.75 thf(fact_2000_zero__less__one,axiom,
% 2.39/2.75 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 2.39/2.75
% 2.39/2.75 % zero_less_one
% 2.39/2.75 thf(fact_2001_zero__less__one,axiom,
% 2.39/2.75 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 2.39/2.75
% 2.39/2.75 % zero_less_one
% 2.39/2.75 thf(fact_2002_zero__less__one,axiom,
% 2.39/2.75 ord_less_int @ zero_zero_int @ one_one_int ).
% 2.39/2.75
% 2.39/2.75 % zero_less_one
% 2.39/2.75 thf(fact_2003_not__one__less__zero,axiom,
% 2.39/2.75 ~ ( ord_le5570908160329646204atural @ one_one_Code_natural @ zero_z2226904508553997617atural ) ).
% 2.39/2.75
% 2.39/2.75 % not_one_less_zero
% 2.39/2.75 thf(fact_2004_not__one__less__zero,axiom,
% 2.39/2.75 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ).
% 2.39/2.75
% 2.39/2.75 % not_one_less_zero
% 2.39/2.75 thf(fact_2005_not__one__less__zero,axiom,
% 2.39/2.75 ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 2.39/2.75
% 2.39/2.75 % not_one_less_zero
% 2.39/2.75 thf(fact_2006_not__one__less__zero,axiom,
% 2.39/2.75 ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 2.39/2.75
% 2.39/2.75 % not_one_less_zero
% 2.39/2.75 thf(fact_2007_not__one__less__zero,axiom,
% 2.39/2.75 ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 2.39/2.75
% 2.39/2.75 % not_one_less_zero
% 2.39/2.75 thf(fact_2008_less__1__mult,axiom,
% 2.39/2.75 ! [M2: code_natural,N: code_natural] :
% 2.39/2.75 ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ M2 )
% 2.39/2.75 => ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ N )
% 2.39/2.75 => ( ord_le5570908160329646204atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ M2 @ N ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % less_1_mult
% 2.39/2.75 thf(fact_2009_less__1__mult,axiom,
% 2.39/2.75 ! [M2: code_integer,N: code_integer] :
% 2.39/2.75 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ M2 )
% 2.39/2.75 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ N )
% 2.39/2.75 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ M2 @ N ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % less_1_mult
% 2.39/2.75 thf(fact_2010_less__1__mult,axiom,
% 2.39/2.75 ! [M2: rat,N: rat] :
% 2.39/2.75 ( ( ord_less_rat @ one_one_rat @ M2 )
% 2.39/2.75 => ( ( ord_less_rat @ one_one_rat @ N )
% 2.39/2.75 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M2 @ N ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % less_1_mult
% 2.39/2.75 thf(fact_2011_less__1__mult,axiom,
% 2.39/2.75 ! [M2: nat,N: nat] :
% 2.39/2.75 ( ( ord_less_nat @ one_one_nat @ M2 )
% 2.39/2.75 => ( ( ord_less_nat @ one_one_nat @ N )
% 2.39/2.75 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M2 @ N ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % less_1_mult
% 2.39/2.75 thf(fact_2012_less__1__mult,axiom,
% 2.39/2.75 ! [M2: int,N: int] :
% 2.39/2.75 ( ( ord_less_int @ one_one_int @ M2 )
% 2.39/2.75 => ( ( ord_less_int @ one_one_int @ N )
% 2.39/2.75 => ( ord_less_int @ one_one_int @ ( times_times_int @ M2 @ N ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % less_1_mult
% 2.39/2.75 thf(fact_2013_less__minus__one__simps_I4_J,axiom,
% 2.39/2.75 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 2.39/2.75
% 2.39/2.75 % less_minus_one_simps(4)
% 2.39/2.75 thf(fact_2014_less__minus__one__simps_I4_J,axiom,
% 2.39/2.75 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 2.39/2.75
% 2.39/2.75 % less_minus_one_simps(4)
% 2.39/2.75 thf(fact_2015_less__minus__one__simps_I4_J,axiom,
% 2.39/2.75 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 2.39/2.75
% 2.39/2.75 % less_minus_one_simps(4)
% 2.39/2.75 thf(fact_2016_less__minus__one__simps_I2_J,axiom,
% 2.39/2.75 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 2.39/2.75
% 2.39/2.75 % less_minus_one_simps(2)
% 2.39/2.75 thf(fact_2017_less__minus__one__simps_I2_J,axiom,
% 2.39/2.75 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 2.39/2.75
% 2.39/2.75 % less_minus_one_simps(2)
% 2.39/2.75 thf(fact_2018_less__minus__one__simps_I2_J,axiom,
% 2.39/2.75 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 2.39/2.75
% 2.39/2.75 % less_minus_one_simps(2)
% 2.39/2.75 thf(fact_2019_splice_Oelims,axiom,
% 2.39/2.75 ! [X: list_P8527749157015355191n_assn,Xa: list_P8527749157015355191n_assn,Y: list_P8527749157015355191n_assn] :
% 2.39/2.75 ( ( ( splice4588524007259616650n_assn @ X @ Xa )
% 2.39/2.75 = Y )
% 2.39/2.75 => ( ( ( X = nil_Pr5671120429643327159n_assn )
% 2.39/2.75 => ( Y != Xa ) )
% 2.39/2.75 => ~ ! [X3: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn] :
% 2.39/2.75 ( ( X
% 2.39/2.75 = ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) )
% 2.39/2.75 => ( Y
% 2.39/2.75 != ( cons_P2971678138204555879n_assn @ X3 @ ( splice4588524007259616650n_assn @ Xa @ Xs2 ) ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % splice.elims
% 2.39/2.75 thf(fact_2020_splice_Oelims,axiom,
% 2.39/2.75 ! [X: list_int,Xa: list_int,Y: list_int] :
% 2.39/2.75 ( ( ( splice_int @ X @ Xa )
% 2.39/2.75 = Y )
% 2.39/2.75 => ( ( ( X = nil_int )
% 2.39/2.75 => ( Y != Xa ) )
% 2.39/2.75 => ~ ! [X3: int,Xs2: list_int] :
% 2.39/2.75 ( ( X
% 2.39/2.75 = ( cons_int @ X3 @ Xs2 ) )
% 2.39/2.75 => ( Y
% 2.39/2.75 != ( cons_int @ X3 @ ( splice_int @ Xa @ Xs2 ) ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % splice.elims
% 2.39/2.75 thf(fact_2021_splice_Oelims,axiom,
% 2.39/2.75 ! [X: list_nat,Xa: list_nat,Y: list_nat] :
% 2.39/2.75 ( ( ( splice_nat @ X @ Xa )
% 2.39/2.75 = Y )
% 2.39/2.75 => ( ( ( X = nil_nat )
% 2.39/2.75 => ( Y != Xa ) )
% 2.39/2.75 => ~ ! [X3: nat,Xs2: list_nat] :
% 2.39/2.75 ( ( X
% 2.39/2.75 = ( cons_nat @ X3 @ Xs2 ) )
% 2.39/2.75 => ( Y
% 2.39/2.75 != ( cons_nat @ X3 @ ( splice_nat @ Xa @ Xs2 ) ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % splice.elims
% 2.39/2.75 thf(fact_2022_measures__lesseq,axiom,
% 2.39/2.75 ! [F2: nat > nat,X: nat,Y: nat,Fs: list_nat_nat] :
% 2.39/2.75 ( ( ord_less_eq_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 2.39/2.75 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( measures_nat @ Fs ) )
% 2.39/2.75 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( measures_nat @ ( cons_nat_nat @ F2 @ Fs ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % measures_lesseq
% 2.39/2.75 thf(fact_2023_measures__lesseq,axiom,
% 2.39/2.75 ! [F2: int > nat,X: int,Y: int,Fs: list_int_nat] :
% 2.39/2.75 ( ( ord_less_eq_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 2.39/2.75 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( measures_int @ Fs ) )
% 2.39/2.75 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( measures_int @ ( cons_int_nat @ F2 @ Fs ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % measures_lesseq
% 2.39/2.75 thf(fact_2024_mult__less__le__imp__less,axiom,
% 2.39/2.75 ! [A: code_natural,B: code_natural,C: code_natural,D2: code_natural] :
% 2.39/2.75 ( ( ord_le5570908160329646204atural @ A @ B )
% 2.39/2.75 => ( ( ord_le1926595141338095240atural @ C @ D2 )
% 2.39/2.75 => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 2.39/2.75 => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ C )
% 2.39/2.75 => ( ord_le5570908160329646204atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ D2 ) ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_less_le_imp_less
% 2.39/2.75 thf(fact_2025_mult__less__le__imp__less,axiom,
% 2.39/2.75 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 2.39/2.75 ( ( ord_le6747313008572928689nteger @ A @ B )
% 2.39/2.75 => ( ( ord_le3102999989581377725nteger @ C @ D2 )
% 2.39/2.75 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.75 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 2.39/2.75 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_less_le_imp_less
% 2.39/2.75 thf(fact_2026_mult__less__le__imp__less,axiom,
% 2.39/2.75 ! [A: rat,B: rat,C: rat,D2: rat] :
% 2.39/2.75 ( ( ord_less_rat @ A @ B )
% 2.39/2.75 => ( ( ord_less_eq_rat @ C @ D2 )
% 2.39/2.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 2.39/2.75 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.75 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_less_le_imp_less
% 2.39/2.75 thf(fact_2027_mult__less__le__imp__less,axiom,
% 2.39/2.75 ! [A: nat,B: nat,C: nat,D2: nat] :
% 2.39/2.75 ( ( ord_less_nat @ A @ B )
% 2.39/2.75 => ( ( ord_less_eq_nat @ C @ D2 )
% 2.39/2.75 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 2.39/2.75 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 2.39/2.75 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_less_le_imp_less
% 2.39/2.75 thf(fact_2028_mult__less__le__imp__less,axiom,
% 2.39/2.75 ! [A: int,B: int,C: int,D2: int] :
% 2.39/2.75 ( ( ord_less_int @ A @ B )
% 2.39/2.75 => ( ( ord_less_eq_int @ C @ D2 )
% 2.39/2.75 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 2.39/2.75 => ( ( ord_less_int @ zero_zero_int @ C )
% 2.39/2.75 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_less_le_imp_less
% 2.39/2.75 thf(fact_2029_mult__le__less__imp__less,axiom,
% 2.39/2.75 ! [A: code_natural,B: code_natural,C: code_natural,D2: code_natural] :
% 2.39/2.75 ( ( ord_le1926595141338095240atural @ A @ B )
% 2.39/2.75 => ( ( ord_le5570908160329646204atural @ C @ D2 )
% 2.39/2.75 => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A )
% 2.39/2.75 => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ C )
% 2.39/2.75 => ( ord_le5570908160329646204atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ D2 ) ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_le_less_imp_less
% 2.39/2.75 thf(fact_2030_mult__le__less__imp__less,axiom,
% 2.39/2.75 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 2.39/2.75 ( ( ord_le3102999989581377725nteger @ A @ B )
% 2.39/2.75 => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 2.39/2.75 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.75 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 2.39/2.75 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_le_less_imp_less
% 2.39/2.75 thf(fact_2031_mult__le__less__imp__less,axiom,
% 2.39/2.75 ! [A: rat,B: rat,C: rat,D2: rat] :
% 2.39/2.75 ( ( ord_less_eq_rat @ A @ B )
% 2.39/2.75 => ( ( ord_less_rat @ C @ D2 )
% 2.39/2.75 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 2.39/2.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 2.39/2.75 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_le_less_imp_less
% 2.39/2.75 thf(fact_2032_mult__le__less__imp__less,axiom,
% 2.39/2.75 ! [A: nat,B: nat,C: nat,D2: nat] :
% 2.39/2.75 ( ( ord_less_eq_nat @ A @ B )
% 2.39/2.75 => ( ( ord_less_nat @ C @ D2 )
% 2.39/2.75 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 2.39/2.75 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 2.39/2.75 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_le_less_imp_less
% 2.39/2.75 thf(fact_2033_mult__le__less__imp__less,axiom,
% 2.39/2.75 ! [A: int,B: int,C: int,D2: int] :
% 2.39/2.75 ( ( ord_less_eq_int @ A @ B )
% 2.39/2.75 => ( ( ord_less_int @ C @ D2 )
% 2.39/2.75 => ( ( ord_less_int @ zero_zero_int @ A )
% 2.39/2.75 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 2.39/2.75 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_le_less_imp_less
% 2.39/2.75 thf(fact_2034_mult__right__le__imp__le,axiom,
% 2.39/2.75 ! [A: code_natural,C: code_natural,B: code_natural] :
% 2.39/2.75 ( ( ord_le1926595141338095240atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ C ) )
% 2.39/2.75 => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ C )
% 2.39/2.75 => ( ord_le1926595141338095240atural @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_right_le_imp_le
% 2.39/2.75 thf(fact_2035_mult__right__le__imp__le,axiom,
% 2.39/2.75 ! [A: code_integer,C: code_integer,B: code_integer] :
% 2.39/2.75 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 2.39/2.75 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 2.39/2.75 => ( ord_le3102999989581377725nteger @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_right_le_imp_le
% 2.39/2.75 thf(fact_2036_mult__right__le__imp__le,axiom,
% 2.39/2.75 ! [A: rat,C: rat,B: rat] :
% 2.39/2.75 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 2.39/2.75 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.75 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_right_le_imp_le
% 2.39/2.75 thf(fact_2037_mult__right__le__imp__le,axiom,
% 2.39/2.75 ! [A: nat,C: nat,B: nat] :
% 2.39/2.75 ( ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 2.39/2.75 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 2.39/2.75 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_right_le_imp_le
% 2.39/2.75 thf(fact_2038_mult__right__le__imp__le,axiom,
% 2.39/2.75 ! [A: int,C: int,B: int] :
% 2.39/2.75 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 2.39/2.75 => ( ( ord_less_int @ zero_zero_int @ C )
% 2.39/2.75 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_right_le_imp_le
% 2.39/2.75 thf(fact_2039_mult__left__le__imp__le,axiom,
% 2.39/2.75 ! [C: code_natural,A: code_natural,B: code_natural] :
% 2.39/2.75 ( ( ord_le1926595141338095240atural @ ( times_2397367101498566445atural @ C @ A ) @ ( times_2397367101498566445atural @ C @ B ) )
% 2.39/2.75 => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ C )
% 2.39/2.75 => ( ord_le1926595141338095240atural @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_left_le_imp_le
% 2.39/2.75 thf(fact_2040_mult__left__le__imp__le,axiom,
% 2.39/2.75 ! [C: code_integer,A: code_integer,B: code_integer] :
% 2.39/2.75 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 2.39/2.75 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 2.39/2.75 => ( ord_le3102999989581377725nteger @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_left_le_imp_le
% 2.39/2.75 thf(fact_2041_mult__left__le__imp__le,axiom,
% 2.39/2.75 ! [C: rat,A: rat,B: rat] :
% 2.39/2.75 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 2.39/2.75 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.75 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_left_le_imp_le
% 2.39/2.75 thf(fact_2042_mult__left__le__imp__le,axiom,
% 2.39/2.75 ! [C: nat,A: nat,B: nat] :
% 2.39/2.75 ( ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 2.39/2.75 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 2.39/2.75 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_left_le_imp_le
% 2.39/2.75 thf(fact_2043_mult__left__le__imp__le,axiom,
% 2.39/2.75 ! [C: int,A: int,B: int] :
% 2.39/2.75 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 2.39/2.75 => ( ( ord_less_int @ zero_zero_int @ C )
% 2.39/2.75 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_left_le_imp_le
% 2.39/2.75 thf(fact_2044_mult__le__cancel__left__pos,axiom,
% 2.39/2.75 ! [C: code_integer,A: code_integer,B: code_integer] :
% 2.39/2.75 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 2.39/2.75 => ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 2.39/2.75 = ( ord_le3102999989581377725nteger @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_le_cancel_left_pos
% 2.39/2.75 thf(fact_2045_mult__le__cancel__left__pos,axiom,
% 2.39/2.75 ! [C: rat,A: rat,B: rat] :
% 2.39/2.75 ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.75 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 2.39/2.75 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_le_cancel_left_pos
% 2.39/2.75 thf(fact_2046_mult__le__cancel__left__pos,axiom,
% 2.39/2.75 ! [C: int,A: int,B: int] :
% 2.39/2.75 ( ( ord_less_int @ zero_zero_int @ C )
% 2.39/2.75 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 2.39/2.75 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_le_cancel_left_pos
% 2.39/2.75 thf(fact_2047_mult__le__cancel__left__neg,axiom,
% 2.39/2.75 ! [C: code_integer,A: code_integer,B: code_integer] :
% 2.39/2.75 ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 2.39/2.75 => ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 2.39/2.75 = ( ord_le3102999989581377725nteger @ B @ A ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_le_cancel_left_neg
% 2.39/2.75 thf(fact_2048_mult__le__cancel__left__neg,axiom,
% 2.39/2.75 ! [C: rat,A: rat,B: rat] :
% 2.39/2.75 ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.75 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 2.39/2.75 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_le_cancel_left_neg
% 2.39/2.75 thf(fact_2049_mult__le__cancel__left__neg,axiom,
% 2.39/2.75 ! [C: int,A: int,B: int] :
% 2.39/2.75 ( ( ord_less_int @ C @ zero_zero_int )
% 2.39/2.75 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 2.39/2.75 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_le_cancel_left_neg
% 2.39/2.75 thf(fact_2050_mult__less__cancel__right,axiom,
% 2.39/2.75 ! [A: code_integer,C: code_integer,B: code_integer] :
% 2.39/2.75 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 2.39/2.75 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 2.39/2.75 => ( ord_le6747313008572928689nteger @ A @ B ) )
% 2.39/2.75 & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 2.39/2.75 => ( ord_le6747313008572928689nteger @ B @ A ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_less_cancel_right
% 2.39/2.75 thf(fact_2051_mult__less__cancel__right,axiom,
% 2.39/2.75 ! [A: rat,C: rat,B: rat] :
% 2.39/2.75 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 2.39/2.75 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 2.39/2.75 => ( ord_less_rat @ A @ B ) )
% 2.39/2.75 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 2.39/2.75 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_less_cancel_right
% 2.39/2.75 thf(fact_2052_mult__less__cancel__right,axiom,
% 2.39/2.75 ! [A: int,C: int,B: int] :
% 2.39/2.75 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 2.39/2.75 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 2.39/2.75 => ( ord_less_int @ A @ B ) )
% 2.39/2.75 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 2.39/2.75 => ( ord_less_int @ B @ A ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_less_cancel_right
% 2.39/2.75 thf(fact_2053_mult__strict__mono_H,axiom,
% 2.39/2.75 ! [A: code_natural,B: code_natural,C: code_natural,D2: code_natural] :
% 2.39/2.75 ( ( ord_le5570908160329646204atural @ A @ B )
% 2.39/2.75 => ( ( ord_le5570908160329646204atural @ C @ D2 )
% 2.39/2.75 => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 2.39/2.75 => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ C )
% 2.39/2.75 => ( ord_le5570908160329646204atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ D2 ) ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_strict_mono'
% 2.39/2.75 thf(fact_2054_mult__strict__mono_H,axiom,
% 2.39/2.75 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 2.39/2.75 ( ( ord_le6747313008572928689nteger @ A @ B )
% 2.39/2.75 => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 2.39/2.75 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.75 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 2.39/2.75 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_strict_mono'
% 2.39/2.75 thf(fact_2055_mult__strict__mono_H,axiom,
% 2.39/2.75 ! [A: rat,B: rat,C: rat,D2: rat] :
% 2.39/2.75 ( ( ord_less_rat @ A @ B )
% 2.39/2.75 => ( ( ord_less_rat @ C @ D2 )
% 2.39/2.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 2.39/2.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 2.39/2.75 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_strict_mono'
% 2.39/2.75 thf(fact_2056_mult__strict__mono_H,axiom,
% 2.39/2.75 ! [A: nat,B: nat,C: nat,D2: nat] :
% 2.39/2.75 ( ( ord_less_nat @ A @ B )
% 2.39/2.75 => ( ( ord_less_nat @ C @ D2 )
% 2.39/2.75 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 2.39/2.75 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 2.39/2.75 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_strict_mono'
% 2.39/2.75 thf(fact_2057_mult__strict__mono_H,axiom,
% 2.39/2.75 ! [A: int,B: int,C: int,D2: int] :
% 2.39/2.75 ( ( ord_less_int @ A @ B )
% 2.39/2.75 => ( ( ord_less_int @ C @ D2 )
% 2.39/2.75 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 2.39/2.75 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 2.39/2.75 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_strict_mono'
% 2.39/2.75 thf(fact_2058_mult__right__less__imp__less,axiom,
% 2.39/2.75 ! [A: code_natural,C: code_natural,B: code_natural] :
% 2.39/2.75 ( ( ord_le5570908160329646204atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ C ) )
% 2.39/2.75 => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ C )
% 2.39/2.75 => ( ord_le5570908160329646204atural @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_right_less_imp_less
% 2.39/2.75 thf(fact_2059_mult__right__less__imp__less,axiom,
% 2.39/2.75 ! [A: code_integer,C: code_integer,B: code_integer] :
% 2.39/2.75 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 2.39/2.75 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 2.39/2.75 => ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_right_less_imp_less
% 2.39/2.75 thf(fact_2060_mult__right__less__imp__less,axiom,
% 2.39/2.75 ! [A: rat,C: rat,B: rat] :
% 2.39/2.75 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 2.39/2.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 2.39/2.75 => ( ord_less_rat @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_right_less_imp_less
% 2.39/2.75 thf(fact_2061_mult__right__less__imp__less,axiom,
% 2.39/2.75 ! [A: nat,C: nat,B: nat] :
% 2.39/2.75 ( ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 2.39/2.75 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 2.39/2.75 => ( ord_less_nat @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_right_less_imp_less
% 2.39/2.75 thf(fact_2062_mult__right__less__imp__less,axiom,
% 2.39/2.75 ! [A: int,C: int,B: int] :
% 2.39/2.75 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 2.39/2.75 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 2.39/2.75 => ( ord_less_int @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_right_less_imp_less
% 2.39/2.75 thf(fact_2063_mult__less__cancel__left,axiom,
% 2.39/2.75 ! [C: code_integer,A: code_integer,B: code_integer] :
% 2.39/2.75 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 2.39/2.75 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 2.39/2.75 => ( ord_le6747313008572928689nteger @ A @ B ) )
% 2.39/2.75 & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 2.39/2.75 => ( ord_le6747313008572928689nteger @ B @ A ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_less_cancel_left
% 2.39/2.75 thf(fact_2064_mult__less__cancel__left,axiom,
% 2.39/2.75 ! [C: rat,A: rat,B: rat] :
% 2.39/2.75 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 2.39/2.75 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 2.39/2.75 => ( ord_less_rat @ A @ B ) )
% 2.39/2.75 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 2.39/2.75 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_less_cancel_left
% 2.39/2.75 thf(fact_2065_mult__less__cancel__left,axiom,
% 2.39/2.75 ! [C: int,A: int,B: int] :
% 2.39/2.75 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 2.39/2.75 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 2.39/2.75 => ( ord_less_int @ A @ B ) )
% 2.39/2.75 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 2.39/2.75 => ( ord_less_int @ B @ A ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_less_cancel_left
% 2.39/2.75 thf(fact_2066_mult__strict__mono,axiom,
% 2.39/2.75 ! [A: code_natural,B: code_natural,C: code_natural,D2: code_natural] :
% 2.39/2.75 ( ( ord_le5570908160329646204atural @ A @ B )
% 2.39/2.75 => ( ( ord_le5570908160329646204atural @ C @ D2 )
% 2.39/2.75 => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ B )
% 2.39/2.75 => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ C )
% 2.39/2.75 => ( ord_le5570908160329646204atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ D2 ) ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_strict_mono
% 2.39/2.75 thf(fact_2067_mult__strict__mono,axiom,
% 2.39/2.75 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 2.39/2.75 ( ( ord_le6747313008572928689nteger @ A @ B )
% 2.39/2.75 => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 2.39/2.75 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 2.39/2.75 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 2.39/2.75 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_strict_mono
% 2.39/2.75 thf(fact_2068_mult__strict__mono,axiom,
% 2.39/2.75 ! [A: rat,B: rat,C: rat,D2: rat] :
% 2.39/2.75 ( ( ord_less_rat @ A @ B )
% 2.39/2.75 => ( ( ord_less_rat @ C @ D2 )
% 2.39/2.75 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 2.39/2.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 2.39/2.75 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_strict_mono
% 2.39/2.75 thf(fact_2069_mult__strict__mono,axiom,
% 2.39/2.75 ! [A: nat,B: nat,C: nat,D2: nat] :
% 2.39/2.75 ( ( ord_less_nat @ A @ B )
% 2.39/2.75 => ( ( ord_less_nat @ C @ D2 )
% 2.39/2.75 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 2.39/2.75 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 2.39/2.75 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_strict_mono
% 2.39/2.75 thf(fact_2070_mult__strict__mono,axiom,
% 2.39/2.75 ! [A: int,B: int,C: int,D2: int] :
% 2.39/2.75 ( ( ord_less_int @ A @ B )
% 2.39/2.75 => ( ( ord_less_int @ C @ D2 )
% 2.39/2.75 => ( ( ord_less_int @ zero_zero_int @ B )
% 2.39/2.75 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 2.39/2.75 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_strict_mono
% 2.39/2.75 thf(fact_2071_mult__left__less__imp__less,axiom,
% 2.39/2.75 ! [C: code_natural,A: code_natural,B: code_natural] :
% 2.39/2.75 ( ( ord_le5570908160329646204atural @ ( times_2397367101498566445atural @ C @ A ) @ ( times_2397367101498566445atural @ C @ B ) )
% 2.39/2.75 => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ C )
% 2.39/2.75 => ( ord_le5570908160329646204atural @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_left_less_imp_less
% 2.39/2.75 thf(fact_2072_mult__left__less__imp__less,axiom,
% 2.39/2.75 ! [C: code_integer,A: code_integer,B: code_integer] :
% 2.39/2.75 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 2.39/2.75 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 2.39/2.75 => ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_left_less_imp_less
% 2.39/2.75 thf(fact_2073_mult__left__less__imp__less,axiom,
% 2.39/2.75 ! [C: rat,A: rat,B: rat] :
% 2.39/2.75 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 2.39/2.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 2.39/2.75 => ( ord_less_rat @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_left_less_imp_less
% 2.39/2.75 thf(fact_2074_mult__left__less__imp__less,axiom,
% 2.39/2.75 ! [C: nat,A: nat,B: nat] :
% 2.39/2.75 ( ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 2.39/2.75 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 2.39/2.75 => ( ord_less_nat @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_left_less_imp_less
% 2.39/2.75 thf(fact_2075_mult__left__less__imp__less,axiom,
% 2.39/2.75 ! [C: int,A: int,B: int] :
% 2.39/2.75 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 2.39/2.75 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 2.39/2.75 => ( ord_less_int @ A @ B ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_left_less_imp_less
% 2.39/2.75 thf(fact_2076_mult__le__cancel__right,axiom,
% 2.39/2.75 ! [A: code_integer,C: code_integer,B: code_integer] :
% 2.39/2.75 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 2.39/2.75 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 2.39/2.75 => ( ord_le3102999989581377725nteger @ A @ B ) )
% 2.39/2.75 & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 2.39/2.75 => ( ord_le3102999989581377725nteger @ B @ A ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_le_cancel_right
% 2.39/2.75 thf(fact_2077_mult__le__cancel__right,axiom,
% 2.39/2.75 ! [A: rat,C: rat,B: rat] :
% 2.39/2.75 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 2.39/2.75 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.75 => ( ord_less_eq_rat @ A @ B ) )
% 2.39/2.75 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.75 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_le_cancel_right
% 2.39/2.75 thf(fact_2078_mult__le__cancel__right,axiom,
% 2.39/2.75 ! [A: int,C: int,B: int] :
% 2.39/2.75 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 2.39/2.75 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 2.39/2.75 => ( ord_less_eq_int @ A @ B ) )
% 2.39/2.75 & ( ( ord_less_int @ C @ zero_zero_int )
% 2.39/2.75 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_le_cancel_right
% 2.39/2.75 thf(fact_2079_mult__le__cancel__left,axiom,
% 2.39/2.75 ! [C: code_integer,A: code_integer,B: code_integer] :
% 2.39/2.75 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 2.39/2.75 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 2.39/2.75 => ( ord_le3102999989581377725nteger @ A @ B ) )
% 2.39/2.75 & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 2.39/2.75 => ( ord_le3102999989581377725nteger @ B @ A ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_le_cancel_left
% 2.39/2.75 thf(fact_2080_mult__le__cancel__left,axiom,
% 2.39/2.75 ! [C: rat,A: rat,B: rat] :
% 2.39/2.75 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 2.39/2.75 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.75 => ( ord_less_eq_rat @ A @ B ) )
% 2.39/2.75 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.75 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_le_cancel_left
% 2.39/2.75 thf(fact_2081_mult__le__cancel__left,axiom,
% 2.39/2.75 ! [C: int,A: int,B: int] :
% 2.39/2.75 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 2.39/2.75 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 2.39/2.75 => ( ord_less_eq_int @ A @ B ) )
% 2.39/2.75 & ( ( ord_less_int @ C @ zero_zero_int )
% 2.39/2.75 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_le_cancel_left
% 2.39/2.75 thf(fact_2082_less__minus__one__simps_I3_J,axiom,
% 2.39/2.75 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 2.39/2.75
% 2.39/2.75 % less_minus_one_simps(3)
% 2.39/2.75 thf(fact_2083_less__minus__one__simps_I3_J,axiom,
% 2.39/2.75 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 2.39/2.75
% 2.39/2.75 % less_minus_one_simps(3)
% 2.39/2.75 thf(fact_2084_less__minus__one__simps_I3_J,axiom,
% 2.39/2.75 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 2.39/2.75
% 2.39/2.75 % less_minus_one_simps(3)
% 2.39/2.75 thf(fact_2085_less__minus__one__simps_I1_J,axiom,
% 2.39/2.75 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 2.39/2.75
% 2.39/2.75 % less_minus_one_simps(1)
% 2.39/2.75 thf(fact_2086_less__minus__one__simps_I1_J,axiom,
% 2.39/2.75 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 2.39/2.75
% 2.39/2.75 % less_minus_one_simps(1)
% 2.39/2.75 thf(fact_2087_less__minus__one__simps_I1_J,axiom,
% 2.39/2.75 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 2.39/2.75
% 2.39/2.75 % less_minus_one_simps(1)
% 2.39/2.75 thf(fact_2088_mult__less__cancel__right2,axiom,
% 2.39/2.75 ! [A: code_integer,C: code_integer] :
% 2.39/2.75 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ C )
% 2.39/2.75 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 2.39/2.75 => ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer ) )
% 2.39/2.75 & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 2.39/2.75 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_less_cancel_right2
% 2.39/2.75 thf(fact_2089_mult__less__cancel__right2,axiom,
% 2.39/2.75 ! [A: rat,C: rat] :
% 2.39/2.75 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ C )
% 2.39/2.75 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 2.39/2.75 => ( ord_less_rat @ A @ one_one_rat ) )
% 2.39/2.75 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 2.39/2.75 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_less_cancel_right2
% 2.39/2.75 thf(fact_2090_mult__less__cancel__right2,axiom,
% 2.39/2.75 ! [A: int,C: int] :
% 2.39/2.75 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ C )
% 2.39/2.75 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 2.39/2.75 => ( ord_less_int @ A @ one_one_int ) )
% 2.39/2.75 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 2.39/2.75 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_less_cancel_right2
% 2.39/2.75 thf(fact_2091_mult__less__cancel__right1,axiom,
% 2.39/2.75 ! [C: code_integer,B: code_integer] :
% 2.39/2.75 ( ( ord_le6747313008572928689nteger @ C @ ( times_3573771949741848930nteger @ B @ C ) )
% 2.39/2.75 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 2.39/2.75 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B ) )
% 2.39/2.75 & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 2.39/2.75 => ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_less_cancel_right1
% 2.39/2.75 thf(fact_2092_mult__less__cancel__right1,axiom,
% 2.39/2.75 ! [C: rat,B: rat] :
% 2.39/2.75 ( ( ord_less_rat @ C @ ( times_times_rat @ B @ C ) )
% 2.39/2.75 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 2.39/2.75 => ( ord_less_rat @ one_one_rat @ B ) )
% 2.39/2.75 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 2.39/2.75 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_less_cancel_right1
% 2.39/2.75 thf(fact_2093_mult__less__cancel__right1,axiom,
% 2.39/2.75 ! [C: int,B: int] :
% 2.39/2.75 ( ( ord_less_int @ C @ ( times_times_int @ B @ C ) )
% 2.39/2.75 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 2.39/2.75 => ( ord_less_int @ one_one_int @ B ) )
% 2.39/2.75 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 2.39/2.75 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_less_cancel_right1
% 2.39/2.75 thf(fact_2094_mult__less__cancel__left2,axiom,
% 2.39/2.75 ! [C: code_integer,A: code_integer] :
% 2.39/2.75 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ C )
% 2.39/2.75 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 2.39/2.75 => ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer ) )
% 2.39/2.75 & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 2.39/2.75 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_less_cancel_left2
% 2.39/2.75 thf(fact_2095_mult__less__cancel__left2,axiom,
% 2.39/2.75 ! [C: rat,A: rat] :
% 2.39/2.75 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ C )
% 2.39/2.75 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 2.39/2.75 => ( ord_less_rat @ A @ one_one_rat ) )
% 2.39/2.75 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 2.39/2.75 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_less_cancel_left2
% 2.39/2.75 thf(fact_2096_mult__less__cancel__left2,axiom,
% 2.39/2.75 ! [C: int,A: int] :
% 2.39/2.75 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ C )
% 2.39/2.75 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 2.39/2.75 => ( ord_less_int @ A @ one_one_int ) )
% 2.39/2.75 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 2.39/2.75 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_less_cancel_left2
% 2.39/2.75 thf(fact_2097_mult__less__cancel__left1,axiom,
% 2.39/2.75 ! [C: code_integer,B: code_integer] :
% 2.39/2.75 ( ( ord_le6747313008572928689nteger @ C @ ( times_3573771949741848930nteger @ C @ B ) )
% 2.39/2.75 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 2.39/2.75 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B ) )
% 2.39/2.75 & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 2.39/2.75 => ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_less_cancel_left1
% 2.39/2.75 thf(fact_2098_mult__less__cancel__left1,axiom,
% 2.39/2.75 ! [C: rat,B: rat] :
% 2.39/2.75 ( ( ord_less_rat @ C @ ( times_times_rat @ C @ B ) )
% 2.39/2.75 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 2.39/2.75 => ( ord_less_rat @ one_one_rat @ B ) )
% 2.39/2.75 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 2.39/2.75 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_less_cancel_left1
% 2.39/2.75 thf(fact_2099_mult__less__cancel__left1,axiom,
% 2.39/2.75 ! [C: int,B: int] :
% 2.39/2.75 ( ( ord_less_int @ C @ ( times_times_int @ C @ B ) )
% 2.39/2.75 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 2.39/2.75 => ( ord_less_int @ one_one_int @ B ) )
% 2.39/2.75 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 2.39/2.75 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_less_cancel_left1
% 2.39/2.75 thf(fact_2100_mult__le__cancel__right2,axiom,
% 2.39/2.75 ! [A: code_integer,C: code_integer] :
% 2.39/2.75 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ C )
% 2.39/2.75 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 2.39/2.75 => ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer ) )
% 2.39/2.75 & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 2.39/2.75 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_le_cancel_right2
% 2.39/2.75 thf(fact_2101_mult__le__cancel__right2,axiom,
% 2.39/2.75 ! [A: rat,C: rat] :
% 2.39/2.75 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ C )
% 2.39/2.75 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.75 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 2.39/2.75 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.75 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_le_cancel_right2
% 2.39/2.75 thf(fact_2102_mult__le__cancel__right2,axiom,
% 2.39/2.75 ! [A: int,C: int] :
% 2.39/2.75 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ C )
% 2.39/2.75 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 2.39/2.75 => ( ord_less_eq_int @ A @ one_one_int ) )
% 2.39/2.75 & ( ( ord_less_int @ C @ zero_zero_int )
% 2.39/2.75 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_le_cancel_right2
% 2.39/2.75 thf(fact_2103_mult__le__cancel__right1,axiom,
% 2.39/2.75 ! [C: code_integer,B: code_integer] :
% 2.39/2.75 ( ( ord_le3102999989581377725nteger @ C @ ( times_3573771949741848930nteger @ B @ C ) )
% 2.39/2.75 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 2.39/2.75 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ B ) )
% 2.39/2.75 & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 2.39/2.75 => ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_le_cancel_right1
% 2.39/2.75 thf(fact_2104_mult__le__cancel__right1,axiom,
% 2.39/2.75 ! [C: rat,B: rat] :
% 2.39/2.75 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ B @ C ) )
% 2.39/2.75 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.75 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 2.39/2.75 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.75 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_le_cancel_right1
% 2.39/2.75 thf(fact_2105_mult__le__cancel__right1,axiom,
% 2.39/2.75 ! [C: int,B: int] :
% 2.39/2.75 ( ( ord_less_eq_int @ C @ ( times_times_int @ B @ C ) )
% 2.39/2.75 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 2.39/2.75 => ( ord_less_eq_int @ one_one_int @ B ) )
% 2.39/2.75 & ( ( ord_less_int @ C @ zero_zero_int )
% 2.39/2.75 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_le_cancel_right1
% 2.39/2.75 thf(fact_2106_mult__le__cancel__left2,axiom,
% 2.39/2.75 ! [C: code_integer,A: code_integer] :
% 2.39/2.75 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ C )
% 2.39/2.75 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 2.39/2.75 => ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer ) )
% 2.39/2.75 & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 2.39/2.75 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_le_cancel_left2
% 2.39/2.75 thf(fact_2107_mult__le__cancel__left2,axiom,
% 2.39/2.75 ! [C: rat,A: rat] :
% 2.39/2.75 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ C )
% 2.39/2.75 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.75 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 2.39/2.75 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.75 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_le_cancel_left2
% 2.39/2.75 thf(fact_2108_mult__le__cancel__left2,axiom,
% 2.39/2.75 ! [C: int,A: int] :
% 2.39/2.75 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ C )
% 2.39/2.75 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 2.39/2.75 => ( ord_less_eq_int @ A @ one_one_int ) )
% 2.39/2.75 & ( ( ord_less_int @ C @ zero_zero_int )
% 2.39/2.75 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_le_cancel_left2
% 2.39/2.75 thf(fact_2109_field__le__mult__one__interval,axiom,
% 2.39/2.75 ! [X: rat,Y: rat] :
% 2.39/2.75 ( ! [Z2: rat] :
% 2.39/2.75 ( ( ord_less_rat @ zero_zero_rat @ Z2 )
% 2.39/2.75 => ( ( ord_less_rat @ Z2 @ one_one_rat )
% 2.39/2.75 => ( ord_less_eq_rat @ ( times_times_rat @ Z2 @ X ) @ Y ) ) )
% 2.39/2.75 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 2.39/2.75
% 2.39/2.75 % field_le_mult_one_interval
% 2.39/2.75 thf(fact_2110_mult__le__cancel__iff1,axiom,
% 2.39/2.75 ! [Z: code_integer,X: code_integer,Y: code_integer] :
% 2.39/2.75 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ Z )
% 2.39/2.75 => ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ X @ Z ) @ ( times_3573771949741848930nteger @ Y @ Z ) )
% 2.39/2.75 = ( ord_le3102999989581377725nteger @ X @ Y ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_le_cancel_iff1
% 2.39/2.75 thf(fact_2111_mult__le__cancel__iff1,axiom,
% 2.39/2.75 ! [Z: rat,X: rat,Y: rat] :
% 2.39/2.75 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 2.39/2.75 => ( ( ord_less_eq_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 2.39/2.75 = ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_le_cancel_iff1
% 2.39/2.75 thf(fact_2112_mult__le__cancel__iff1,axiom,
% 2.39/2.75 ! [Z: int,X: int,Y: int] :
% 2.39/2.75 ( ( ord_less_int @ zero_zero_int @ Z )
% 2.39/2.75 => ( ( ord_less_eq_int @ ( times_times_int @ X @ Z ) @ ( times_times_int @ Y @ Z ) )
% 2.39/2.75 = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 2.39/2.75
% 2.39/2.75 % mult_le_cancel_iff1
% 2.39/2.75 thf(fact_2113_mult__le__cancel__iff2,axiom,
% 2.39/2.76 ! [Z: code_integer,X: code_integer,Y: code_integer] :
% 2.39/2.76 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ Z )
% 2.39/2.76 => ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ Z @ X ) @ ( times_3573771949741848930nteger @ Z @ Y ) )
% 2.39/2.76 = ( ord_le3102999989581377725nteger @ X @ Y ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % mult_le_cancel_iff2
% 2.39/2.76 thf(fact_2114_mult__le__cancel__iff2,axiom,
% 2.39/2.76 ! [Z: rat,X: rat,Y: rat] :
% 2.39/2.76 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 2.39/2.76 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ X ) @ ( times_times_rat @ Z @ Y ) )
% 2.39/2.76 = ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % mult_le_cancel_iff2
% 2.39/2.76 thf(fact_2115_mult__le__cancel__iff2,axiom,
% 2.39/2.76 ! [Z: int,X: int,Y: int] :
% 2.39/2.76 ( ( ord_less_int @ zero_zero_int @ Z )
% 2.39/2.76 => ( ( ord_less_eq_int @ ( times_times_int @ Z @ X ) @ ( times_times_int @ Z @ Y ) )
% 2.39/2.76 = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % mult_le_cancel_iff2
% 2.39/2.76 thf(fact_2116_mult__less__iff1,axiom,
% 2.39/2.76 ! [Z: code_integer,X: code_integer,Y: code_integer] :
% 2.39/2.76 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ Z )
% 2.39/2.76 => ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ X @ Z ) @ ( times_3573771949741848930nteger @ Y @ Z ) )
% 2.39/2.76 = ( ord_le6747313008572928689nteger @ X @ Y ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % mult_less_iff1
% 2.39/2.76 thf(fact_2117_mult__less__iff1,axiom,
% 2.39/2.76 ! [Z: rat,X: rat,Y: rat] :
% 2.39/2.76 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 2.39/2.76 => ( ( ord_less_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 2.39/2.76 = ( ord_less_rat @ X @ Y ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % mult_less_iff1
% 2.39/2.76 thf(fact_2118_mult__less__iff1,axiom,
% 2.39/2.76 ! [Z: int,X: int,Y: int] :
% 2.39/2.76 ( ( ord_less_int @ zero_zero_int @ Z )
% 2.39/2.76 => ( ( ord_less_int @ ( times_times_int @ X @ Z ) @ ( times_times_int @ Y @ Z ) )
% 2.39/2.76 = ( ord_less_int @ X @ Y ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % mult_less_iff1
% 2.39/2.76 thf(fact_2119_quicksort_Ocases,axiom,
% 2.39/2.76 ! [X: list_int] :
% 2.39/2.76 ( ( X != nil_int )
% 2.39/2.76 => ~ ! [X3: int,Xs2: list_int] :
% 2.39/2.76 ( X
% 2.39/2.76 != ( cons_int @ X3 @ Xs2 ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % quicksort.cases
% 2.39/2.76 thf(fact_2120_quicksort_Ocases,axiom,
% 2.39/2.76 ! [X: list_nat] :
% 2.39/2.76 ( ( X != nil_nat )
% 2.39/2.76 => ~ ! [X3: nat,Xs2: list_nat] :
% 2.39/2.76 ( X
% 2.39/2.76 != ( cons_nat @ X3 @ Xs2 ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % quicksort.cases
% 2.39/2.76 thf(fact_2121_subset__eq__mset__impl_Ocases,axiom,
% 2.39/2.76 ! [X: produc337509097454979815n_assn] :
% 2.39/2.76 ( ! [Ys3: list_P8527749157015355191n_assn] :
% 2.39/2.76 ( X
% 2.39/2.76 != ( produc3014731801419794263n_assn @ nil_Pr5671120429643327159n_assn @ Ys3 ) )
% 2.39/2.76 => ~ ! [X3: produc6575502325842934193n_assn,Xs2: list_P8527749157015355191n_assn,Ys3: list_P8527749157015355191n_assn] :
% 2.39/2.76 ( X
% 2.39/2.76 != ( produc3014731801419794263n_assn @ ( cons_P2971678138204555879n_assn @ X3 @ Xs2 ) @ Ys3 ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % subset_eq_mset_impl.cases
% 2.39/2.76 thf(fact_2122_subset__eq__mset__impl_Ocases,axiom,
% 2.39/2.76 ! [X: produc1186641810826059865st_int] :
% 2.39/2.76 ( ! [Ys3: list_int] :
% 2.39/2.76 ( X
% 2.39/2.76 != ( produc364263696895485585st_int @ nil_int @ Ys3 ) )
% 2.39/2.76 => ~ ! [X3: int,Xs2: list_int,Ys3: list_int] :
% 2.39/2.76 ( X
% 2.39/2.76 != ( produc364263696895485585st_int @ ( cons_int @ X3 @ Xs2 ) @ Ys3 ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % subset_eq_mset_impl.cases
% 2.39/2.76 thf(fact_2123_subset__eq__mset__impl_Ocases,axiom,
% 2.39/2.76 ! [X: produc1828647624359046049st_nat] :
% 2.39/2.76 ( ! [Ys3: list_nat] :
% 2.39/2.76 ( X
% 2.39/2.76 != ( produc2694037385005941721st_nat @ nil_nat @ Ys3 ) )
% 2.39/2.76 => ~ ! [X3: nat,Xs2: list_nat,Ys3: list_nat] :
% 2.39/2.76 ( X
% 2.39/2.76 != ( produc2694037385005941721st_nat @ ( cons_nat @ X3 @ Xs2 ) @ Ys3 ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % subset_eq_mset_impl.cases
% 2.39/2.76 thf(fact_2124_inf__top_Osemilattice__neutr__order__axioms,axiom,
% 2.39/2.76 semila4918476307565957903at_nat @ inf_in2572325071724192079at_nat @ top_to4669805908274784177at_nat @ ord_le3146513528884898305at_nat @ ord_le7866589430770878221at_nat ).
% 2.39/2.76
% 2.39/2.76 % inf_top.semilattice_neutr_order_axioms
% 2.39/2.76 thf(fact_2125_inf__top_Osemilattice__neutr__order__axioms,axiom,
% 2.39/2.76 semila8052717425514686422_int_o @ inf_in3604695632404883862_int_o @ top_to1578927101902068148_int_o @ ord_le8369615600986905444_int_o @ ord_le8213806771718485336_int_o ).
% 2.39/2.76
% 2.39/2.76 % inf_top.semilattice_neutr_order_axioms
% 2.39/2.76 thf(fact_2126_inf__top_Osemilattice__neutr__order__axioms,axiom,
% 2.39/2.76 semila4423693302617054363t_unit @ inf_in4660618365625256667t_unit @ top_to1996260823553986621t_unit @ ord_le3507040750410214029t_unit @ ord_le8056459307392131481t_unit ).
% 2.39/2.76
% 2.39/2.76 % inf_top.semilattice_neutr_order_axioms
% 2.39/2.76 thf(fact_2127_inf__top_Osemilattice__neutr__order__axioms,axiom,
% 2.39/2.76 semila8603258263270017530r_assn @ inf_inf_assn @ top_top_assn @ ord_less_eq_assn @ ord_less_assn ).
% 2.39/2.76
% 2.39/2.76 % inf_top.semilattice_neutr_order_axioms
% 2.39/2.76 thf(fact_2128_inf__top_Osemilattice__neutr__order__axioms,axiom,
% 2.39/2.76 semila1667268886620078168et_nat @ inf_inf_set_nat @ top_top_set_nat @ ord_less_eq_set_nat @ ord_less_set_nat ).
% 2.39/2.76
% 2.39/2.76 % inf_top.semilattice_neutr_order_axioms
% 2.39/2.76 thf(fact_2129_sgn__neg,axiom,
% 2.39/2.76 ! [A: int] :
% 2.39/2.76 ( ( ord_less_int @ A @ zero_zero_int )
% 2.39/2.76 => ( ( sgn_sgn_int @ A )
% 2.39/2.76 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % sgn_neg
% 2.39/2.76 thf(fact_2130_sgn__neg,axiom,
% 2.39/2.76 ! [A: rat] :
% 2.39/2.76 ( ( ord_less_rat @ A @ zero_zero_rat )
% 2.39/2.76 => ( ( sgn_sgn_rat @ A )
% 2.39/2.76 = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % sgn_neg
% 2.39/2.76 thf(fact_2131_sgn__neg,axiom,
% 2.39/2.76 ! [A: code_integer] :
% 2.39/2.76 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 2.39/2.76 => ( ( sgn_sgn_Code_integer @ A )
% 2.39/2.76 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % sgn_neg
% 2.39/2.76 thf(fact_2132_insert__Nil,axiom,
% 2.39/2.76 ! [X: produc6575502325842934193n_assn] :
% 2.39/2.76 ( ( insert3246601298802261197n_assn @ X @ nil_Pr5671120429643327159n_assn )
% 2.39/2.76 = ( cons_P2971678138204555879n_assn @ X @ nil_Pr5671120429643327159n_assn ) ) ).
% 2.39/2.76
% 2.39/2.76 % insert_Nil
% 2.39/2.76 thf(fact_2133_insert__Nil,axiom,
% 2.39/2.76 ! [X: int] :
% 2.39/2.76 ( ( insert_int @ X @ nil_int )
% 2.39/2.76 = ( cons_int @ X @ nil_int ) ) ).
% 2.39/2.76
% 2.39/2.76 % insert_Nil
% 2.39/2.76 thf(fact_2134_insert__Nil,axiom,
% 2.39/2.76 ! [X: nat] :
% 2.39/2.76 ( ( insert_nat @ X @ nil_nat )
% 2.39/2.76 = ( cons_nat @ X @ nil_nat ) ) ).
% 2.39/2.76
% 2.39/2.76 % insert_Nil
% 2.39/2.76 thf(fact_2135_convex__bound__lt,axiom,
% 2.39/2.76 ! [X: code_integer,A: code_integer,Y: code_integer,U: code_integer,V2: code_integer] :
% 2.39/2.76 ( ( ord_le6747313008572928689nteger @ X @ A )
% 2.39/2.76 => ( ( ord_le6747313008572928689nteger @ Y @ A )
% 2.39/2.76 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ U )
% 2.39/2.76 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ V2 )
% 2.39/2.76 => ( ( ( plus_p5714425477246183910nteger @ U @ V2 )
% 2.39/2.76 = one_one_Code_integer )
% 2.39/2.76 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ U @ X ) @ ( times_3573771949741848930nteger @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % convex_bound_lt
% 2.39/2.76 thf(fact_2136_convex__bound__lt,axiom,
% 2.39/2.76 ! [X: rat,A: rat,Y: rat,U: rat,V2: rat] :
% 2.39/2.76 ( ( ord_less_rat @ X @ A )
% 2.39/2.76 => ( ( ord_less_rat @ Y @ A )
% 2.39/2.76 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 2.39/2.76 => ( ( ord_less_eq_rat @ zero_zero_rat @ V2 )
% 2.39/2.76 => ( ( ( plus_plus_rat @ U @ V2 )
% 2.39/2.76 = one_one_rat )
% 2.39/2.76 => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % convex_bound_lt
% 2.39/2.76 thf(fact_2137_convex__bound__lt,axiom,
% 2.39/2.76 ! [X: int,A: int,Y: int,U: int,V2: int] :
% 2.39/2.76 ( ( ord_less_int @ X @ A )
% 2.39/2.76 => ( ( ord_less_int @ Y @ A )
% 2.39/2.76 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 2.39/2.76 => ( ( ord_less_eq_int @ zero_zero_int @ V2 )
% 2.39/2.76 => ( ( ( plus_plus_int @ U @ V2 )
% 2.39/2.76 = one_one_int )
% 2.39/2.76 => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % convex_bound_lt
% 2.39/2.76 thf(fact_2138_add__left__cancel,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.76 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 2.39/2.76 = ( plus_p5714425477246183910nteger @ A @ C ) )
% 2.39/2.76 = ( B = C ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_left_cancel
% 2.39/2.76 thf(fact_2139_add__left__cancel,axiom,
% 2.39/2.76 ! [A: rat,B: rat,C: rat] :
% 2.39/2.76 ( ( ( plus_plus_rat @ A @ B )
% 2.39/2.76 = ( plus_plus_rat @ A @ C ) )
% 2.39/2.76 = ( B = C ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_left_cancel
% 2.39/2.76 thf(fact_2140_add__left__cancel,axiom,
% 2.39/2.76 ! [A: nat,B: nat,C: nat] :
% 2.39/2.76 ( ( ( plus_plus_nat @ A @ B )
% 2.39/2.76 = ( plus_plus_nat @ A @ C ) )
% 2.39/2.76 = ( B = C ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_left_cancel
% 2.39/2.76 thf(fact_2141_add__left__cancel,axiom,
% 2.39/2.76 ! [A: int,B: int,C: int] :
% 2.39/2.76 ( ( ( plus_plus_int @ A @ B )
% 2.39/2.76 = ( plus_plus_int @ A @ C ) )
% 2.39/2.76 = ( B = C ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_left_cancel
% 2.39/2.76 thf(fact_2142_add__right__cancel,axiom,
% 2.39/2.76 ! [B: code_integer,A: code_integer,C: code_integer] :
% 2.39/2.76 ( ( ( plus_p5714425477246183910nteger @ B @ A )
% 2.39/2.76 = ( plus_p5714425477246183910nteger @ C @ A ) )
% 2.39/2.76 = ( B = C ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_right_cancel
% 2.39/2.76 thf(fact_2143_add__right__cancel,axiom,
% 2.39/2.76 ! [B: rat,A: rat,C: rat] :
% 2.39/2.76 ( ( ( plus_plus_rat @ B @ A )
% 2.39/2.76 = ( plus_plus_rat @ C @ A ) )
% 2.39/2.76 = ( B = C ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_right_cancel
% 2.39/2.76 thf(fact_2144_add__right__cancel,axiom,
% 2.39/2.76 ! [B: nat,A: nat,C: nat] :
% 2.39/2.76 ( ( ( plus_plus_nat @ B @ A )
% 2.39/2.76 = ( plus_plus_nat @ C @ A ) )
% 2.39/2.76 = ( B = C ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_right_cancel
% 2.39/2.76 thf(fact_2145_add__right__cancel,axiom,
% 2.39/2.76 ! [B: int,A: int,C: int] :
% 2.39/2.76 ( ( ( plus_plus_int @ B @ A )
% 2.39/2.76 = ( plus_plus_int @ C @ A ) )
% 2.39/2.76 = ( B = C ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_right_cancel
% 2.39/2.76 thf(fact_2146_add__le__cancel__left,axiom,
% 2.39/2.76 ! [C: code_integer,A: code_integer,B: code_integer] :
% 2.39/2.76 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ C @ A ) @ ( plus_p5714425477246183910nteger @ C @ B ) )
% 2.39/2.76 = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_le_cancel_left
% 2.39/2.76 thf(fact_2147_add__le__cancel__left,axiom,
% 2.39/2.76 ! [C: rat,A: rat,B: rat] :
% 2.39/2.76 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 2.39/2.76 = ( ord_less_eq_rat @ A @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_le_cancel_left
% 2.39/2.76 thf(fact_2148_add__le__cancel__left,axiom,
% 2.39/2.76 ! [C: nat,A: nat,B: nat] :
% 2.39/2.76 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 2.39/2.76 = ( ord_less_eq_nat @ A @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_le_cancel_left
% 2.39/2.76 thf(fact_2149_add__le__cancel__left,axiom,
% 2.39/2.76 ! [C: int,A: int,B: int] :
% 2.39/2.76 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 2.39/2.76 = ( ord_less_eq_int @ A @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_le_cancel_left
% 2.39/2.76 thf(fact_2150_add__le__cancel__right,axiom,
% 2.39/2.76 ! [A: code_integer,C: code_integer,B: code_integer] :
% 2.39/2.76 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 2.39/2.76 = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_le_cancel_right
% 2.39/2.76 thf(fact_2151_add__le__cancel__right,axiom,
% 2.39/2.76 ! [A: rat,C: rat,B: rat] :
% 2.39/2.76 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 2.39/2.76 = ( ord_less_eq_rat @ A @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_le_cancel_right
% 2.39/2.76 thf(fact_2152_add__le__cancel__right,axiom,
% 2.39/2.76 ! [A: nat,C: nat,B: nat] :
% 2.39/2.76 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 2.39/2.76 = ( ord_less_eq_nat @ A @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_le_cancel_right
% 2.39/2.76 thf(fact_2153_add__le__cancel__right,axiom,
% 2.39/2.76 ! [A: int,C: int,B: int] :
% 2.39/2.76 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 2.39/2.76 = ( ord_less_eq_int @ A @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_le_cancel_right
% 2.39/2.76 thf(fact_2154_add_Oright__neutral,axiom,
% 2.39/2.76 ! [A: nat] :
% 2.39/2.76 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 2.39/2.76 = A ) ).
% 2.39/2.76
% 2.39/2.76 % add.right_neutral
% 2.39/2.76 thf(fact_2155_add_Oright__neutral,axiom,
% 2.39/2.76 ! [A: int] :
% 2.39/2.76 ( ( plus_plus_int @ A @ zero_zero_int )
% 2.39/2.76 = A ) ).
% 2.39/2.76
% 2.39/2.76 % add.right_neutral
% 2.39/2.76 thf(fact_2156_add_Oright__neutral,axiom,
% 2.39/2.76 ! [A: rat] :
% 2.39/2.76 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 2.39/2.76 = A ) ).
% 2.39/2.76
% 2.39/2.76 % add.right_neutral
% 2.39/2.76 thf(fact_2157_add_Oright__neutral,axiom,
% 2.39/2.76 ! [A: code_integer] :
% 2.39/2.76 ( ( plus_p5714425477246183910nteger @ A @ zero_z3403309356797280102nteger )
% 2.39/2.76 = A ) ).
% 2.39/2.76
% 2.39/2.76 % add.right_neutral
% 2.39/2.76 thf(fact_2158_add_Oright__neutral,axiom,
% 2.39/2.76 ! [A: code_natural] :
% 2.39/2.76 ( ( plus_p4538020629002901425atural @ A @ zero_z2226904508553997617atural )
% 2.39/2.76 = A ) ).
% 2.39/2.76
% 2.39/2.76 % add.right_neutral
% 2.39/2.76 thf(fact_2159_double__zero__sym,axiom,
% 2.39/2.76 ! [A: int] :
% 2.39/2.76 ( ( zero_zero_int
% 2.39/2.76 = ( plus_plus_int @ A @ A ) )
% 2.39/2.76 = ( A = zero_zero_int ) ) ).
% 2.39/2.76
% 2.39/2.76 % double_zero_sym
% 2.39/2.76 thf(fact_2160_double__zero__sym,axiom,
% 2.39/2.76 ! [A: rat] :
% 2.39/2.76 ( ( zero_zero_rat
% 2.39/2.76 = ( plus_plus_rat @ A @ A ) )
% 2.39/2.76 = ( A = zero_zero_rat ) ) ).
% 2.39/2.76
% 2.39/2.76 % double_zero_sym
% 2.39/2.76 thf(fact_2161_double__zero__sym,axiom,
% 2.39/2.76 ! [A: code_integer] :
% 2.39/2.76 ( ( zero_z3403309356797280102nteger
% 2.39/2.76 = ( plus_p5714425477246183910nteger @ A @ A ) )
% 2.39/2.76 = ( A = zero_z3403309356797280102nteger ) ) ).
% 2.39/2.76
% 2.39/2.76 % double_zero_sym
% 2.39/2.76 thf(fact_2162_add__cancel__left__left,axiom,
% 2.39/2.76 ! [B: nat,A: nat] :
% 2.39/2.76 ( ( ( plus_plus_nat @ B @ A )
% 2.39/2.76 = A )
% 2.39/2.76 = ( B = zero_zero_nat ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_cancel_left_left
% 2.39/2.76 thf(fact_2163_add__cancel__left__left,axiom,
% 2.39/2.76 ! [B: int,A: int] :
% 2.39/2.76 ( ( ( plus_plus_int @ B @ A )
% 2.39/2.76 = A )
% 2.39/2.76 = ( B = zero_zero_int ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_cancel_left_left
% 2.39/2.76 thf(fact_2164_add__cancel__left__left,axiom,
% 2.39/2.76 ! [B: rat,A: rat] :
% 2.39/2.76 ( ( ( plus_plus_rat @ B @ A )
% 2.39/2.76 = A )
% 2.39/2.76 = ( B = zero_zero_rat ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_cancel_left_left
% 2.39/2.76 thf(fact_2165_add__cancel__left__left,axiom,
% 2.39/2.76 ! [B: code_integer,A: code_integer] :
% 2.39/2.76 ( ( ( plus_p5714425477246183910nteger @ B @ A )
% 2.39/2.76 = A )
% 2.39/2.76 = ( B = zero_z3403309356797280102nteger ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_cancel_left_left
% 2.39/2.76 thf(fact_2166_add__cancel__left__left,axiom,
% 2.39/2.76 ! [B: code_natural,A: code_natural] :
% 2.39/2.76 ( ( ( plus_p4538020629002901425atural @ B @ A )
% 2.39/2.76 = A )
% 2.39/2.76 = ( B = zero_z2226904508553997617atural ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_cancel_left_left
% 2.39/2.76 thf(fact_2167_add__cancel__left__right,axiom,
% 2.39/2.76 ! [A: nat,B: nat] :
% 2.39/2.76 ( ( ( plus_plus_nat @ A @ B )
% 2.39/2.76 = A )
% 2.39/2.76 = ( B = zero_zero_nat ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_cancel_left_right
% 2.39/2.76 thf(fact_2168_add__cancel__left__right,axiom,
% 2.39/2.76 ! [A: int,B: int] :
% 2.39/2.76 ( ( ( plus_plus_int @ A @ B )
% 2.39/2.76 = A )
% 2.39/2.76 = ( B = zero_zero_int ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_cancel_left_right
% 2.39/2.76 thf(fact_2169_add__cancel__left__right,axiom,
% 2.39/2.76 ! [A: rat,B: rat] :
% 2.39/2.76 ( ( ( plus_plus_rat @ A @ B )
% 2.39/2.76 = A )
% 2.39/2.76 = ( B = zero_zero_rat ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_cancel_left_right
% 2.39/2.76 thf(fact_2170_add__cancel__left__right,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer] :
% 2.39/2.76 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 2.39/2.76 = A )
% 2.39/2.76 = ( B = zero_z3403309356797280102nteger ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_cancel_left_right
% 2.39/2.76 thf(fact_2171_add__cancel__left__right,axiom,
% 2.39/2.76 ! [A: code_natural,B: code_natural] :
% 2.39/2.76 ( ( ( plus_p4538020629002901425atural @ A @ B )
% 2.39/2.76 = A )
% 2.39/2.76 = ( B = zero_z2226904508553997617atural ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_cancel_left_right
% 2.39/2.76 thf(fact_2172_add__cancel__right__left,axiom,
% 2.39/2.76 ! [A: nat,B: nat] :
% 2.39/2.76 ( ( A
% 2.39/2.76 = ( plus_plus_nat @ B @ A ) )
% 2.39/2.76 = ( B = zero_zero_nat ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_cancel_right_left
% 2.39/2.76 thf(fact_2173_add__cancel__right__left,axiom,
% 2.39/2.76 ! [A: int,B: int] :
% 2.39/2.76 ( ( A
% 2.39/2.76 = ( plus_plus_int @ B @ A ) )
% 2.39/2.76 = ( B = zero_zero_int ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_cancel_right_left
% 2.39/2.76 thf(fact_2174_add__cancel__right__left,axiom,
% 2.39/2.76 ! [A: rat,B: rat] :
% 2.39/2.76 ( ( A
% 2.39/2.76 = ( plus_plus_rat @ B @ A ) )
% 2.39/2.76 = ( B = zero_zero_rat ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_cancel_right_left
% 2.39/2.76 thf(fact_2175_add__cancel__right__left,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer] :
% 2.39/2.76 ( ( A
% 2.39/2.76 = ( plus_p5714425477246183910nteger @ B @ A ) )
% 2.39/2.76 = ( B = zero_z3403309356797280102nteger ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_cancel_right_left
% 2.39/2.76 thf(fact_2176_add__cancel__right__left,axiom,
% 2.39/2.76 ! [A: code_natural,B: code_natural] :
% 2.39/2.76 ( ( A
% 2.39/2.76 = ( plus_p4538020629002901425atural @ B @ A ) )
% 2.39/2.76 = ( B = zero_z2226904508553997617atural ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_cancel_right_left
% 2.39/2.76 thf(fact_2177_add__cancel__right__right,axiom,
% 2.39/2.76 ! [A: nat,B: nat] :
% 2.39/2.76 ( ( A
% 2.39/2.76 = ( plus_plus_nat @ A @ B ) )
% 2.39/2.76 = ( B = zero_zero_nat ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_cancel_right_right
% 2.39/2.76 thf(fact_2178_add__cancel__right__right,axiom,
% 2.39/2.76 ! [A: int,B: int] :
% 2.39/2.76 ( ( A
% 2.39/2.76 = ( plus_plus_int @ A @ B ) )
% 2.39/2.76 = ( B = zero_zero_int ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_cancel_right_right
% 2.39/2.76 thf(fact_2179_add__cancel__right__right,axiom,
% 2.39/2.76 ! [A: rat,B: rat] :
% 2.39/2.76 ( ( A
% 2.39/2.76 = ( plus_plus_rat @ A @ B ) )
% 2.39/2.76 = ( B = zero_zero_rat ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_cancel_right_right
% 2.39/2.76 thf(fact_2180_add__cancel__right__right,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer] :
% 2.39/2.76 ( ( A
% 2.39/2.76 = ( plus_p5714425477246183910nteger @ A @ B ) )
% 2.39/2.76 = ( B = zero_z3403309356797280102nteger ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_cancel_right_right
% 2.39/2.76 thf(fact_2181_add__cancel__right__right,axiom,
% 2.39/2.76 ! [A: code_natural,B: code_natural] :
% 2.39/2.76 ( ( A
% 2.39/2.76 = ( plus_p4538020629002901425atural @ A @ B ) )
% 2.39/2.76 = ( B = zero_z2226904508553997617atural ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_cancel_right_right
% 2.39/2.76 thf(fact_2182_add__eq__0__iff__both__eq__0,axiom,
% 2.39/2.76 ! [X: nat,Y: nat] :
% 2.39/2.76 ( ( ( plus_plus_nat @ X @ Y )
% 2.39/2.76 = zero_zero_nat )
% 2.39/2.76 = ( ( X = zero_zero_nat )
% 2.39/2.76 & ( Y = zero_zero_nat ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_eq_0_iff_both_eq_0
% 2.39/2.76 thf(fact_2183_zero__eq__add__iff__both__eq__0,axiom,
% 2.39/2.76 ! [X: nat,Y: nat] :
% 2.39/2.76 ( ( zero_zero_nat
% 2.39/2.76 = ( plus_plus_nat @ X @ Y ) )
% 2.39/2.76 = ( ( X = zero_zero_nat )
% 2.39/2.76 & ( Y = zero_zero_nat ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % zero_eq_add_iff_both_eq_0
% 2.39/2.76 thf(fact_2184_add__0,axiom,
% 2.39/2.76 ! [A: nat] :
% 2.39/2.76 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 2.39/2.76 = A ) ).
% 2.39/2.76
% 2.39/2.76 % add_0
% 2.39/2.76 thf(fact_2185_add__0,axiom,
% 2.39/2.76 ! [A: int] :
% 2.39/2.76 ( ( plus_plus_int @ zero_zero_int @ A )
% 2.39/2.76 = A ) ).
% 2.39/2.76
% 2.39/2.76 % add_0
% 2.39/2.76 thf(fact_2186_add__0,axiom,
% 2.39/2.76 ! [A: rat] :
% 2.39/2.76 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 2.39/2.76 = A ) ).
% 2.39/2.76
% 2.39/2.76 % add_0
% 2.39/2.76 thf(fact_2187_add__0,axiom,
% 2.39/2.76 ! [A: code_integer] :
% 2.39/2.76 ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.76 = A ) ).
% 2.39/2.76
% 2.39/2.76 % add_0
% 2.39/2.76 thf(fact_2188_add__0,axiom,
% 2.39/2.76 ! [A: code_natural] :
% 2.39/2.76 ( ( plus_p4538020629002901425atural @ zero_z2226904508553997617atural @ A )
% 2.39/2.76 = A ) ).
% 2.39/2.76
% 2.39/2.76 % add_0
% 2.39/2.76 thf(fact_2189_add__less__cancel__left,axiom,
% 2.39/2.76 ! [C: code_integer,A: code_integer,B: code_integer] :
% 2.39/2.76 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ C @ A ) @ ( plus_p5714425477246183910nteger @ C @ B ) )
% 2.39/2.76 = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_less_cancel_left
% 2.39/2.76 thf(fact_2190_add__less__cancel__left,axiom,
% 2.39/2.76 ! [C: rat,A: rat,B: rat] :
% 2.39/2.76 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 2.39/2.76 = ( ord_less_rat @ A @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_less_cancel_left
% 2.39/2.76 thf(fact_2191_add__less__cancel__left,axiom,
% 2.39/2.76 ! [C: nat,A: nat,B: nat] :
% 2.39/2.76 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 2.39/2.76 = ( ord_less_nat @ A @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_less_cancel_left
% 2.39/2.76 thf(fact_2192_add__less__cancel__left,axiom,
% 2.39/2.76 ! [C: int,A: int,B: int] :
% 2.39/2.76 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 2.39/2.76 = ( ord_less_int @ A @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_less_cancel_left
% 2.39/2.76 thf(fact_2193_add__less__cancel__right,axiom,
% 2.39/2.76 ! [A: code_integer,C: code_integer,B: code_integer] :
% 2.39/2.76 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 2.39/2.76 = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_less_cancel_right
% 2.39/2.76 thf(fact_2194_add__less__cancel__right,axiom,
% 2.39/2.76 ! [A: rat,C: rat,B: rat] :
% 2.39/2.76 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 2.39/2.76 = ( ord_less_rat @ A @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_less_cancel_right
% 2.39/2.76 thf(fact_2195_add__less__cancel__right,axiom,
% 2.39/2.76 ! [A: nat,C: nat,B: nat] :
% 2.39/2.76 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 2.39/2.76 = ( ord_less_nat @ A @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_less_cancel_right
% 2.39/2.76 thf(fact_2196_add__less__cancel__right,axiom,
% 2.39/2.76 ! [A: int,C: int,B: int] :
% 2.39/2.76 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 2.39/2.76 = ( ord_less_int @ A @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_less_cancel_right
% 2.39/2.76 thf(fact_2197_add__minus__cancel,axiom,
% 2.39/2.76 ! [A: int,B: int] :
% 2.39/2.76 ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
% 2.39/2.76 = B ) ).
% 2.39/2.76
% 2.39/2.76 % add_minus_cancel
% 2.39/2.76 thf(fact_2198_add__minus__cancel,axiom,
% 2.39/2.76 ! [A: rat,B: rat] :
% 2.39/2.76 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B ) )
% 2.39/2.76 = B ) ).
% 2.39/2.76
% 2.39/2.76 % add_minus_cancel
% 2.39/2.76 thf(fact_2199_add__minus__cancel,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer] :
% 2.39/2.76 ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) )
% 2.39/2.76 = B ) ).
% 2.39/2.76
% 2.39/2.76 % add_minus_cancel
% 2.39/2.76 thf(fact_2200_minus__add__cancel,axiom,
% 2.39/2.76 ! [A: int,B: int] :
% 2.39/2.76 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
% 2.39/2.76 = B ) ).
% 2.39/2.76
% 2.39/2.76 % minus_add_cancel
% 2.39/2.76 thf(fact_2201_minus__add__cancel,axiom,
% 2.39/2.76 ! [A: rat,B: rat] :
% 2.39/2.76 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( plus_plus_rat @ A @ B ) )
% 2.39/2.76 = B ) ).
% 2.39/2.76
% 2.39/2.76 % minus_add_cancel
% 2.39/2.76 thf(fact_2202_minus__add__cancel,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer] :
% 2.39/2.76 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 2.39/2.76 = B ) ).
% 2.39/2.76
% 2.39/2.76 % minus_add_cancel
% 2.39/2.76 thf(fact_2203_minus__add__distrib,axiom,
% 2.39/2.76 ! [A: int,B: int] :
% 2.39/2.76 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 2.39/2.76 = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % minus_add_distrib
% 2.39/2.76 thf(fact_2204_minus__add__distrib,axiom,
% 2.39/2.76 ! [A: rat,B: rat] :
% 2.39/2.76 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 2.39/2.76 = ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % minus_add_distrib
% 2.39/2.76 thf(fact_2205_minus__add__distrib,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer] :
% 2.39/2.76 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 2.39/2.76 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % minus_add_distrib
% 2.39/2.76 thf(fact_2206_sgn__1,axiom,
% 2.39/2.76 ( ( sgn_sgn_int @ one_one_int )
% 2.39/2.76 = one_one_int ) ).
% 2.39/2.76
% 2.39/2.76 % sgn_1
% 2.39/2.76 thf(fact_2207_sgn__1,axiom,
% 2.39/2.76 ( ( sgn_sgn_rat @ one_one_rat )
% 2.39/2.76 = one_one_rat ) ).
% 2.39/2.76
% 2.39/2.76 % sgn_1
% 2.39/2.76 thf(fact_2208_sgn__1,axiom,
% 2.39/2.76 ( ( sgn_sgn_Code_integer @ one_one_Code_integer )
% 2.39/2.76 = one_one_Code_integer ) ).
% 2.39/2.76
% 2.39/2.76 % sgn_1
% 2.39/2.76 thf(fact_2209_add__le__same__cancel1,axiom,
% 2.39/2.76 ! [B: code_integer,A: code_integer] :
% 2.39/2.76 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 2.39/2.76 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_le_same_cancel1
% 2.39/2.76 thf(fact_2210_add__le__same__cancel1,axiom,
% 2.39/2.76 ! [B: code_natural,A: code_natural] :
% 2.39/2.76 ( ( ord_le1926595141338095240atural @ ( plus_p4538020629002901425atural @ B @ A ) @ B )
% 2.39/2.76 = ( ord_le1926595141338095240atural @ A @ zero_z2226904508553997617atural ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_le_same_cancel1
% 2.39/2.76 thf(fact_2211_add__le__same__cancel1,axiom,
% 2.39/2.76 ! [B: rat,A: rat] :
% 2.39/2.76 ( ( ord_less_eq_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 2.39/2.76 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_le_same_cancel1
% 2.39/2.76 thf(fact_2212_add__le__same__cancel1,axiom,
% 2.39/2.76 ! [B: nat,A: nat] :
% 2.39/2.76 ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 2.39/2.76 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_le_same_cancel1
% 2.39/2.76 thf(fact_2213_add__le__same__cancel1,axiom,
% 2.39/2.76 ! [B: int,A: int] :
% 2.39/2.76 ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
% 2.39/2.76 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_le_same_cancel1
% 2.39/2.76 thf(fact_2214_add__le__same__cancel2,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer] :
% 2.39/2.76 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 2.39/2.76 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_le_same_cancel2
% 2.39/2.76 thf(fact_2215_add__le__same__cancel2,axiom,
% 2.39/2.76 ! [A: code_natural,B: code_natural] :
% 2.39/2.76 ( ( ord_le1926595141338095240atural @ ( plus_p4538020629002901425atural @ A @ B ) @ B )
% 2.39/2.76 = ( ord_le1926595141338095240atural @ A @ zero_z2226904508553997617atural ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_le_same_cancel2
% 2.39/2.76 thf(fact_2216_add__le__same__cancel2,axiom,
% 2.39/2.76 ! [A: rat,B: rat] :
% 2.39/2.76 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 2.39/2.76 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_le_same_cancel2
% 2.39/2.76 thf(fact_2217_add__le__same__cancel2,axiom,
% 2.39/2.76 ! [A: nat,B: nat] :
% 2.39/2.76 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 2.39/2.76 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_le_same_cancel2
% 2.39/2.76 thf(fact_2218_add__le__same__cancel2,axiom,
% 2.39/2.76 ! [A: int,B: int] :
% 2.39/2.76 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
% 2.39/2.76 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_le_same_cancel2
% 2.39/2.76 thf(fact_2219_le__add__same__cancel1,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer] :
% 2.39/2.76 ( ( ord_le3102999989581377725nteger @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 2.39/2.76 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % le_add_same_cancel1
% 2.39/2.76 thf(fact_2220_le__add__same__cancel1,axiom,
% 2.39/2.76 ! [A: code_natural,B: code_natural] :
% 2.39/2.76 ( ( ord_le1926595141338095240atural @ A @ ( plus_p4538020629002901425atural @ A @ B ) )
% 2.39/2.76 = ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % le_add_same_cancel1
% 2.39/2.76 thf(fact_2221_le__add__same__cancel1,axiom,
% 2.39/2.76 ! [A: rat,B: rat] :
% 2.39/2.76 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 2.39/2.76 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % le_add_same_cancel1
% 2.39/2.76 thf(fact_2222_le__add__same__cancel1,axiom,
% 2.39/2.76 ! [A: nat,B: nat] :
% 2.39/2.76 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 2.39/2.76 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % le_add_same_cancel1
% 2.39/2.76 thf(fact_2223_le__add__same__cancel1,axiom,
% 2.39/2.76 ! [A: int,B: int] :
% 2.39/2.76 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
% 2.39/2.76 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % le_add_same_cancel1
% 2.39/2.76 thf(fact_2224_le__add__same__cancel2,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer] :
% 2.39/2.76 ( ( ord_le3102999989581377725nteger @ A @ ( plus_p5714425477246183910nteger @ B @ A ) )
% 2.39/2.76 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % le_add_same_cancel2
% 2.39/2.76 thf(fact_2225_le__add__same__cancel2,axiom,
% 2.39/2.76 ! [A: code_natural,B: code_natural] :
% 2.39/2.76 ( ( ord_le1926595141338095240atural @ A @ ( plus_p4538020629002901425atural @ B @ A ) )
% 2.39/2.76 = ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % le_add_same_cancel2
% 2.39/2.76 thf(fact_2226_le__add__same__cancel2,axiom,
% 2.39/2.76 ! [A: rat,B: rat] :
% 2.39/2.76 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 2.39/2.76 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % le_add_same_cancel2
% 2.39/2.76 thf(fact_2227_le__add__same__cancel2,axiom,
% 2.39/2.76 ! [A: nat,B: nat] :
% 2.39/2.76 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 2.39/2.76 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % le_add_same_cancel2
% 2.39/2.76 thf(fact_2228_le__add__same__cancel2,axiom,
% 2.39/2.76 ! [A: int,B: int] :
% 2.39/2.76 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
% 2.39/2.76 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % le_add_same_cancel2
% 2.39/2.76 thf(fact_2229_double__add__le__zero__iff__single__add__le__zero,axiom,
% 2.39/2.76 ! [A: code_integer] :
% 2.39/2.76 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ A ) @ zero_z3403309356797280102nteger )
% 2.39/2.76 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 2.39/2.76
% 2.39/2.76 % double_add_le_zero_iff_single_add_le_zero
% 2.39/2.76 thf(fact_2230_double__add__le__zero__iff__single__add__le__zero,axiom,
% 2.39/2.76 ! [A: rat] :
% 2.39/2.76 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 2.39/2.76 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 2.39/2.76
% 2.39/2.76 % double_add_le_zero_iff_single_add_le_zero
% 2.39/2.76 thf(fact_2231_double__add__le__zero__iff__single__add__le__zero,axiom,
% 2.39/2.76 ! [A: int] :
% 2.39/2.76 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 2.39/2.76 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 2.39/2.76
% 2.39/2.76 % double_add_le_zero_iff_single_add_le_zero
% 2.39/2.76 thf(fact_2232_zero__le__double__add__iff__zero__le__single__add,axiom,
% 2.39/2.76 ! [A: code_integer] :
% 2.39/2.76 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ A ) )
% 2.39/2.76 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 2.39/2.76
% 2.39/2.76 % zero_le_double_add_iff_zero_le_single_add
% 2.39/2.76 thf(fact_2233_zero__le__double__add__iff__zero__le__single__add,axiom,
% 2.39/2.76 ! [A: rat] :
% 2.39/2.76 ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 2.39/2.76 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 2.39/2.76
% 2.39/2.76 % zero_le_double_add_iff_zero_le_single_add
% 2.39/2.76 thf(fact_2234_zero__le__double__add__iff__zero__le__single__add,axiom,
% 2.39/2.76 ! [A: int] :
% 2.39/2.76 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 2.39/2.76 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 2.39/2.76
% 2.39/2.76 % zero_le_double_add_iff_zero_le_single_add
% 2.39/2.76 thf(fact_2235_add__less__same__cancel1,axiom,
% 2.39/2.76 ! [B: code_natural,A: code_natural] :
% 2.39/2.76 ( ( ord_le5570908160329646204atural @ ( plus_p4538020629002901425atural @ B @ A ) @ B )
% 2.39/2.76 = ( ord_le5570908160329646204atural @ A @ zero_z2226904508553997617atural ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_less_same_cancel1
% 2.39/2.76 thf(fact_2236_add__less__same__cancel1,axiom,
% 2.39/2.76 ! [B: code_integer,A: code_integer] :
% 2.39/2.76 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 2.39/2.76 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_less_same_cancel1
% 2.39/2.76 thf(fact_2237_add__less__same__cancel1,axiom,
% 2.39/2.76 ! [B: rat,A: rat] :
% 2.39/2.76 ( ( ord_less_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 2.39/2.76 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_less_same_cancel1
% 2.39/2.76 thf(fact_2238_add__less__same__cancel1,axiom,
% 2.39/2.76 ! [B: nat,A: nat] :
% 2.39/2.76 ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 2.39/2.76 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_less_same_cancel1
% 2.39/2.76 thf(fact_2239_add__less__same__cancel1,axiom,
% 2.39/2.76 ! [B: int,A: int] :
% 2.39/2.76 ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
% 2.39/2.76 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_less_same_cancel1
% 2.39/2.76 thf(fact_2240_add__less__same__cancel2,axiom,
% 2.39/2.76 ! [A: code_natural,B: code_natural] :
% 2.39/2.76 ( ( ord_le5570908160329646204atural @ ( plus_p4538020629002901425atural @ A @ B ) @ B )
% 2.39/2.76 = ( ord_le5570908160329646204atural @ A @ zero_z2226904508553997617atural ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_less_same_cancel2
% 2.39/2.76 thf(fact_2241_add__less__same__cancel2,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer] :
% 2.39/2.76 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 2.39/2.76 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_less_same_cancel2
% 2.39/2.76 thf(fact_2242_add__less__same__cancel2,axiom,
% 2.39/2.76 ! [A: rat,B: rat] :
% 2.39/2.76 ( ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 2.39/2.76 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_less_same_cancel2
% 2.39/2.76 thf(fact_2243_add__less__same__cancel2,axiom,
% 2.39/2.76 ! [A: nat,B: nat] :
% 2.39/2.76 ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 2.39/2.76 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_less_same_cancel2
% 2.39/2.76 thf(fact_2244_add__less__same__cancel2,axiom,
% 2.39/2.76 ! [A: int,B: int] :
% 2.39/2.76 ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
% 2.39/2.76 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_less_same_cancel2
% 2.39/2.76 thf(fact_2245_less__add__same__cancel1,axiom,
% 2.39/2.76 ! [A: code_natural,B: code_natural] :
% 2.39/2.76 ( ( ord_le5570908160329646204atural @ A @ ( plus_p4538020629002901425atural @ A @ B ) )
% 2.39/2.76 = ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % less_add_same_cancel1
% 2.39/2.76 thf(fact_2246_less__add__same__cancel1,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer] :
% 2.39/2.76 ( ( ord_le6747313008572928689nteger @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 2.39/2.76 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % less_add_same_cancel1
% 2.39/2.76 thf(fact_2247_less__add__same__cancel1,axiom,
% 2.39/2.76 ! [A: rat,B: rat] :
% 2.39/2.76 ( ( ord_less_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 2.39/2.76 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % less_add_same_cancel1
% 2.39/2.76 thf(fact_2248_less__add__same__cancel1,axiom,
% 2.39/2.76 ! [A: nat,B: nat] :
% 2.39/2.76 ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 2.39/2.76 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % less_add_same_cancel1
% 2.39/2.76 thf(fact_2249_less__add__same__cancel1,axiom,
% 2.39/2.76 ! [A: int,B: int] :
% 2.39/2.76 ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
% 2.39/2.76 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % less_add_same_cancel1
% 2.39/2.76 thf(fact_2250_less__add__same__cancel2,axiom,
% 2.39/2.76 ! [A: code_natural,B: code_natural] :
% 2.39/2.76 ( ( ord_le5570908160329646204atural @ A @ ( plus_p4538020629002901425atural @ B @ A ) )
% 2.39/2.76 = ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % less_add_same_cancel2
% 2.39/2.76 thf(fact_2251_less__add__same__cancel2,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer] :
% 2.39/2.76 ( ( ord_le6747313008572928689nteger @ A @ ( plus_p5714425477246183910nteger @ B @ A ) )
% 2.39/2.76 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % less_add_same_cancel2
% 2.39/2.76 thf(fact_2252_less__add__same__cancel2,axiom,
% 2.39/2.76 ! [A: rat,B: rat] :
% 2.39/2.76 ( ( ord_less_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 2.39/2.76 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % less_add_same_cancel2
% 2.39/2.76 thf(fact_2253_less__add__same__cancel2,axiom,
% 2.39/2.76 ! [A: nat,B: nat] :
% 2.39/2.76 ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 2.39/2.76 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % less_add_same_cancel2
% 2.39/2.76 thf(fact_2254_less__add__same__cancel2,axiom,
% 2.39/2.76 ! [A: int,B: int] :
% 2.39/2.76 ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
% 2.39/2.76 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % less_add_same_cancel2
% 2.39/2.76 thf(fact_2255_double__add__less__zero__iff__single__add__less__zero,axiom,
% 2.39/2.76 ! [A: code_integer] :
% 2.39/2.76 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ A ) @ zero_z3403309356797280102nteger )
% 2.39/2.76 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 2.39/2.76
% 2.39/2.76 % double_add_less_zero_iff_single_add_less_zero
% 2.39/2.76 thf(fact_2256_double__add__less__zero__iff__single__add__less__zero,axiom,
% 2.39/2.76 ! [A: rat] :
% 2.39/2.76 ( ( ord_less_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 2.39/2.76 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 2.39/2.76
% 2.39/2.76 % double_add_less_zero_iff_single_add_less_zero
% 2.39/2.76 thf(fact_2257_double__add__less__zero__iff__single__add__less__zero,axiom,
% 2.39/2.76 ! [A: int] :
% 2.39/2.76 ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 2.39/2.76 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 2.39/2.76
% 2.39/2.76 % double_add_less_zero_iff_single_add_less_zero
% 2.39/2.76 thf(fact_2258_zero__less__double__add__iff__zero__less__single__add,axiom,
% 2.39/2.76 ! [A: code_integer] :
% 2.39/2.76 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ A ) )
% 2.39/2.76 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 2.39/2.76
% 2.39/2.76 % zero_less_double_add_iff_zero_less_single_add
% 2.39/2.76 thf(fact_2259_zero__less__double__add__iff__zero__less__single__add,axiom,
% 2.39/2.76 ! [A: rat] :
% 2.39/2.76 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 2.39/2.76 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 2.39/2.76
% 2.39/2.76 % zero_less_double_add_iff_zero_less_single_add
% 2.39/2.76 thf(fact_2260_zero__less__double__add__iff__zero__less__single__add,axiom,
% 2.39/2.76 ! [A: int] :
% 2.39/2.76 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 2.39/2.76 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 2.39/2.76
% 2.39/2.76 % zero_less_double_add_iff_zero_less_single_add
% 2.39/2.76 thf(fact_2261_add_Oright__inverse,axiom,
% 2.39/2.76 ! [A: int] :
% 2.39/2.76 ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 2.39/2.76 = zero_zero_int ) ).
% 2.39/2.76
% 2.39/2.76 % add.right_inverse
% 2.39/2.76 thf(fact_2262_add_Oright__inverse,axiom,
% 2.39/2.76 ! [A: rat] :
% 2.39/2.76 ( ( plus_plus_rat @ A @ ( uminus_uminus_rat @ A ) )
% 2.39/2.76 = zero_zero_rat ) ).
% 2.39/2.76
% 2.39/2.76 % add.right_inverse
% 2.39/2.76 thf(fact_2263_add_Oright__inverse,axiom,
% 2.39/2.76 ! [A: code_integer] :
% 2.39/2.76 ( ( plus_p5714425477246183910nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 2.39/2.76 = zero_z3403309356797280102nteger ) ).
% 2.39/2.76
% 2.39/2.76 % add.right_inverse
% 2.39/2.76 thf(fact_2264_ab__left__minus,axiom,
% 2.39/2.76 ! [A: int] :
% 2.39/2.76 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 2.39/2.76 = zero_zero_int ) ).
% 2.39/2.76
% 2.39/2.76 % ab_left_minus
% 2.39/2.76 thf(fact_2265_ab__left__minus,axiom,
% 2.39/2.76 ! [A: rat] :
% 2.39/2.76 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 2.39/2.76 = zero_zero_rat ) ).
% 2.39/2.76
% 2.39/2.76 % ab_left_minus
% 2.39/2.76 thf(fact_2266_ab__left__minus,axiom,
% 2.39/2.76 ! [A: code_integer] :
% 2.39/2.76 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 2.39/2.76 = zero_z3403309356797280102nteger ) ).
% 2.39/2.76
% 2.39/2.76 % ab_left_minus
% 2.39/2.76 thf(fact_2267_add__neg__numeral__special_I7_J,axiom,
% 2.39/2.76 ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 2.39/2.76 = zero_zero_int ) ).
% 2.39/2.76
% 2.39/2.76 % add_neg_numeral_special(7)
% 2.39/2.76 thf(fact_2268_add__neg__numeral__special_I7_J,axiom,
% 2.39/2.76 ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 2.39/2.76 = zero_zero_rat ) ).
% 2.39/2.76
% 2.39/2.76 % add_neg_numeral_special(7)
% 2.39/2.76 thf(fact_2269_add__neg__numeral__special_I7_J,axiom,
% 2.39/2.76 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 2.39/2.76 = zero_z3403309356797280102nteger ) ).
% 2.39/2.76
% 2.39/2.76 % add_neg_numeral_special(7)
% 2.39/2.76 thf(fact_2270_add__neg__numeral__special_I8_J,axiom,
% 2.39/2.76 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 2.39/2.76 = zero_zero_int ) ).
% 2.39/2.76
% 2.39/2.76 % add_neg_numeral_special(8)
% 2.39/2.76 thf(fact_2271_add__neg__numeral__special_I8_J,axiom,
% 2.39/2.76 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 2.39/2.76 = zero_zero_rat ) ).
% 2.39/2.76
% 2.39/2.76 % add_neg_numeral_special(8)
% 2.39/2.76 thf(fact_2272_add__neg__numeral__special_I8_J,axiom,
% 2.39/2.76 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 2.39/2.76 = zero_z3403309356797280102nteger ) ).
% 2.39/2.76
% 2.39/2.76 % add_neg_numeral_special(8)
% 2.39/2.76 thf(fact_2273_sgn__pos,axiom,
% 2.39/2.76 ! [A: code_integer] :
% 2.39/2.76 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.76 => ( ( sgn_sgn_Code_integer @ A )
% 2.39/2.76 = one_one_Code_integer ) ) ).
% 2.39/2.76
% 2.39/2.76 % sgn_pos
% 2.39/2.76 thf(fact_2274_sgn__pos,axiom,
% 2.39/2.76 ! [A: rat] :
% 2.39/2.76 ( ( ord_less_rat @ zero_zero_rat @ A )
% 2.39/2.76 => ( ( sgn_sgn_rat @ A )
% 2.39/2.76 = one_one_rat ) ) ).
% 2.39/2.76
% 2.39/2.76 % sgn_pos
% 2.39/2.76 thf(fact_2275_sgn__pos,axiom,
% 2.39/2.76 ! [A: int] :
% 2.39/2.76 ( ( ord_less_int @ zero_zero_int @ A )
% 2.39/2.76 => ( ( sgn_sgn_int @ A )
% 2.39/2.76 = one_one_int ) ) ).
% 2.39/2.76
% 2.39/2.76 % sgn_pos
% 2.39/2.76 thf(fact_2276_nat__geq__1__eq__neqz,axiom,
% 2.39/2.76 ! [X: nat] :
% 2.39/2.76 ( ( ord_less_eq_nat @ one_one_nat @ X )
% 2.39/2.76 = ( X != zero_zero_nat ) ) ).
% 2.39/2.76
% 2.39/2.76 % nat_geq_1_eq_neqz
% 2.39/2.76 thf(fact_2277_add__mono__thms__linordered__semiring_I4_J,axiom,
% 2.39/2.76 ! [I2: code_integer,J: code_integer,K: code_integer,L: code_integer] :
% 2.39/2.76 ( ( ( I2 = J )
% 2.39/2.76 & ( K = L ) )
% 2.39/2.76 => ( ( plus_p5714425477246183910nteger @ I2 @ K )
% 2.39/2.76 = ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono_thms_linordered_semiring(4)
% 2.39/2.76 thf(fact_2278_add__mono__thms__linordered__semiring_I4_J,axiom,
% 2.39/2.76 ! [I2: rat,J: rat,K: rat,L: rat] :
% 2.39/2.76 ( ( ( I2 = J )
% 2.39/2.76 & ( K = L ) )
% 2.39/2.76 => ( ( plus_plus_rat @ I2 @ K )
% 2.39/2.76 = ( plus_plus_rat @ J @ L ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono_thms_linordered_semiring(4)
% 2.39/2.76 thf(fact_2279_add__mono__thms__linordered__semiring_I4_J,axiom,
% 2.39/2.76 ! [I2: nat,J: nat,K: nat,L: nat] :
% 2.39/2.76 ( ( ( I2 = J )
% 2.39/2.76 & ( K = L ) )
% 2.39/2.76 => ( ( plus_plus_nat @ I2 @ K )
% 2.39/2.76 = ( plus_plus_nat @ J @ L ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono_thms_linordered_semiring(4)
% 2.39/2.76 thf(fact_2280_add__mono__thms__linordered__semiring_I4_J,axiom,
% 2.39/2.76 ! [I2: int,J: int,K: int,L: int] :
% 2.39/2.76 ( ( ( I2 = J )
% 2.39/2.76 & ( K = L ) )
% 2.39/2.76 => ( ( plus_plus_int @ I2 @ K )
% 2.39/2.76 = ( plus_plus_int @ J @ L ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono_thms_linordered_semiring(4)
% 2.39/2.76 thf(fact_2281_group__cancel_Oadd1,axiom,
% 2.39/2.76 ! [A3: code_integer,K: code_integer,A: code_integer,B: code_integer] :
% 2.39/2.76 ( ( A3
% 2.39/2.76 = ( plus_p5714425477246183910nteger @ K @ A ) )
% 2.39/2.76 => ( ( plus_p5714425477246183910nteger @ A3 @ B )
% 2.39/2.76 = ( plus_p5714425477246183910nteger @ K @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % group_cancel.add1
% 2.39/2.76 thf(fact_2282_group__cancel_Oadd1,axiom,
% 2.39/2.76 ! [A3: rat,K: rat,A: rat,B: rat] :
% 2.39/2.76 ( ( A3
% 2.39/2.76 = ( plus_plus_rat @ K @ A ) )
% 2.39/2.76 => ( ( plus_plus_rat @ A3 @ B )
% 2.39/2.76 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % group_cancel.add1
% 2.39/2.76 thf(fact_2283_group__cancel_Oadd1,axiom,
% 2.39/2.76 ! [A3: nat,K: nat,A: nat,B: nat] :
% 2.39/2.76 ( ( A3
% 2.39/2.76 = ( plus_plus_nat @ K @ A ) )
% 2.39/2.76 => ( ( plus_plus_nat @ A3 @ B )
% 2.39/2.76 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % group_cancel.add1
% 2.39/2.76 thf(fact_2284_group__cancel_Oadd1,axiom,
% 2.39/2.76 ! [A3: int,K: int,A: int,B: int] :
% 2.39/2.76 ( ( A3
% 2.39/2.76 = ( plus_plus_int @ K @ A ) )
% 2.39/2.76 => ( ( plus_plus_int @ A3 @ B )
% 2.39/2.76 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % group_cancel.add1
% 2.39/2.76 thf(fact_2285_group__cancel_Oadd2,axiom,
% 2.39/2.76 ! [B3: code_integer,K: code_integer,B: code_integer,A: code_integer] :
% 2.39/2.76 ( ( B3
% 2.39/2.76 = ( plus_p5714425477246183910nteger @ K @ B ) )
% 2.39/2.76 => ( ( plus_p5714425477246183910nteger @ A @ B3 )
% 2.39/2.76 = ( plus_p5714425477246183910nteger @ K @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % group_cancel.add2
% 2.39/2.76 thf(fact_2286_group__cancel_Oadd2,axiom,
% 2.39/2.76 ! [B3: rat,K: rat,B: rat,A: rat] :
% 2.39/2.76 ( ( B3
% 2.39/2.76 = ( plus_plus_rat @ K @ B ) )
% 2.39/2.76 => ( ( plus_plus_rat @ A @ B3 )
% 2.39/2.76 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % group_cancel.add2
% 2.39/2.76 thf(fact_2287_group__cancel_Oadd2,axiom,
% 2.39/2.76 ! [B3: nat,K: nat,B: nat,A: nat] :
% 2.39/2.76 ( ( B3
% 2.39/2.76 = ( plus_plus_nat @ K @ B ) )
% 2.39/2.76 => ( ( plus_plus_nat @ A @ B3 )
% 2.39/2.76 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % group_cancel.add2
% 2.39/2.76 thf(fact_2288_group__cancel_Oadd2,axiom,
% 2.39/2.76 ! [B3: int,K: int,B: int,A: int] :
% 2.39/2.76 ( ( B3
% 2.39/2.76 = ( plus_plus_int @ K @ B ) )
% 2.39/2.76 => ( ( plus_plus_int @ A @ B3 )
% 2.39/2.76 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % group_cancel.add2
% 2.39/2.76 thf(fact_2289_add_Oright__assoc,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.76 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 2.39/2.76 = ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add.right_assoc
% 2.39/2.76 thf(fact_2290_add_Oright__assoc,axiom,
% 2.39/2.76 ! [A: rat,B: rat,C: rat] :
% 2.39/2.76 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 2.39/2.76 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add.right_assoc
% 2.39/2.76 thf(fact_2291_add_Oright__assoc,axiom,
% 2.39/2.76 ! [A: nat,B: nat,C: nat] :
% 2.39/2.76 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 2.39/2.76 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add.right_assoc
% 2.39/2.76 thf(fact_2292_add_Oright__assoc,axiom,
% 2.39/2.76 ! [A: int,B: int,C: int] :
% 2.39/2.76 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 2.39/2.76 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add.right_assoc
% 2.39/2.76 thf(fact_2293_add_Oright__commute,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.76 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 2.39/2.76 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % add.right_commute
% 2.39/2.76 thf(fact_2294_add_Oright__commute,axiom,
% 2.39/2.76 ! [A: rat,B: rat,C: rat] :
% 2.39/2.76 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 2.39/2.76 = ( plus_plus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % add.right_commute
% 2.39/2.76 thf(fact_2295_add_Oright__commute,axiom,
% 2.39/2.76 ! [A: nat,B: nat,C: nat] :
% 2.39/2.76 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 2.39/2.76 = ( plus_plus_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % add.right_commute
% 2.39/2.76 thf(fact_2296_add_Oright__commute,axiom,
% 2.39/2.76 ! [A: int,B: int,C: int] :
% 2.39/2.76 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 2.39/2.76 = ( plus_plus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % add.right_commute
% 2.39/2.76 thf(fact_2297_add_Oassoc,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.76 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 2.39/2.76 = ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add.assoc
% 2.39/2.76 thf(fact_2298_add_Oassoc,axiom,
% 2.39/2.76 ! [A: rat,B: rat,C: rat] :
% 2.39/2.76 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 2.39/2.76 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add.assoc
% 2.39/2.76 thf(fact_2299_add_Oassoc,axiom,
% 2.39/2.76 ! [A: nat,B: nat,C: nat] :
% 2.39/2.76 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 2.39/2.76 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add.assoc
% 2.39/2.76 thf(fact_2300_add_Oassoc,axiom,
% 2.39/2.76 ! [A: int,B: int,C: int] :
% 2.39/2.76 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 2.39/2.76 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add.assoc
% 2.39/2.76 thf(fact_2301_add_Oleft__cancel,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.76 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 2.39/2.76 = ( plus_p5714425477246183910nteger @ A @ C ) )
% 2.39/2.76 = ( B = C ) ) ).
% 2.39/2.76
% 2.39/2.76 % add.left_cancel
% 2.39/2.76 thf(fact_2302_add_Oleft__cancel,axiom,
% 2.39/2.76 ! [A: rat,B: rat,C: rat] :
% 2.39/2.76 ( ( ( plus_plus_rat @ A @ B )
% 2.39/2.76 = ( plus_plus_rat @ A @ C ) )
% 2.39/2.76 = ( B = C ) ) ).
% 2.39/2.76
% 2.39/2.76 % add.left_cancel
% 2.39/2.76 thf(fact_2303_add_Oleft__cancel,axiom,
% 2.39/2.76 ! [A: int,B: int,C: int] :
% 2.39/2.76 ( ( ( plus_plus_int @ A @ B )
% 2.39/2.76 = ( plus_plus_int @ A @ C ) )
% 2.39/2.76 = ( B = C ) ) ).
% 2.39/2.76
% 2.39/2.76 % add.left_cancel
% 2.39/2.76 thf(fact_2304_add_Oright__cancel,axiom,
% 2.39/2.76 ! [B: code_integer,A: code_integer,C: code_integer] :
% 2.39/2.76 ( ( ( plus_p5714425477246183910nteger @ B @ A )
% 2.39/2.76 = ( plus_p5714425477246183910nteger @ C @ A ) )
% 2.39/2.76 = ( B = C ) ) ).
% 2.39/2.76
% 2.39/2.76 % add.right_cancel
% 2.39/2.76 thf(fact_2305_add_Oright__cancel,axiom,
% 2.39/2.76 ! [B: rat,A: rat,C: rat] :
% 2.39/2.76 ( ( ( plus_plus_rat @ B @ A )
% 2.39/2.76 = ( plus_plus_rat @ C @ A ) )
% 2.39/2.76 = ( B = C ) ) ).
% 2.39/2.76
% 2.39/2.76 % add.right_cancel
% 2.39/2.76 thf(fact_2306_add_Oright__cancel,axiom,
% 2.39/2.76 ! [B: int,A: int,C: int] :
% 2.39/2.76 ( ( ( plus_plus_int @ B @ A )
% 2.39/2.76 = ( plus_plus_int @ C @ A ) )
% 2.39/2.76 = ( B = C ) ) ).
% 2.39/2.76
% 2.39/2.76 % add.right_cancel
% 2.39/2.76 thf(fact_2307_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 2.39/2.76 ( plus_p5714425477246183910nteger
% 2.39/2.76 = ( ^ [A2: code_integer,B2: code_integer] : ( plus_p5714425477246183910nteger @ B2 @ A2 ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % ab_semigroup_add_class.add.commute
% 2.39/2.76 thf(fact_2308_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 2.39/2.76 ( plus_plus_rat
% 2.39/2.76 = ( ^ [A2: rat,B2: rat] : ( plus_plus_rat @ B2 @ A2 ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % ab_semigroup_add_class.add.commute
% 2.39/2.76 thf(fact_2309_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 2.39/2.76 ( plus_plus_nat
% 2.39/2.76 = ( ^ [A2: nat,B2: nat] : ( plus_plus_nat @ B2 @ A2 ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % ab_semigroup_add_class.add.commute
% 2.39/2.76 thf(fact_2310_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 2.39/2.76 ( plus_plus_int
% 2.39/2.76 = ( ^ [A2: int,B2: int] : ( plus_plus_int @ B2 @ A2 ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % ab_semigroup_add_class.add.commute
% 2.39/2.76 thf(fact_2311_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 2.39/2.76 ! [B: code_integer,A: code_integer,C: code_integer] :
% 2.39/2.76 ( ( plus_p5714425477246183910nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) )
% 2.39/2.76 = ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % ab_semigroup_add_class.add.left_commute
% 2.39/2.76 thf(fact_2312_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 2.39/2.76 ! [B: rat,A: rat,C: rat] :
% 2.39/2.76 ( ( plus_plus_rat @ B @ ( plus_plus_rat @ A @ C ) )
% 2.39/2.76 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % ab_semigroup_add_class.add.left_commute
% 2.39/2.76 thf(fact_2313_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 2.39/2.76 ! [B: nat,A: nat,C: nat] :
% 2.39/2.76 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 2.39/2.76 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % ab_semigroup_add_class.add.left_commute
% 2.39/2.76 thf(fact_2314_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 2.39/2.76 ! [B: int,A: int,C: int] :
% 2.39/2.76 ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) )
% 2.39/2.76 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % ab_semigroup_add_class.add.left_commute
% 2.39/2.76 thf(fact_2315_add__left__imp__eq,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.76 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 2.39/2.76 = ( plus_p5714425477246183910nteger @ A @ C ) )
% 2.39/2.76 => ( B = C ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_left_imp_eq
% 2.39/2.76 thf(fact_2316_add__left__imp__eq,axiom,
% 2.39/2.76 ! [A: rat,B: rat,C: rat] :
% 2.39/2.76 ( ( ( plus_plus_rat @ A @ B )
% 2.39/2.76 = ( plus_plus_rat @ A @ C ) )
% 2.39/2.76 => ( B = C ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_left_imp_eq
% 2.39/2.76 thf(fact_2317_add__left__imp__eq,axiom,
% 2.39/2.76 ! [A: nat,B: nat,C: nat] :
% 2.39/2.76 ( ( ( plus_plus_nat @ A @ B )
% 2.39/2.76 = ( plus_plus_nat @ A @ C ) )
% 2.39/2.76 => ( B = C ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_left_imp_eq
% 2.39/2.76 thf(fact_2318_add__left__imp__eq,axiom,
% 2.39/2.76 ! [A: int,B: int,C: int] :
% 2.39/2.76 ( ( ( plus_plus_int @ A @ B )
% 2.39/2.76 = ( plus_plus_int @ A @ C ) )
% 2.39/2.76 => ( B = C ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_left_imp_eq
% 2.39/2.76 thf(fact_2319_add__right__imp__eq,axiom,
% 2.39/2.76 ! [B: code_integer,A: code_integer,C: code_integer] :
% 2.39/2.76 ( ( ( plus_p5714425477246183910nteger @ B @ A )
% 2.39/2.76 = ( plus_p5714425477246183910nteger @ C @ A ) )
% 2.39/2.76 => ( B = C ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_right_imp_eq
% 2.39/2.76 thf(fact_2320_add__right__imp__eq,axiom,
% 2.39/2.76 ! [B: rat,A: rat,C: rat] :
% 2.39/2.76 ( ( ( plus_plus_rat @ B @ A )
% 2.39/2.76 = ( plus_plus_rat @ C @ A ) )
% 2.39/2.76 => ( B = C ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_right_imp_eq
% 2.39/2.76 thf(fact_2321_add__right__imp__eq,axiom,
% 2.39/2.76 ! [B: nat,A: nat,C: nat] :
% 2.39/2.76 ( ( ( plus_plus_nat @ B @ A )
% 2.39/2.76 = ( plus_plus_nat @ C @ A ) )
% 2.39/2.76 => ( B = C ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_right_imp_eq
% 2.39/2.76 thf(fact_2322_add__right__imp__eq,axiom,
% 2.39/2.76 ! [B: int,A: int,C: int] :
% 2.39/2.76 ( ( ( plus_plus_int @ B @ A )
% 2.39/2.76 = ( plus_plus_int @ C @ A ) )
% 2.39/2.76 => ( B = C ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_right_imp_eq
% 2.39/2.76 thf(fact_2323_add__mono__thms__linordered__semiring_I3_J,axiom,
% 2.39/2.76 ! [I2: code_integer,J: code_integer,K: code_integer,L: code_integer] :
% 2.39/2.76 ( ( ( ord_le3102999989581377725nteger @ I2 @ J )
% 2.39/2.76 & ( K = L ) )
% 2.39/2.76 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ I2 @ K ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono_thms_linordered_semiring(3)
% 2.39/2.76 thf(fact_2324_add__mono__thms__linordered__semiring_I3_J,axiom,
% 2.39/2.76 ! [I2: rat,J: rat,K: rat,L: rat] :
% 2.39/2.76 ( ( ( ord_less_eq_rat @ I2 @ J )
% 2.39/2.76 & ( K = L ) )
% 2.39/2.76 => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono_thms_linordered_semiring(3)
% 2.39/2.76 thf(fact_2325_add__mono__thms__linordered__semiring_I3_J,axiom,
% 2.39/2.76 ! [I2: nat,J: nat,K: nat,L: nat] :
% 2.39/2.76 ( ( ( ord_less_eq_nat @ I2 @ J )
% 2.39/2.76 & ( K = L ) )
% 2.39/2.76 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono_thms_linordered_semiring(3)
% 2.39/2.76 thf(fact_2326_add__mono__thms__linordered__semiring_I3_J,axiom,
% 2.39/2.76 ! [I2: int,J: int,K: int,L: int] :
% 2.39/2.76 ( ( ( ord_less_eq_int @ I2 @ J )
% 2.39/2.76 & ( K = L ) )
% 2.39/2.76 => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono_thms_linordered_semiring(3)
% 2.39/2.76 thf(fact_2327_add__mono__thms__linordered__semiring_I2_J,axiom,
% 2.39/2.76 ! [I2: code_integer,J: code_integer,K: code_integer,L: code_integer] :
% 2.39/2.76 ( ( ( I2 = J )
% 2.39/2.76 & ( ord_le3102999989581377725nteger @ K @ L ) )
% 2.39/2.76 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ I2 @ K ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono_thms_linordered_semiring(2)
% 2.39/2.76 thf(fact_2328_add__mono__thms__linordered__semiring_I2_J,axiom,
% 2.39/2.76 ! [I2: rat,J: rat,K: rat,L: rat] :
% 2.39/2.76 ( ( ( I2 = J )
% 2.39/2.76 & ( ord_less_eq_rat @ K @ L ) )
% 2.39/2.76 => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono_thms_linordered_semiring(2)
% 2.39/2.76 thf(fact_2329_add__mono__thms__linordered__semiring_I2_J,axiom,
% 2.39/2.76 ! [I2: nat,J: nat,K: nat,L: nat] :
% 2.39/2.76 ( ( ( I2 = J )
% 2.39/2.76 & ( ord_less_eq_nat @ K @ L ) )
% 2.39/2.76 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono_thms_linordered_semiring(2)
% 2.39/2.76 thf(fact_2330_add__mono__thms__linordered__semiring_I2_J,axiom,
% 2.39/2.76 ! [I2: int,J: int,K: int,L: int] :
% 2.39/2.76 ( ( ( I2 = J )
% 2.39/2.76 & ( ord_less_eq_int @ K @ L ) )
% 2.39/2.76 => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono_thms_linordered_semiring(2)
% 2.39/2.76 thf(fact_2331_add__mono__thms__linordered__semiring_I1_J,axiom,
% 2.39/2.76 ! [I2: code_integer,J: code_integer,K: code_integer,L: code_integer] :
% 2.39/2.76 ( ( ( ord_le3102999989581377725nteger @ I2 @ J )
% 2.39/2.76 & ( ord_le3102999989581377725nteger @ K @ L ) )
% 2.39/2.76 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ I2 @ K ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono_thms_linordered_semiring(1)
% 2.39/2.76 thf(fact_2332_add__mono__thms__linordered__semiring_I1_J,axiom,
% 2.39/2.76 ! [I2: rat,J: rat,K: rat,L: rat] :
% 2.39/2.76 ( ( ( ord_less_eq_rat @ I2 @ J )
% 2.39/2.76 & ( ord_less_eq_rat @ K @ L ) )
% 2.39/2.76 => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono_thms_linordered_semiring(1)
% 2.39/2.76 thf(fact_2333_add__mono__thms__linordered__semiring_I1_J,axiom,
% 2.39/2.76 ! [I2: nat,J: nat,K: nat,L: nat] :
% 2.39/2.76 ( ( ( ord_less_eq_nat @ I2 @ J )
% 2.39/2.76 & ( ord_less_eq_nat @ K @ L ) )
% 2.39/2.76 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono_thms_linordered_semiring(1)
% 2.39/2.76 thf(fact_2334_add__mono__thms__linordered__semiring_I1_J,axiom,
% 2.39/2.76 ! [I2: int,J: int,K: int,L: int] :
% 2.39/2.76 ( ( ( ord_less_eq_int @ I2 @ J )
% 2.39/2.76 & ( ord_less_eq_int @ K @ L ) )
% 2.39/2.76 => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono_thms_linordered_semiring(1)
% 2.39/2.76 thf(fact_2335_add__mono,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 2.39/2.76 ( ( ord_le3102999989581377725nteger @ A @ B )
% 2.39/2.76 => ( ( ord_le3102999989581377725nteger @ C @ D2 )
% 2.39/2.76 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ D2 ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono
% 2.39/2.76 thf(fact_2336_add__mono,axiom,
% 2.39/2.76 ! [A: rat,B: rat,C: rat,D2: rat] :
% 2.39/2.76 ( ( ord_less_eq_rat @ A @ B )
% 2.39/2.76 => ( ( ord_less_eq_rat @ C @ D2 )
% 2.39/2.76 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono
% 2.39/2.76 thf(fact_2337_add__mono,axiom,
% 2.39/2.76 ! [A: nat,B: nat,C: nat,D2: nat] :
% 2.39/2.76 ( ( ord_less_eq_nat @ A @ B )
% 2.39/2.76 => ( ( ord_less_eq_nat @ C @ D2 )
% 2.39/2.76 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono
% 2.39/2.76 thf(fact_2338_add__mono,axiom,
% 2.39/2.76 ! [A: int,B: int,C: int,D2: int] :
% 2.39/2.76 ( ( ord_less_eq_int @ A @ B )
% 2.39/2.76 => ( ( ord_less_eq_int @ C @ D2 )
% 2.39/2.76 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono
% 2.39/2.76 thf(fact_2339_add__left__mono,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.76 ( ( ord_le3102999989581377725nteger @ A @ B )
% 2.39/2.76 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ C @ A ) @ ( plus_p5714425477246183910nteger @ C @ B ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_left_mono
% 2.39/2.76 thf(fact_2340_add__left__mono,axiom,
% 2.39/2.76 ! [A: rat,B: rat,C: rat] :
% 2.39/2.76 ( ( ord_less_eq_rat @ A @ B )
% 2.39/2.76 => ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_left_mono
% 2.39/2.76 thf(fact_2341_add__left__mono,axiom,
% 2.39/2.76 ! [A: nat,B: nat,C: nat] :
% 2.39/2.76 ( ( ord_less_eq_nat @ A @ B )
% 2.39/2.76 => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_left_mono
% 2.39/2.76 thf(fact_2342_add__left__mono,axiom,
% 2.39/2.76 ! [A: int,B: int,C: int] :
% 2.39/2.76 ( ( ord_less_eq_int @ A @ B )
% 2.39/2.76 => ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_left_mono
% 2.39/2.76 thf(fact_2343_less__eqE,axiom,
% 2.39/2.76 ! [A: nat,B: nat] :
% 2.39/2.76 ( ( ord_less_eq_nat @ A @ B )
% 2.39/2.76 => ~ ! [C3: nat] :
% 2.39/2.76 ( B
% 2.39/2.76 != ( plus_plus_nat @ A @ C3 ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % less_eqE
% 2.39/2.76 thf(fact_2344_add__right__mono,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.76 ( ( ord_le3102999989581377725nteger @ A @ B )
% 2.39/2.76 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_right_mono
% 2.39/2.76 thf(fact_2345_add__right__mono,axiom,
% 2.39/2.76 ! [A: rat,B: rat,C: rat] :
% 2.39/2.76 ( ( ord_less_eq_rat @ A @ B )
% 2.39/2.76 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_right_mono
% 2.39/2.76 thf(fact_2346_add__right__mono,axiom,
% 2.39/2.76 ! [A: nat,B: nat,C: nat] :
% 2.39/2.76 ( ( ord_less_eq_nat @ A @ B )
% 2.39/2.76 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_right_mono
% 2.39/2.76 thf(fact_2347_add__right__mono,axiom,
% 2.39/2.76 ! [A: int,B: int,C: int] :
% 2.39/2.76 ( ( ord_less_eq_int @ A @ B )
% 2.39/2.76 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_right_mono
% 2.39/2.76 thf(fact_2348_le__iff__add,axiom,
% 2.39/2.76 ( ord_less_eq_nat
% 2.39/2.76 = ( ^ [A2: nat,B2: nat] :
% 2.39/2.76 ? [C4: nat] :
% 2.39/2.76 ( B2
% 2.39/2.76 = ( plus_plus_nat @ A2 @ C4 ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % le_iff_add
% 2.39/2.76 thf(fact_2349_add__le__imp__le__left,axiom,
% 2.39/2.76 ! [C: code_integer,A: code_integer,B: code_integer] :
% 2.39/2.76 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ C @ A ) @ ( plus_p5714425477246183910nteger @ C @ B ) )
% 2.39/2.76 => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_le_imp_le_left
% 2.39/2.76 thf(fact_2350_add__le__imp__le__left,axiom,
% 2.39/2.76 ! [C: rat,A: rat,B: rat] :
% 2.39/2.76 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 2.39/2.76 => ( ord_less_eq_rat @ A @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_le_imp_le_left
% 2.39/2.76 thf(fact_2351_add__le__imp__le__left,axiom,
% 2.39/2.76 ! [C: nat,A: nat,B: nat] :
% 2.39/2.76 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 2.39/2.76 => ( ord_less_eq_nat @ A @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_le_imp_le_left
% 2.39/2.76 thf(fact_2352_add__le__imp__le__left,axiom,
% 2.39/2.76 ! [C: int,A: int,B: int] :
% 2.39/2.76 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 2.39/2.76 => ( ord_less_eq_int @ A @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_le_imp_le_left
% 2.39/2.76 thf(fact_2353_add__le__imp__le__right,axiom,
% 2.39/2.76 ! [A: code_integer,C: code_integer,B: code_integer] :
% 2.39/2.76 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 2.39/2.76 => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_le_imp_le_right
% 2.39/2.76 thf(fact_2354_add__le__imp__le__right,axiom,
% 2.39/2.76 ! [A: rat,C: rat,B: rat] :
% 2.39/2.76 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 2.39/2.76 => ( ord_less_eq_rat @ A @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_le_imp_le_right
% 2.39/2.76 thf(fact_2355_add__le__imp__le__right,axiom,
% 2.39/2.76 ! [A: nat,C: nat,B: nat] :
% 2.39/2.76 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 2.39/2.76 => ( ord_less_eq_nat @ A @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_le_imp_le_right
% 2.39/2.76 thf(fact_2356_add__le__imp__le__right,axiom,
% 2.39/2.76 ! [A: int,C: int,B: int] :
% 2.39/2.76 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 2.39/2.76 => ( ord_less_eq_int @ A @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_le_imp_le_right
% 2.39/2.76 thf(fact_2357_comm__monoid__add__class_Oadd__0,axiom,
% 2.39/2.76 ! [A: nat] :
% 2.39/2.76 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 2.39/2.76 = A ) ).
% 2.39/2.76
% 2.39/2.76 % comm_monoid_add_class.add_0
% 2.39/2.76 thf(fact_2358_comm__monoid__add__class_Oadd__0,axiom,
% 2.39/2.76 ! [A: int] :
% 2.39/2.76 ( ( plus_plus_int @ zero_zero_int @ A )
% 2.39/2.76 = A ) ).
% 2.39/2.76
% 2.39/2.76 % comm_monoid_add_class.add_0
% 2.39/2.76 thf(fact_2359_comm__monoid__add__class_Oadd__0,axiom,
% 2.39/2.76 ! [A: rat] :
% 2.39/2.76 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 2.39/2.76 = A ) ).
% 2.39/2.76
% 2.39/2.76 % comm_monoid_add_class.add_0
% 2.39/2.76 thf(fact_2360_comm__monoid__add__class_Oadd__0,axiom,
% 2.39/2.76 ! [A: code_integer] :
% 2.39/2.76 ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.76 = A ) ).
% 2.39/2.76
% 2.39/2.76 % comm_monoid_add_class.add_0
% 2.39/2.76 thf(fact_2361_comm__monoid__add__class_Oadd__0,axiom,
% 2.39/2.76 ! [A: code_natural] :
% 2.39/2.76 ( ( plus_p4538020629002901425atural @ zero_z2226904508553997617atural @ A )
% 2.39/2.76 = A ) ).
% 2.39/2.76
% 2.39/2.76 % comm_monoid_add_class.add_0
% 2.39/2.76 thf(fact_2362_add_Ocomm__neutral,axiom,
% 2.39/2.76 ! [A: nat] :
% 2.39/2.76 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 2.39/2.76 = A ) ).
% 2.39/2.76
% 2.39/2.76 % add.comm_neutral
% 2.39/2.76 thf(fact_2363_add_Ocomm__neutral,axiom,
% 2.39/2.76 ! [A: int] :
% 2.39/2.76 ( ( plus_plus_int @ A @ zero_zero_int )
% 2.39/2.76 = A ) ).
% 2.39/2.76
% 2.39/2.76 % add.comm_neutral
% 2.39/2.76 thf(fact_2364_add_Ocomm__neutral,axiom,
% 2.39/2.76 ! [A: rat] :
% 2.39/2.76 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 2.39/2.76 = A ) ).
% 2.39/2.76
% 2.39/2.76 % add.comm_neutral
% 2.39/2.76 thf(fact_2365_add_Ocomm__neutral,axiom,
% 2.39/2.76 ! [A: code_integer] :
% 2.39/2.76 ( ( plus_p5714425477246183910nteger @ A @ zero_z3403309356797280102nteger )
% 2.39/2.76 = A ) ).
% 2.39/2.76
% 2.39/2.76 % add.comm_neutral
% 2.39/2.76 thf(fact_2366_add_Ocomm__neutral,axiom,
% 2.39/2.76 ! [A: code_natural] :
% 2.39/2.76 ( ( plus_p4538020629002901425atural @ A @ zero_z2226904508553997617atural )
% 2.39/2.76 = A ) ).
% 2.39/2.76
% 2.39/2.76 % add.comm_neutral
% 2.39/2.76 thf(fact_2367_add_Ogroup__left__neutral,axiom,
% 2.39/2.76 ! [A: int] :
% 2.39/2.76 ( ( plus_plus_int @ zero_zero_int @ A )
% 2.39/2.76 = A ) ).
% 2.39/2.76
% 2.39/2.76 % add.group_left_neutral
% 2.39/2.76 thf(fact_2368_add_Ogroup__left__neutral,axiom,
% 2.39/2.76 ! [A: rat] :
% 2.39/2.76 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 2.39/2.76 = A ) ).
% 2.39/2.76
% 2.39/2.76 % add.group_left_neutral
% 2.39/2.76 thf(fact_2369_add_Ogroup__left__neutral,axiom,
% 2.39/2.76 ! [A: code_integer] :
% 2.39/2.76 ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.76 = A ) ).
% 2.39/2.76
% 2.39/2.76 % add.group_left_neutral
% 2.39/2.76 thf(fact_2370_add__mono__thms__linordered__field_I5_J,axiom,
% 2.39/2.76 ! [I2: code_integer,J: code_integer,K: code_integer,L: code_integer] :
% 2.39/2.76 ( ( ( ord_le6747313008572928689nteger @ I2 @ J )
% 2.39/2.76 & ( ord_le6747313008572928689nteger @ K @ L ) )
% 2.39/2.76 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ I2 @ K ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono_thms_linordered_field(5)
% 2.39/2.76 thf(fact_2371_add__mono__thms__linordered__field_I5_J,axiom,
% 2.39/2.76 ! [I2: rat,J: rat,K: rat,L: rat] :
% 2.39/2.76 ( ( ( ord_less_rat @ I2 @ J )
% 2.39/2.76 & ( ord_less_rat @ K @ L ) )
% 2.39/2.76 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono_thms_linordered_field(5)
% 2.39/2.76 thf(fact_2372_add__mono__thms__linordered__field_I5_J,axiom,
% 2.39/2.76 ! [I2: nat,J: nat,K: nat,L: nat] :
% 2.39/2.76 ( ( ( ord_less_nat @ I2 @ J )
% 2.39/2.76 & ( ord_less_nat @ K @ L ) )
% 2.39/2.76 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono_thms_linordered_field(5)
% 2.39/2.76 thf(fact_2373_add__mono__thms__linordered__field_I5_J,axiom,
% 2.39/2.76 ! [I2: int,J: int,K: int,L: int] :
% 2.39/2.76 ( ( ( ord_less_int @ I2 @ J )
% 2.39/2.76 & ( ord_less_int @ K @ L ) )
% 2.39/2.76 => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono_thms_linordered_field(5)
% 2.39/2.76 thf(fact_2374_add__mono__thms__linordered__field_I2_J,axiom,
% 2.39/2.76 ! [I2: code_integer,J: code_integer,K: code_integer,L: code_integer] :
% 2.39/2.76 ( ( ( I2 = J )
% 2.39/2.76 & ( ord_le6747313008572928689nteger @ K @ L ) )
% 2.39/2.76 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ I2 @ K ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono_thms_linordered_field(2)
% 2.39/2.76 thf(fact_2375_add__mono__thms__linordered__field_I2_J,axiom,
% 2.39/2.76 ! [I2: rat,J: rat,K: rat,L: rat] :
% 2.39/2.76 ( ( ( I2 = J )
% 2.39/2.76 & ( ord_less_rat @ K @ L ) )
% 2.39/2.76 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono_thms_linordered_field(2)
% 2.39/2.76 thf(fact_2376_add__mono__thms__linordered__field_I2_J,axiom,
% 2.39/2.76 ! [I2: nat,J: nat,K: nat,L: nat] :
% 2.39/2.76 ( ( ( I2 = J )
% 2.39/2.76 & ( ord_less_nat @ K @ L ) )
% 2.39/2.76 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono_thms_linordered_field(2)
% 2.39/2.76 thf(fact_2377_add__mono__thms__linordered__field_I2_J,axiom,
% 2.39/2.76 ! [I2: int,J: int,K: int,L: int] :
% 2.39/2.76 ( ( ( I2 = J )
% 2.39/2.76 & ( ord_less_int @ K @ L ) )
% 2.39/2.76 => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono_thms_linordered_field(2)
% 2.39/2.76 thf(fact_2378_add__mono__thms__linordered__field_I1_J,axiom,
% 2.39/2.76 ! [I2: code_integer,J: code_integer,K: code_integer,L: code_integer] :
% 2.39/2.76 ( ( ( ord_le6747313008572928689nteger @ I2 @ J )
% 2.39/2.76 & ( K = L ) )
% 2.39/2.76 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ I2 @ K ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono_thms_linordered_field(1)
% 2.39/2.76 thf(fact_2379_add__mono__thms__linordered__field_I1_J,axiom,
% 2.39/2.76 ! [I2: rat,J: rat,K: rat,L: rat] :
% 2.39/2.76 ( ( ( ord_less_rat @ I2 @ J )
% 2.39/2.76 & ( K = L ) )
% 2.39/2.76 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono_thms_linordered_field(1)
% 2.39/2.76 thf(fact_2380_add__mono__thms__linordered__field_I1_J,axiom,
% 2.39/2.76 ! [I2: nat,J: nat,K: nat,L: nat] :
% 2.39/2.76 ( ( ( ord_less_nat @ I2 @ J )
% 2.39/2.76 & ( K = L ) )
% 2.39/2.76 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono_thms_linordered_field(1)
% 2.39/2.76 thf(fact_2381_add__mono__thms__linordered__field_I1_J,axiom,
% 2.39/2.76 ! [I2: int,J: int,K: int,L: int] :
% 2.39/2.76 ( ( ( ord_less_int @ I2 @ J )
% 2.39/2.76 & ( K = L ) )
% 2.39/2.76 => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono_thms_linordered_field(1)
% 2.39/2.76 thf(fact_2382_add__strict__mono,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 2.39/2.76 ( ( ord_le6747313008572928689nteger @ A @ B )
% 2.39/2.76 => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 2.39/2.76 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ D2 ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_strict_mono
% 2.39/2.76 thf(fact_2383_add__strict__mono,axiom,
% 2.39/2.76 ! [A: rat,B: rat,C: rat,D2: rat] :
% 2.39/2.76 ( ( ord_less_rat @ A @ B )
% 2.39/2.76 => ( ( ord_less_rat @ C @ D2 )
% 2.39/2.76 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_strict_mono
% 2.39/2.76 thf(fact_2384_add__strict__mono,axiom,
% 2.39/2.76 ! [A: nat,B: nat,C: nat,D2: nat] :
% 2.39/2.76 ( ( ord_less_nat @ A @ B )
% 2.39/2.76 => ( ( ord_less_nat @ C @ D2 )
% 2.39/2.76 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_strict_mono
% 2.39/2.76 thf(fact_2385_add__strict__mono,axiom,
% 2.39/2.76 ! [A: int,B: int,C: int,D2: int] :
% 2.39/2.76 ( ( ord_less_int @ A @ B )
% 2.39/2.76 => ( ( ord_less_int @ C @ D2 )
% 2.39/2.76 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_strict_mono
% 2.39/2.76 thf(fact_2386_add__strict__left__mono,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.76 ( ( ord_le6747313008572928689nteger @ A @ B )
% 2.39/2.76 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ C @ A ) @ ( plus_p5714425477246183910nteger @ C @ B ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_strict_left_mono
% 2.39/2.76 thf(fact_2387_add__strict__left__mono,axiom,
% 2.39/2.76 ! [A: rat,B: rat,C: rat] :
% 2.39/2.76 ( ( ord_less_rat @ A @ B )
% 2.39/2.76 => ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_strict_left_mono
% 2.39/2.76 thf(fact_2388_add__strict__left__mono,axiom,
% 2.39/2.76 ! [A: nat,B: nat,C: nat] :
% 2.39/2.76 ( ( ord_less_nat @ A @ B )
% 2.39/2.76 => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_strict_left_mono
% 2.39/2.76 thf(fact_2389_add__strict__left__mono,axiom,
% 2.39/2.76 ! [A: int,B: int,C: int] :
% 2.39/2.76 ( ( ord_less_int @ A @ B )
% 2.39/2.76 => ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_strict_left_mono
% 2.39/2.76 thf(fact_2390_add__strict__right__mono,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.76 ( ( ord_le6747313008572928689nteger @ A @ B )
% 2.39/2.76 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_strict_right_mono
% 2.39/2.76 thf(fact_2391_add__strict__right__mono,axiom,
% 2.39/2.76 ! [A: rat,B: rat,C: rat] :
% 2.39/2.76 ( ( ord_less_rat @ A @ B )
% 2.39/2.76 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_strict_right_mono
% 2.39/2.76 thf(fact_2392_add__strict__right__mono,axiom,
% 2.39/2.76 ! [A: nat,B: nat,C: nat] :
% 2.39/2.76 ( ( ord_less_nat @ A @ B )
% 2.39/2.76 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_strict_right_mono
% 2.39/2.76 thf(fact_2393_add__strict__right__mono,axiom,
% 2.39/2.76 ! [A: int,B: int,C: int] :
% 2.39/2.76 ( ( ord_less_int @ A @ B )
% 2.39/2.76 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_strict_right_mono
% 2.39/2.76 thf(fact_2394_add__less__imp__less__left,axiom,
% 2.39/2.76 ! [C: code_integer,A: code_integer,B: code_integer] :
% 2.39/2.76 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ C @ A ) @ ( plus_p5714425477246183910nteger @ C @ B ) )
% 2.39/2.76 => ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_less_imp_less_left
% 2.39/2.76 thf(fact_2395_add__less__imp__less__left,axiom,
% 2.39/2.76 ! [C: rat,A: rat,B: rat] :
% 2.39/2.76 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 2.39/2.76 => ( ord_less_rat @ A @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_less_imp_less_left
% 2.39/2.76 thf(fact_2396_add__less__imp__less__left,axiom,
% 2.39/2.76 ! [C: nat,A: nat,B: nat] :
% 2.39/2.76 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 2.39/2.76 => ( ord_less_nat @ A @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_less_imp_less_left
% 2.39/2.76 thf(fact_2397_add__less__imp__less__left,axiom,
% 2.39/2.76 ! [C: int,A: int,B: int] :
% 2.39/2.76 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 2.39/2.76 => ( ord_less_int @ A @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_less_imp_less_left
% 2.39/2.76 thf(fact_2398_add__less__imp__less__right,axiom,
% 2.39/2.76 ! [A: code_integer,C: code_integer,B: code_integer] :
% 2.39/2.76 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 2.39/2.76 => ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_less_imp_less_right
% 2.39/2.76 thf(fact_2399_add__less__imp__less__right,axiom,
% 2.39/2.76 ! [A: rat,C: rat,B: rat] :
% 2.39/2.76 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 2.39/2.76 => ( ord_less_rat @ A @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_less_imp_less_right
% 2.39/2.76 thf(fact_2400_add__less__imp__less__right,axiom,
% 2.39/2.76 ! [A: nat,C: nat,B: nat] :
% 2.39/2.76 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 2.39/2.76 => ( ord_less_nat @ A @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_less_imp_less_right
% 2.39/2.76 thf(fact_2401_add__less__imp__less__right,axiom,
% 2.39/2.76 ! [A: int,C: int,B: int] :
% 2.39/2.76 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 2.39/2.76 => ( ord_less_int @ A @ B ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_less_imp_less_right
% 2.39/2.76 thf(fact_2402_combine__common__factor,axiom,
% 2.39/2.76 ! [A: rat,E2: rat,B: rat,C: rat] :
% 2.39/2.76 ( ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ C ) )
% 2.39/2.76 = ( plus_plus_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ E2 ) @ C ) ) ).
% 2.39/2.76
% 2.39/2.76 % combine_common_factor
% 2.39/2.76 thf(fact_2403_combine__common__factor,axiom,
% 2.39/2.76 ! [A: nat,E2: nat,B: nat,C: nat] :
% 2.39/2.76 ( ( plus_plus_nat @ ( times_times_nat @ A @ E2 ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E2 ) @ C ) )
% 2.39/2.76 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E2 ) @ C ) ) ).
% 2.39/2.76
% 2.39/2.76 % combine_common_factor
% 2.39/2.76 thf(fact_2404_combine__common__factor,axiom,
% 2.39/2.76 ! [A: int,E2: int,B: int,C: int] :
% 2.39/2.76 ( ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ C ) )
% 2.39/2.76 = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B ) @ E2 ) @ C ) ) ).
% 2.39/2.76
% 2.39/2.76 % combine_common_factor
% 2.39/2.76 thf(fact_2405_combine__common__factor,axiom,
% 2.39/2.76 ! [A: code_integer,E2: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.76 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E2 ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E2 ) @ C ) )
% 2.39/2.76 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ E2 ) @ C ) ) ).
% 2.39/2.76
% 2.39/2.76 % combine_common_factor
% 2.39/2.76 thf(fact_2406_combine__common__factor,axiom,
% 2.39/2.76 ! [A: code_natural,E2: code_natural,B: code_natural,C: code_natural] :
% 2.39/2.76 ( ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ A @ E2 ) @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ E2 ) @ C ) )
% 2.39/2.76 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( plus_p4538020629002901425atural @ A @ B ) @ E2 ) @ C ) ) ).
% 2.39/2.76
% 2.39/2.76 % combine_common_factor
% 2.39/2.76 thf(fact_2407_distrib__right,axiom,
% 2.39/2.76 ! [A: rat,B: rat,C: rat] :
% 2.39/2.76 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 2.39/2.76 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % distrib_right
% 2.39/2.76 thf(fact_2408_distrib__right,axiom,
% 2.39/2.76 ! [A: nat,B: nat,C: nat] :
% 2.39/2.76 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 2.39/2.76 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % distrib_right
% 2.39/2.76 thf(fact_2409_distrib__right,axiom,
% 2.39/2.76 ! [A: int,B: int,C: int] :
% 2.39/2.76 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 2.39/2.76 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % distrib_right
% 2.39/2.76 thf(fact_2410_distrib__right,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.76 ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 2.39/2.76 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % distrib_right
% 2.39/2.76 thf(fact_2411_distrib__right,axiom,
% 2.39/2.76 ! [A: code_natural,B: code_natural,C: code_natural] :
% 2.39/2.76 ( ( times_2397367101498566445atural @ ( plus_p4538020629002901425atural @ A @ B ) @ C )
% 2.39/2.76 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ C ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % distrib_right
% 2.39/2.76 thf(fact_2412_distrib__left,axiom,
% 2.39/2.76 ! [A: rat,B: rat,C: rat] :
% 2.39/2.76 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 2.39/2.76 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % distrib_left
% 2.39/2.76 thf(fact_2413_distrib__left,axiom,
% 2.39/2.76 ! [A: nat,B: nat,C: nat] :
% 2.39/2.76 ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 2.39/2.76 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % distrib_left
% 2.39/2.76 thf(fact_2414_distrib__left,axiom,
% 2.39/2.76 ! [A: int,B: int,C: int] :
% 2.39/2.76 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 2.39/2.76 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % distrib_left
% 2.39/2.76 thf(fact_2415_distrib__left,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.76 ( ( times_3573771949741848930nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 2.39/2.76 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % distrib_left
% 2.39/2.76 thf(fact_2416_distrib__left,axiom,
% 2.39/2.76 ! [A: code_natural,B: code_natural,C: code_natural] :
% 2.39/2.76 ( ( times_2397367101498566445atural @ A @ ( plus_p4538020629002901425atural @ B @ C ) )
% 2.39/2.76 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ A @ B ) @ ( times_2397367101498566445atural @ A @ C ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % distrib_left
% 2.39/2.76 thf(fact_2417_comm__semiring__class_Odistrib,axiom,
% 2.39/2.76 ! [A: rat,B: rat,C: rat] :
% 2.39/2.76 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 2.39/2.76 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % comm_semiring_class.distrib
% 2.39/2.76 thf(fact_2418_comm__semiring__class_Odistrib,axiom,
% 2.39/2.76 ! [A: nat,B: nat,C: nat] :
% 2.39/2.76 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 2.39/2.76 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % comm_semiring_class.distrib
% 2.39/2.76 thf(fact_2419_comm__semiring__class_Odistrib,axiom,
% 2.39/2.76 ! [A: int,B: int,C: int] :
% 2.39/2.76 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 2.39/2.76 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % comm_semiring_class.distrib
% 2.39/2.76 thf(fact_2420_comm__semiring__class_Odistrib,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.76 ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 2.39/2.76 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % comm_semiring_class.distrib
% 2.39/2.76 thf(fact_2421_comm__semiring__class_Odistrib,axiom,
% 2.39/2.76 ! [A: code_natural,B: code_natural,C: code_natural] :
% 2.39/2.76 ( ( times_2397367101498566445atural @ ( plus_p4538020629002901425atural @ A @ B ) @ C )
% 2.39/2.76 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ C ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % comm_semiring_class.distrib
% 2.39/2.76 thf(fact_2422_ring__class_Oring__distribs_I1_J,axiom,
% 2.39/2.76 ! [A: rat,B: rat,C: rat] :
% 2.39/2.76 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 2.39/2.76 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % ring_class.ring_distribs(1)
% 2.39/2.76 thf(fact_2423_ring__class_Oring__distribs_I1_J,axiom,
% 2.39/2.76 ! [A: int,B: int,C: int] :
% 2.39/2.76 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 2.39/2.76 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % ring_class.ring_distribs(1)
% 2.39/2.76 thf(fact_2424_ring__class_Oring__distribs_I1_J,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.76 ( ( times_3573771949741848930nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 2.39/2.76 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % ring_class.ring_distribs(1)
% 2.39/2.76 thf(fact_2425_ring__class_Oring__distribs_I2_J,axiom,
% 2.39/2.76 ! [A: rat,B: rat,C: rat] :
% 2.39/2.76 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 2.39/2.76 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % ring_class.ring_distribs(2)
% 2.39/2.76 thf(fact_2426_ring__class_Oring__distribs_I2_J,axiom,
% 2.39/2.76 ! [A: int,B: int,C: int] :
% 2.39/2.76 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 2.39/2.76 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % ring_class.ring_distribs(2)
% 2.39/2.76 thf(fact_2427_ring__class_Oring__distribs_I2_J,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.76 ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 2.39/2.76 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % ring_class.ring_distribs(2)
% 2.39/2.76 thf(fact_2428_group__cancel_Oneg1,axiom,
% 2.39/2.76 ! [A3: int,K: int,A: int] :
% 2.39/2.76 ( ( A3
% 2.39/2.76 = ( plus_plus_int @ K @ A ) )
% 2.39/2.76 => ( ( uminus_uminus_int @ A3 )
% 2.39/2.76 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % group_cancel.neg1
% 2.39/2.76 thf(fact_2429_group__cancel_Oneg1,axiom,
% 2.39/2.76 ! [A3: rat,K: rat,A: rat] :
% 2.39/2.76 ( ( A3
% 2.39/2.76 = ( plus_plus_rat @ K @ A ) )
% 2.39/2.76 => ( ( uminus_uminus_rat @ A3 )
% 2.39/2.76 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( uminus_uminus_rat @ A ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % group_cancel.neg1
% 2.39/2.76 thf(fact_2430_group__cancel_Oneg1,axiom,
% 2.39/2.76 ! [A3: code_integer,K: code_integer,A: code_integer] :
% 2.39/2.76 ( ( A3
% 2.39/2.76 = ( plus_p5714425477246183910nteger @ K @ A ) )
% 2.39/2.76 => ( ( uminus1351360451143612070nteger @ A3 )
% 2.39/2.76 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( uminus1351360451143612070nteger @ A ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % group_cancel.neg1
% 2.39/2.76 thf(fact_2431_add_Oinverse__distrib__swap,axiom,
% 2.39/2.76 ! [A: int,B: int] :
% 2.39/2.76 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 2.39/2.76 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add.inverse_distrib_swap
% 2.39/2.76 thf(fact_2432_add_Oinverse__distrib__swap,axiom,
% 2.39/2.76 ! [A: rat,B: rat] :
% 2.39/2.76 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 2.39/2.76 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add.inverse_distrib_swap
% 2.39/2.76 thf(fact_2433_add_Oinverse__distrib__swap,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer] :
% 2.39/2.76 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 2.39/2.76 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add.inverse_distrib_swap
% 2.39/2.76 thf(fact_2434_sgn__mult,axiom,
% 2.39/2.76 ! [A: rat,B: rat] :
% 2.39/2.76 ( ( sgn_sgn_rat @ ( times_times_rat @ A @ B ) )
% 2.39/2.76 = ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( sgn_sgn_rat @ B ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % sgn_mult
% 2.39/2.76 thf(fact_2435_sgn__mult,axiom,
% 2.39/2.76 ! [A: int,B: int] :
% 2.39/2.76 ( ( sgn_sgn_int @ ( times_times_int @ A @ B ) )
% 2.39/2.76 = ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ B ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % sgn_mult
% 2.39/2.76 thf(fact_2436_sgn__mult,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer] :
% 2.39/2.76 ( ( sgn_sgn_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 2.39/2.76 = ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ B ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % sgn_mult
% 2.39/2.76 thf(fact_2437_add_Oabel__semigroup__axioms,axiom,
% 2.39/2.76 abel_s8772020223019846471nteger @ plus_p5714425477246183910nteger ).
% 2.39/2.76
% 2.39/2.76 % add.abel_semigroup_axioms
% 2.39/2.76 thf(fact_2438_add_Oabel__semigroup__axioms,axiom,
% 2.39/2.76 abel_semigroup_rat @ plus_plus_rat ).
% 2.39/2.76
% 2.39/2.76 % add.abel_semigroup_axioms
% 2.39/2.76 thf(fact_2439_add_Oabel__semigroup__axioms,axiom,
% 2.39/2.76 abel_semigroup_nat @ plus_plus_nat ).
% 2.39/2.76
% 2.39/2.76 % add.abel_semigroup_axioms
% 2.39/2.76 thf(fact_2440_add_Oabel__semigroup__axioms,axiom,
% 2.39/2.76 abel_semigroup_int @ plus_plus_int ).
% 2.39/2.76
% 2.39/2.76 % add.abel_semigroup_axioms
% 2.39/2.76 thf(fact_2441_add_Osemigroup__axioms,axiom,
% 2.39/2.76 semigr7036097719740861967nteger @ plus_p5714425477246183910nteger ).
% 2.39/2.76
% 2.39/2.76 % add.semigroup_axioms
% 2.39/2.76 thf(fact_2442_add_Osemigroup__axioms,axiom,
% 2.39/2.76 semigroup_rat @ plus_plus_rat ).
% 2.39/2.76
% 2.39/2.76 % add.semigroup_axioms
% 2.39/2.76 thf(fact_2443_add_Osemigroup__axioms,axiom,
% 2.39/2.76 semigroup_nat @ plus_plus_nat ).
% 2.39/2.76
% 2.39/2.76 % add.semigroup_axioms
% 2.39/2.76 thf(fact_2444_add_Osemigroup__axioms,axiom,
% 2.39/2.76 semigroup_int @ plus_plus_int ).
% 2.39/2.76
% 2.39/2.76 % add.semigroup_axioms
% 2.39/2.76 thf(fact_2445_add_Oac__operator__axioms,axiom,
% 2.39/2.76 syntax414191934074104506nteger @ plus_p5714425477246183910nteger ).
% 2.39/2.76
% 2.39/2.76 % add.ac_operator_axioms
% 2.39/2.76 thf(fact_2446_add_Oac__operator__axioms,axiom,
% 2.39/2.76 syntax8165409007564224565or_rat @ plus_plus_rat ).
% 2.39/2.76
% 2.39/2.76 % add.ac_operator_axioms
% 2.39/2.76 thf(fact_2447_add_Oac__operator__axioms,axiom,
% 2.39/2.76 syntax8800539067650720301or_nat @ plus_plus_nat ).
% 2.39/2.76
% 2.39/2.76 % add.ac_operator_axioms
% 2.39/2.76 thf(fact_2448_add_Oac__operator__axioms,axiom,
% 2.39/2.76 syntax8798048597141670025or_int @ plus_plus_int ).
% 2.39/2.76
% 2.39/2.76 % add.ac_operator_axioms
% 2.39/2.76 thf(fact_2449_add_Osafe__commute,axiom,
% 2.39/2.76 ! [X: code_integer,Y: code_integer,A: code_integer,B: code_integer] :
% 2.39/2.76 ( ( syntax380677951125133566nteger @ ( plus_p5714425477246183910nteger @ X @ Y ) @ A )
% 2.39/2.76 => ( ( plus_p5714425477246183910nteger @ A @ B )
% 2.39/2.76 = ( plus_p5714425477246183910nteger @ B @ A ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add.safe_commute
% 2.39/2.76 thf(fact_2450_add_Osafe__commute,axiom,
% 2.39/2.76 ! [X: rat,Y: rat,A: rat,B: rat] :
% 2.39/2.76 ( ( syntax3730441303064801268at_rat @ ( plus_plus_rat @ X @ Y ) @ A )
% 2.39/2.76 => ( ( plus_plus_rat @ A @ B )
% 2.39/2.76 = ( plus_plus_rat @ B @ A ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add.safe_commute
% 2.39/2.76 thf(fact_2451_add_Osafe__commute,axiom,
% 2.39/2.76 ! [X: nat,Y: nat,A: nat,B: nat] :
% 2.39/2.76 ( ( syntax4682126007086162916at_nat @ ( plus_plus_nat @ X @ Y ) @ A )
% 2.39/2.76 => ( ( plus_plus_nat @ A @ B )
% 2.39/2.76 = ( plus_plus_nat @ B @ A ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add.safe_commute
% 2.39/2.76 thf(fact_2452_add_Osafe__commute,axiom,
% 2.39/2.76 ! [X: int,Y: int,A: int,B: int] :
% 2.39/2.76 ( ( syntax5678989248478167196nt_int @ ( plus_plus_int @ X @ Y ) @ A )
% 2.39/2.76 => ( ( plus_plus_int @ A @ B )
% 2.39/2.76 = ( plus_plus_int @ B @ A ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add.safe_commute
% 2.39/2.76 thf(fact_2453_add__decreasing,axiom,
% 2.39/2.76 ! [A: code_integer,C: code_integer,B: code_integer] :
% 2.39/2.76 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 2.39/2.76 => ( ( ord_le3102999989581377725nteger @ C @ B )
% 2.39/2.76 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ B ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_decreasing
% 2.39/2.76 thf(fact_2454_add__decreasing,axiom,
% 2.39/2.76 ! [A: code_natural,C: code_natural,B: code_natural] :
% 2.39/2.76 ( ( ord_le1926595141338095240atural @ A @ zero_z2226904508553997617atural )
% 2.39/2.76 => ( ( ord_le1926595141338095240atural @ C @ B )
% 2.39/2.76 => ( ord_le1926595141338095240atural @ ( plus_p4538020629002901425atural @ A @ C ) @ B ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_decreasing
% 2.39/2.76 thf(fact_2455_add__decreasing,axiom,
% 2.39/2.76 ! [A: rat,C: rat,B: rat] :
% 2.39/2.76 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 2.39/2.76 => ( ( ord_less_eq_rat @ C @ B )
% 2.39/2.76 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_decreasing
% 2.39/2.76 thf(fact_2456_add__decreasing,axiom,
% 2.39/2.76 ! [A: nat,C: nat,B: nat] :
% 2.39/2.76 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 2.39/2.76 => ( ( ord_less_eq_nat @ C @ B )
% 2.39/2.76 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_decreasing
% 2.39/2.76 thf(fact_2457_add__decreasing,axiom,
% 2.39/2.76 ! [A: int,C: int,B: int] :
% 2.39/2.76 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 2.39/2.76 => ( ( ord_less_eq_int @ C @ B )
% 2.39/2.76 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_decreasing
% 2.39/2.76 thf(fact_2458_add__increasing,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.76 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.76 => ( ( ord_le3102999989581377725nteger @ B @ C )
% 2.39/2.76 => ( ord_le3102999989581377725nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_increasing
% 2.39/2.76 thf(fact_2459_add__increasing,axiom,
% 2.39/2.76 ! [A: code_natural,B: code_natural,C: code_natural] :
% 2.39/2.76 ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 2.39/2.76 => ( ( ord_le1926595141338095240atural @ B @ C )
% 2.39/2.76 => ( ord_le1926595141338095240atural @ B @ ( plus_p4538020629002901425atural @ A @ C ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_increasing
% 2.39/2.76 thf(fact_2460_add__increasing,axiom,
% 2.39/2.76 ! [A: rat,B: rat,C: rat] :
% 2.39/2.76 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 2.39/2.76 => ( ( ord_less_eq_rat @ B @ C )
% 2.39/2.76 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_increasing
% 2.39/2.76 thf(fact_2461_add__increasing,axiom,
% 2.39/2.76 ! [A: nat,B: nat,C: nat] :
% 2.39/2.76 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 2.39/2.76 => ( ( ord_less_eq_nat @ B @ C )
% 2.39/2.76 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_increasing
% 2.39/2.76 thf(fact_2462_add__increasing,axiom,
% 2.39/2.76 ! [A: int,B: int,C: int] :
% 2.39/2.76 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 2.39/2.76 => ( ( ord_less_eq_int @ B @ C )
% 2.39/2.76 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_increasing
% 2.39/2.76 thf(fact_2463_add__decreasing2,axiom,
% 2.39/2.76 ! [C: code_integer,A: code_integer,B: code_integer] :
% 2.39/2.76 ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 2.39/2.76 => ( ( ord_le3102999989581377725nteger @ A @ B )
% 2.39/2.76 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ B ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_decreasing2
% 2.39/2.76 thf(fact_2464_add__decreasing2,axiom,
% 2.39/2.76 ! [C: code_natural,A: code_natural,B: code_natural] :
% 2.39/2.76 ( ( ord_le1926595141338095240atural @ C @ zero_z2226904508553997617atural )
% 2.39/2.76 => ( ( ord_le1926595141338095240atural @ A @ B )
% 2.39/2.76 => ( ord_le1926595141338095240atural @ ( plus_p4538020629002901425atural @ A @ C ) @ B ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_decreasing2
% 2.39/2.76 thf(fact_2465_add__decreasing2,axiom,
% 2.39/2.76 ! [C: rat,A: rat,B: rat] :
% 2.39/2.76 ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 2.39/2.76 => ( ( ord_less_eq_rat @ A @ B )
% 2.39/2.76 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_decreasing2
% 2.39/2.76 thf(fact_2466_add__decreasing2,axiom,
% 2.39/2.76 ! [C: nat,A: nat,B: nat] :
% 2.39/2.76 ( ( ord_less_eq_nat @ C @ zero_zero_nat )
% 2.39/2.76 => ( ( ord_less_eq_nat @ A @ B )
% 2.39/2.76 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_decreasing2
% 2.39/2.76 thf(fact_2467_add__decreasing2,axiom,
% 2.39/2.76 ! [C: int,A: int,B: int] :
% 2.39/2.76 ( ( ord_less_eq_int @ C @ zero_zero_int )
% 2.39/2.76 => ( ( ord_less_eq_int @ A @ B )
% 2.39/2.76 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_decreasing2
% 2.39/2.76 thf(fact_2468_add__increasing2,axiom,
% 2.39/2.76 ! [C: code_integer,B: code_integer,A: code_integer] :
% 2.39/2.76 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 2.39/2.76 => ( ( ord_le3102999989581377725nteger @ B @ A )
% 2.39/2.76 => ( ord_le3102999989581377725nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_increasing2
% 2.39/2.76 thf(fact_2469_add__increasing2,axiom,
% 2.39/2.76 ! [C: code_natural,B: code_natural,A: code_natural] :
% 2.39/2.76 ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ C )
% 2.39/2.76 => ( ( ord_le1926595141338095240atural @ B @ A )
% 2.39/2.76 => ( ord_le1926595141338095240atural @ B @ ( plus_p4538020629002901425atural @ A @ C ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_increasing2
% 2.39/2.76 thf(fact_2470_add__increasing2,axiom,
% 2.39/2.76 ! [C: rat,B: rat,A: rat] :
% 2.39/2.76 ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 2.39/2.76 => ( ( ord_less_eq_rat @ B @ A )
% 2.39/2.76 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_increasing2
% 2.39/2.76 thf(fact_2471_add__increasing2,axiom,
% 2.39/2.76 ! [C: nat,B: nat,A: nat] :
% 2.39/2.76 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 2.39/2.76 => ( ( ord_less_eq_nat @ B @ A )
% 2.39/2.76 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_increasing2
% 2.39/2.76 thf(fact_2472_add__increasing2,axiom,
% 2.39/2.76 ! [C: int,B: int,A: int] :
% 2.39/2.76 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 2.39/2.76 => ( ( ord_less_eq_int @ B @ A )
% 2.39/2.76 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_increasing2
% 2.39/2.76 thf(fact_2473_add__nonneg__nonneg,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer] :
% 2.39/2.76 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.76 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 2.39/2.76 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_nonneg_nonneg
% 2.39/2.76 thf(fact_2474_add__nonneg__nonneg,axiom,
% 2.39/2.76 ! [A: code_natural,B: code_natural] :
% 2.39/2.76 ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 2.39/2.76 => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ B )
% 2.39/2.76 => ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ ( plus_p4538020629002901425atural @ A @ B ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_nonneg_nonneg
% 2.39/2.76 thf(fact_2475_add__nonneg__nonneg,axiom,
% 2.39/2.76 ! [A: rat,B: rat] :
% 2.39/2.76 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 2.39/2.76 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 2.39/2.76 => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_nonneg_nonneg
% 2.39/2.76 thf(fact_2476_add__nonneg__nonneg,axiom,
% 2.39/2.76 ! [A: nat,B: nat] :
% 2.39/2.76 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 2.39/2.76 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 2.39/2.76 => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_nonneg_nonneg
% 2.39/2.76 thf(fact_2477_add__nonneg__nonneg,axiom,
% 2.39/2.76 ! [A: int,B: int] :
% 2.39/2.76 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 2.39/2.76 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 2.39/2.76 => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_nonneg_nonneg
% 2.39/2.76 thf(fact_2478_add__nonpos__nonpos,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer] :
% 2.39/2.76 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 2.39/2.76 => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 2.39/2.76 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_nonpos_nonpos
% 2.39/2.76 thf(fact_2479_add__nonpos__nonpos,axiom,
% 2.39/2.76 ! [A: code_natural,B: code_natural] :
% 2.39/2.76 ( ( ord_le1926595141338095240atural @ A @ zero_z2226904508553997617atural )
% 2.39/2.76 => ( ( ord_le1926595141338095240atural @ B @ zero_z2226904508553997617atural )
% 2.39/2.76 => ( ord_le1926595141338095240atural @ ( plus_p4538020629002901425atural @ A @ B ) @ zero_z2226904508553997617atural ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_nonpos_nonpos
% 2.39/2.76 thf(fact_2480_add__nonpos__nonpos,axiom,
% 2.39/2.76 ! [A: rat,B: rat] :
% 2.39/2.76 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 2.39/2.76 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 2.39/2.76 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_nonpos_nonpos
% 2.39/2.76 thf(fact_2481_add__nonpos__nonpos,axiom,
% 2.39/2.76 ! [A: nat,B: nat] :
% 2.39/2.76 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 2.39/2.76 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 2.39/2.76 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_nonpos_nonpos
% 2.39/2.76 thf(fact_2482_add__nonpos__nonpos,axiom,
% 2.39/2.76 ! [A: int,B: int] :
% 2.39/2.76 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 2.39/2.76 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 2.39/2.76 => ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_nonpos_nonpos
% 2.39/2.76 thf(fact_2483_add__nonneg__eq__0__iff,axiom,
% 2.39/2.76 ! [X: code_integer,Y: code_integer] :
% 2.39/2.76 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 2.39/2.76 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 2.39/2.76 => ( ( ( plus_p5714425477246183910nteger @ X @ Y )
% 2.39/2.76 = zero_z3403309356797280102nteger )
% 2.39/2.76 = ( ( X = zero_z3403309356797280102nteger )
% 2.39/2.76 & ( Y = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_nonneg_eq_0_iff
% 2.39/2.76 thf(fact_2484_add__nonneg__eq__0__iff,axiom,
% 2.39/2.76 ! [X: code_natural,Y: code_natural] :
% 2.39/2.76 ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ X )
% 2.39/2.76 => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ Y )
% 2.39/2.76 => ( ( ( plus_p4538020629002901425atural @ X @ Y )
% 2.39/2.76 = zero_z2226904508553997617atural )
% 2.39/2.76 = ( ( X = zero_z2226904508553997617atural )
% 2.39/2.76 & ( Y = zero_z2226904508553997617atural ) ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_nonneg_eq_0_iff
% 2.39/2.76 thf(fact_2485_add__nonneg__eq__0__iff,axiom,
% 2.39/2.76 ! [X: rat,Y: rat] :
% 2.39/2.76 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 2.39/2.76 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 2.39/2.76 => ( ( ( plus_plus_rat @ X @ Y )
% 2.39/2.76 = zero_zero_rat )
% 2.39/2.76 = ( ( X = zero_zero_rat )
% 2.39/2.76 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_nonneg_eq_0_iff
% 2.39/2.76 thf(fact_2486_add__nonneg__eq__0__iff,axiom,
% 2.39/2.76 ! [X: nat,Y: nat] :
% 2.39/2.76 ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 2.39/2.76 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 2.39/2.76 => ( ( ( plus_plus_nat @ X @ Y )
% 2.39/2.76 = zero_zero_nat )
% 2.39/2.76 = ( ( X = zero_zero_nat )
% 2.39/2.76 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_nonneg_eq_0_iff
% 2.39/2.76 thf(fact_2487_add__nonneg__eq__0__iff,axiom,
% 2.39/2.76 ! [X: int,Y: int] :
% 2.39/2.76 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 2.39/2.76 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 2.39/2.76 => ( ( ( plus_plus_int @ X @ Y )
% 2.39/2.76 = zero_zero_int )
% 2.39/2.76 = ( ( X = zero_zero_int )
% 2.39/2.76 & ( Y = zero_zero_int ) ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_nonneg_eq_0_iff
% 2.39/2.76 thf(fact_2488_add__nonpos__eq__0__iff,axiom,
% 2.39/2.76 ! [X: code_integer,Y: code_integer] :
% 2.39/2.76 ( ( ord_le3102999989581377725nteger @ X @ zero_z3403309356797280102nteger )
% 2.39/2.76 => ( ( ord_le3102999989581377725nteger @ Y @ zero_z3403309356797280102nteger )
% 2.39/2.76 => ( ( ( plus_p5714425477246183910nteger @ X @ Y )
% 2.39/2.76 = zero_z3403309356797280102nteger )
% 2.39/2.76 = ( ( X = zero_z3403309356797280102nteger )
% 2.39/2.76 & ( Y = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_nonpos_eq_0_iff
% 2.39/2.76 thf(fact_2489_add__nonpos__eq__0__iff,axiom,
% 2.39/2.76 ! [X: code_natural,Y: code_natural] :
% 2.39/2.76 ( ( ord_le1926595141338095240atural @ X @ zero_z2226904508553997617atural )
% 2.39/2.76 => ( ( ord_le1926595141338095240atural @ Y @ zero_z2226904508553997617atural )
% 2.39/2.76 => ( ( ( plus_p4538020629002901425atural @ X @ Y )
% 2.39/2.76 = zero_z2226904508553997617atural )
% 2.39/2.76 = ( ( X = zero_z2226904508553997617atural )
% 2.39/2.76 & ( Y = zero_z2226904508553997617atural ) ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_nonpos_eq_0_iff
% 2.39/2.76 thf(fact_2490_add__nonpos__eq__0__iff,axiom,
% 2.39/2.76 ! [X: rat,Y: rat] :
% 2.39/2.76 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 2.39/2.76 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 2.39/2.76 => ( ( ( plus_plus_rat @ X @ Y )
% 2.39/2.76 = zero_zero_rat )
% 2.39/2.76 = ( ( X = zero_zero_rat )
% 2.39/2.76 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_nonpos_eq_0_iff
% 2.39/2.76 thf(fact_2491_add__nonpos__eq__0__iff,axiom,
% 2.39/2.76 ! [X: nat,Y: nat] :
% 2.39/2.76 ( ( ord_less_eq_nat @ X @ zero_zero_nat )
% 2.39/2.76 => ( ( ord_less_eq_nat @ Y @ zero_zero_nat )
% 2.39/2.76 => ( ( ( plus_plus_nat @ X @ Y )
% 2.39/2.76 = zero_zero_nat )
% 2.39/2.76 = ( ( X = zero_zero_nat )
% 2.39/2.76 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_nonpos_eq_0_iff
% 2.39/2.76 thf(fact_2492_add__nonpos__eq__0__iff,axiom,
% 2.39/2.76 ! [X: int,Y: int] :
% 2.39/2.76 ( ( ord_less_eq_int @ X @ zero_zero_int )
% 2.39/2.76 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 2.39/2.76 => ( ( ( plus_plus_int @ X @ Y )
% 2.39/2.76 = zero_zero_int )
% 2.39/2.76 = ( ( X = zero_zero_int )
% 2.39/2.76 & ( Y = zero_zero_int ) ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_nonpos_eq_0_iff
% 2.39/2.76 thf(fact_2493_add__mono__thms__linordered__field_I4_J,axiom,
% 2.39/2.76 ! [I2: code_integer,J: code_integer,K: code_integer,L: code_integer] :
% 2.39/2.76 ( ( ( ord_le3102999989581377725nteger @ I2 @ J )
% 2.39/2.76 & ( ord_le6747313008572928689nteger @ K @ L ) )
% 2.39/2.76 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ I2 @ K ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono_thms_linordered_field(4)
% 2.39/2.76 thf(fact_2494_add__mono__thms__linordered__field_I4_J,axiom,
% 2.39/2.76 ! [I2: rat,J: rat,K: rat,L: rat] :
% 2.39/2.76 ( ( ( ord_less_eq_rat @ I2 @ J )
% 2.39/2.76 & ( ord_less_rat @ K @ L ) )
% 2.39/2.76 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono_thms_linordered_field(4)
% 2.39/2.76 thf(fact_2495_add__mono__thms__linordered__field_I4_J,axiom,
% 2.39/2.76 ! [I2: nat,J: nat,K: nat,L: nat] :
% 2.39/2.76 ( ( ( ord_less_eq_nat @ I2 @ J )
% 2.39/2.76 & ( ord_less_nat @ K @ L ) )
% 2.39/2.76 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono_thms_linordered_field(4)
% 2.39/2.76 thf(fact_2496_add__mono__thms__linordered__field_I4_J,axiom,
% 2.39/2.76 ! [I2: int,J: int,K: int,L: int] :
% 2.39/2.76 ( ( ( ord_less_eq_int @ I2 @ J )
% 2.39/2.76 & ( ord_less_int @ K @ L ) )
% 2.39/2.76 => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono_thms_linordered_field(4)
% 2.39/2.76 thf(fact_2497_add__mono__thms__linordered__field_I3_J,axiom,
% 2.39/2.76 ! [I2: code_integer,J: code_integer,K: code_integer,L: code_integer] :
% 2.39/2.76 ( ( ( ord_le6747313008572928689nteger @ I2 @ J )
% 2.39/2.76 & ( ord_le3102999989581377725nteger @ K @ L ) )
% 2.39/2.76 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ I2 @ K ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono_thms_linordered_field(3)
% 2.39/2.76 thf(fact_2498_add__mono__thms__linordered__field_I3_J,axiom,
% 2.39/2.76 ! [I2: rat,J: rat,K: rat,L: rat] :
% 2.39/2.76 ( ( ( ord_less_rat @ I2 @ J )
% 2.39/2.76 & ( ord_less_eq_rat @ K @ L ) )
% 2.39/2.76 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono_thms_linordered_field(3)
% 2.39/2.76 thf(fact_2499_add__mono__thms__linordered__field_I3_J,axiom,
% 2.39/2.76 ! [I2: nat,J: nat,K: nat,L: nat] :
% 2.39/2.76 ( ( ( ord_less_nat @ I2 @ J )
% 2.39/2.76 & ( ord_less_eq_nat @ K @ L ) )
% 2.39/2.76 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono_thms_linordered_field(3)
% 2.39/2.76 thf(fact_2500_add__mono__thms__linordered__field_I3_J,axiom,
% 2.39/2.76 ! [I2: int,J: int,K: int,L: int] :
% 2.39/2.76 ( ( ( ord_less_int @ I2 @ J )
% 2.39/2.76 & ( ord_less_eq_int @ K @ L ) )
% 2.39/2.76 => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono_thms_linordered_field(3)
% 2.39/2.76 thf(fact_2501_add__le__less__mono,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 2.39/2.76 ( ( ord_le3102999989581377725nteger @ A @ B )
% 2.39/2.76 => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 2.39/2.76 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ D2 ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_le_less_mono
% 2.39/2.76 thf(fact_2502_add__le__less__mono,axiom,
% 2.39/2.76 ! [A: rat,B: rat,C: rat,D2: rat] :
% 2.39/2.76 ( ( ord_less_eq_rat @ A @ B )
% 2.39/2.76 => ( ( ord_less_rat @ C @ D2 )
% 2.39/2.76 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_le_less_mono
% 2.39/2.76 thf(fact_2503_add__le__less__mono,axiom,
% 2.39/2.76 ! [A: nat,B: nat,C: nat,D2: nat] :
% 2.39/2.76 ( ( ord_less_eq_nat @ A @ B )
% 2.39/2.76 => ( ( ord_less_nat @ C @ D2 )
% 2.39/2.76 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_le_less_mono
% 2.39/2.76 thf(fact_2504_add__le__less__mono,axiom,
% 2.39/2.76 ! [A: int,B: int,C: int,D2: int] :
% 2.39/2.76 ( ( ord_less_eq_int @ A @ B )
% 2.39/2.76 => ( ( ord_less_int @ C @ D2 )
% 2.39/2.76 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_le_less_mono
% 2.39/2.76 thf(fact_2505_add__less__le__mono,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 2.39/2.76 ( ( ord_le6747313008572928689nteger @ A @ B )
% 2.39/2.76 => ( ( ord_le3102999989581377725nteger @ C @ D2 )
% 2.39/2.76 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ D2 ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_less_le_mono
% 2.39/2.76 thf(fact_2506_add__less__le__mono,axiom,
% 2.39/2.76 ! [A: rat,B: rat,C: rat,D2: rat] :
% 2.39/2.76 ( ( ord_less_rat @ A @ B )
% 2.39/2.76 => ( ( ord_less_eq_rat @ C @ D2 )
% 2.39/2.76 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_less_le_mono
% 2.39/2.76 thf(fact_2507_add__less__le__mono,axiom,
% 2.39/2.76 ! [A: nat,B: nat,C: nat,D2: nat] :
% 2.39/2.76 ( ( ord_less_nat @ A @ B )
% 2.39/2.76 => ( ( ord_less_eq_nat @ C @ D2 )
% 2.39/2.76 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_less_le_mono
% 2.39/2.76 thf(fact_2508_add__less__le__mono,axiom,
% 2.39/2.76 ! [A: int,B: int,C: int,D2: int] :
% 2.39/2.76 ( ( ord_less_int @ A @ B )
% 2.39/2.76 => ( ( ord_less_eq_int @ C @ D2 )
% 2.39/2.76 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_less_le_mono
% 2.39/2.76 thf(fact_2509_add__neg__neg,axiom,
% 2.39/2.76 ! [A: code_natural,B: code_natural] :
% 2.39/2.76 ( ( ord_le5570908160329646204atural @ A @ zero_z2226904508553997617atural )
% 2.39/2.76 => ( ( ord_le5570908160329646204atural @ B @ zero_z2226904508553997617atural )
% 2.39/2.76 => ( ord_le5570908160329646204atural @ ( plus_p4538020629002901425atural @ A @ B ) @ zero_z2226904508553997617atural ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_neg_neg
% 2.39/2.76 thf(fact_2510_add__neg__neg,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer] :
% 2.39/2.76 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 2.39/2.76 => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 2.39/2.76 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_neg_neg
% 2.39/2.76 thf(fact_2511_add__neg__neg,axiom,
% 2.39/2.76 ! [A: rat,B: rat] :
% 2.39/2.76 ( ( ord_less_rat @ A @ zero_zero_rat )
% 2.39/2.76 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 2.39/2.76 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_neg_neg
% 2.39/2.76 thf(fact_2512_add__neg__neg,axiom,
% 2.39/2.76 ! [A: nat,B: nat] :
% 2.39/2.76 ( ( ord_less_nat @ A @ zero_zero_nat )
% 2.39/2.76 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 2.39/2.76 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_neg_neg
% 2.39/2.76 thf(fact_2513_add__neg__neg,axiom,
% 2.39/2.76 ! [A: int,B: int] :
% 2.39/2.76 ( ( ord_less_int @ A @ zero_zero_int )
% 2.39/2.76 => ( ( ord_less_int @ B @ zero_zero_int )
% 2.39/2.76 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_neg_neg
% 2.39/2.76 thf(fact_2514_add__pos__pos,axiom,
% 2.39/2.76 ! [A: code_natural,B: code_natural] :
% 2.39/2.76 ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A )
% 2.39/2.76 => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ B )
% 2.39/2.76 => ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ ( plus_p4538020629002901425atural @ A @ B ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_pos_pos
% 2.39/2.76 thf(fact_2515_add__pos__pos,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer] :
% 2.39/2.76 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.76 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 2.39/2.76 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_pos_pos
% 2.39/2.76 thf(fact_2516_add__pos__pos,axiom,
% 2.39/2.76 ! [A: rat,B: rat] :
% 2.39/2.76 ( ( ord_less_rat @ zero_zero_rat @ A )
% 2.39/2.76 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 2.39/2.76 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_pos_pos
% 2.39/2.76 thf(fact_2517_add__pos__pos,axiom,
% 2.39/2.76 ! [A: nat,B: nat] :
% 2.39/2.76 ( ( ord_less_nat @ zero_zero_nat @ A )
% 2.39/2.76 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 2.39/2.76 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_pos_pos
% 2.39/2.76 thf(fact_2518_add__pos__pos,axiom,
% 2.39/2.76 ! [A: int,B: int] :
% 2.39/2.76 ( ( ord_less_int @ zero_zero_int @ A )
% 2.39/2.76 => ( ( ord_less_int @ zero_zero_int @ B )
% 2.39/2.76 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_pos_pos
% 2.39/2.76 thf(fact_2519_canonically__ordered__monoid__add__class_OlessE,axiom,
% 2.39/2.76 ! [A: nat,B: nat] :
% 2.39/2.76 ( ( ord_less_nat @ A @ B )
% 2.39/2.76 => ~ ! [C3: nat] :
% 2.39/2.76 ( ( B
% 2.39/2.76 = ( plus_plus_nat @ A @ C3 ) )
% 2.39/2.76 => ( C3 = zero_zero_nat ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % canonically_ordered_monoid_add_class.lessE
% 2.39/2.76 thf(fact_2520_pos__add__strict,axiom,
% 2.39/2.76 ! [A: code_natural,B: code_natural,C: code_natural] :
% 2.39/2.76 ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A )
% 2.39/2.76 => ( ( ord_le5570908160329646204atural @ B @ C )
% 2.39/2.76 => ( ord_le5570908160329646204atural @ B @ ( plus_p4538020629002901425atural @ A @ C ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % pos_add_strict
% 2.39/2.76 thf(fact_2521_pos__add__strict,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.76 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.76 => ( ( ord_le6747313008572928689nteger @ B @ C )
% 2.39/2.76 => ( ord_le6747313008572928689nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % pos_add_strict
% 2.39/2.76 thf(fact_2522_pos__add__strict,axiom,
% 2.39/2.76 ! [A: rat,B: rat,C: rat] :
% 2.39/2.76 ( ( ord_less_rat @ zero_zero_rat @ A )
% 2.39/2.76 => ( ( ord_less_rat @ B @ C )
% 2.39/2.76 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % pos_add_strict
% 2.39/2.76 thf(fact_2523_pos__add__strict,axiom,
% 2.39/2.76 ! [A: nat,B: nat,C: nat] :
% 2.39/2.76 ( ( ord_less_nat @ zero_zero_nat @ A )
% 2.39/2.76 => ( ( ord_less_nat @ B @ C )
% 2.39/2.76 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % pos_add_strict
% 2.39/2.76 thf(fact_2524_pos__add__strict,axiom,
% 2.39/2.76 ! [A: int,B: int,C: int] :
% 2.39/2.76 ( ( ord_less_int @ zero_zero_int @ A )
% 2.39/2.76 => ( ( ord_less_int @ B @ C )
% 2.39/2.76 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % pos_add_strict
% 2.39/2.76 thf(fact_2525_add__mono1,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer] :
% 2.39/2.76 ( ( ord_le6747313008572928689nteger @ A @ B )
% 2.39/2.76 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ B @ one_one_Code_integer ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono1
% 2.39/2.76 thf(fact_2526_add__mono1,axiom,
% 2.39/2.76 ! [A: rat,B: rat] :
% 2.39/2.76 ( ( ord_less_rat @ A @ B )
% 2.39/2.76 => ( ord_less_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( plus_plus_rat @ B @ one_one_rat ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono1
% 2.39/2.76 thf(fact_2527_add__mono1,axiom,
% 2.39/2.76 ! [A: nat,B: nat] :
% 2.39/2.76 ( ( ord_less_nat @ A @ B )
% 2.39/2.76 => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono1
% 2.39/2.76 thf(fact_2528_add__mono1,axiom,
% 2.39/2.76 ! [A: int,B: int] :
% 2.39/2.76 ( ( ord_less_int @ A @ B )
% 2.39/2.76 => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_mono1
% 2.39/2.76 thf(fact_2529_less__add__one,axiom,
% 2.39/2.76 ! [A: code_integer] : ( ord_le6747313008572928689nteger @ A @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) ) ).
% 2.39/2.76
% 2.39/2.76 % less_add_one
% 2.39/2.76 thf(fact_2530_less__add__one,axiom,
% 2.39/2.76 ! [A: rat] : ( ord_less_rat @ A @ ( plus_plus_rat @ A @ one_one_rat ) ) ).
% 2.39/2.76
% 2.39/2.76 % less_add_one
% 2.39/2.76 thf(fact_2531_less__add__one,axiom,
% 2.39/2.76 ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 2.39/2.76
% 2.39/2.76 % less_add_one
% 2.39/2.76 thf(fact_2532_less__add__one,axiom,
% 2.39/2.76 ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 2.39/2.76
% 2.39/2.76 % less_add_one
% 2.39/2.76 thf(fact_2533_add__eq__0__iff,axiom,
% 2.39/2.76 ! [A: int,B: int] :
% 2.39/2.76 ( ( ( plus_plus_int @ A @ B )
% 2.39/2.76 = zero_zero_int )
% 2.39/2.76 = ( B
% 2.39/2.76 = ( uminus_uminus_int @ A ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_eq_0_iff
% 2.39/2.76 thf(fact_2534_add__eq__0__iff,axiom,
% 2.39/2.76 ! [A: rat,B: rat] :
% 2.39/2.76 ( ( ( plus_plus_rat @ A @ B )
% 2.39/2.76 = zero_zero_rat )
% 2.39/2.76 = ( B
% 2.39/2.76 = ( uminus_uminus_rat @ A ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_eq_0_iff
% 2.39/2.76 thf(fact_2535_add__eq__0__iff,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer] :
% 2.39/2.76 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 2.39/2.76 = zero_z3403309356797280102nteger )
% 2.39/2.76 = ( B
% 2.39/2.76 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 2.39/2.76
% 2.39/2.76 % add_eq_0_iff
% 2.39/2.76 thf(fact_2536_ab__group__add__class_Oab__left__minus,axiom,
% 2.39/2.76 ! [A: int] :
% 2.39/2.76 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 2.39/2.76 = zero_zero_int ) ).
% 2.39/2.76
% 2.39/2.76 % ab_group_add_class.ab_left_minus
% 2.39/2.76 thf(fact_2537_ab__group__add__class_Oab__left__minus,axiom,
% 2.39/2.76 ! [A: rat] :
% 2.39/2.76 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 2.39/2.76 = zero_zero_rat ) ).
% 2.39/2.76
% 2.39/2.76 % ab_group_add_class.ab_left_minus
% 2.39/2.76 thf(fact_2538_ab__group__add__class_Oab__left__minus,axiom,
% 2.39/2.76 ! [A: code_integer] :
% 2.39/2.76 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 2.39/2.76 = zero_z3403309356797280102nteger ) ).
% 2.39/2.76
% 2.39/2.76 % ab_group_add_class.ab_left_minus
% 2.39/2.76 thf(fact_2539_add_Oinverse__unique,axiom,
% 2.39/2.76 ! [A: int,B: int] :
% 2.39/2.76 ( ( ( plus_plus_int @ A @ B )
% 2.39/2.76 = zero_zero_int )
% 2.39/2.76 => ( ( uminus_uminus_int @ A )
% 2.39/2.76 = B ) ) ).
% 2.39/2.76
% 2.39/2.76 % add.inverse_unique
% 2.39/2.76 thf(fact_2540_add_Oinverse__unique,axiom,
% 2.39/2.76 ! [A: rat,B: rat] :
% 2.39/2.76 ( ( ( plus_plus_rat @ A @ B )
% 2.39/2.76 = zero_zero_rat )
% 2.39/2.76 => ( ( uminus_uminus_rat @ A )
% 2.39/2.76 = B ) ) ).
% 2.39/2.76
% 2.39/2.76 % add.inverse_unique
% 2.39/2.76 thf(fact_2541_add_Oinverse__unique,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer] :
% 2.39/2.76 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 2.39/2.76 = zero_z3403309356797280102nteger )
% 2.39/2.76 => ( ( uminus1351360451143612070nteger @ A )
% 2.39/2.76 = B ) ) ).
% 2.39/2.76
% 2.39/2.76 % add.inverse_unique
% 2.39/2.76 thf(fact_2542_eq__neg__iff__add__eq__0,axiom,
% 2.39/2.76 ! [A: int,B: int] :
% 2.39/2.76 ( ( A
% 2.39/2.76 = ( uminus_uminus_int @ B ) )
% 2.39/2.76 = ( ( plus_plus_int @ A @ B )
% 2.39/2.76 = zero_zero_int ) ) ).
% 2.39/2.76
% 2.39/2.76 % eq_neg_iff_add_eq_0
% 2.39/2.76 thf(fact_2543_eq__neg__iff__add__eq__0,axiom,
% 2.39/2.76 ! [A: rat,B: rat] :
% 2.39/2.76 ( ( A
% 2.39/2.76 = ( uminus_uminus_rat @ B ) )
% 2.39/2.76 = ( ( plus_plus_rat @ A @ B )
% 2.39/2.76 = zero_zero_rat ) ) ).
% 2.39/2.76
% 2.39/2.76 % eq_neg_iff_add_eq_0
% 2.39/2.76 thf(fact_2544_eq__neg__iff__add__eq__0,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer] :
% 2.39/2.76 ( ( A
% 2.39/2.76 = ( uminus1351360451143612070nteger @ B ) )
% 2.39/2.76 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 2.39/2.76 = zero_z3403309356797280102nteger ) ) ).
% 2.39/2.76
% 2.39/2.76 % eq_neg_iff_add_eq_0
% 2.39/2.76 thf(fact_2545_neg__eq__iff__add__eq__0,axiom,
% 2.39/2.76 ! [A: int,B: int] :
% 2.39/2.76 ( ( ( uminus_uminus_int @ A )
% 2.39/2.76 = B )
% 2.39/2.76 = ( ( plus_plus_int @ A @ B )
% 2.39/2.76 = zero_zero_int ) ) ).
% 2.39/2.76
% 2.39/2.76 % neg_eq_iff_add_eq_0
% 2.39/2.76 thf(fact_2546_neg__eq__iff__add__eq__0,axiom,
% 2.39/2.76 ! [A: rat,B: rat] :
% 2.39/2.76 ( ( ( uminus_uminus_rat @ A )
% 2.39/2.76 = B )
% 2.39/2.76 = ( ( plus_plus_rat @ A @ B )
% 2.39/2.76 = zero_zero_rat ) ) ).
% 2.39/2.76
% 2.39/2.76 % neg_eq_iff_add_eq_0
% 2.39/2.76 thf(fact_2547_neg__eq__iff__add__eq__0,axiom,
% 2.39/2.76 ! [A: code_integer,B: code_integer] :
% 2.39/2.76 ( ( ( uminus1351360451143612070nteger @ A )
% 2.39/2.76 = B )
% 2.39/2.76 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 2.39/2.76 = zero_z3403309356797280102nteger ) ) ).
% 2.39/2.76
% 2.39/2.76 % neg_eq_iff_add_eq_0
% 2.39/2.76 thf(fact_2548_sgn__minus__1,axiom,
% 2.39/2.76 ( ( sgn_sgn_int @ ( uminus_uminus_int @ one_one_int ) )
% 2.39/2.76 = ( uminus_uminus_int @ one_one_int ) ) ).
% 2.39/2.76
% 2.39/2.76 % sgn_minus_1
% 2.39/2.76 thf(fact_2549_sgn__minus__1,axiom,
% 2.39/2.76 ( ( sgn_sgn_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 2.39/2.76 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 2.39/2.77
% 2.39/2.77 % sgn_minus_1
% 2.39/2.77 thf(fact_2550_sgn__minus__1,axiom,
% 2.39/2.77 ( ( sgn_sgn_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 2.39/2.77 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 2.39/2.77
% 2.39/2.77 % sgn_minus_1
% 2.39/2.77 thf(fact_2551_add_Ocomm__monoid__axioms,axiom,
% 2.39/2.77 comm_monoid_nat @ plus_plus_nat @ zero_zero_nat ).
% 2.39/2.77
% 2.39/2.77 % add.comm_monoid_axioms
% 2.39/2.77 thf(fact_2552_add_Ocomm__monoid__axioms,axiom,
% 2.39/2.77 comm_monoid_int @ plus_plus_int @ zero_zero_int ).
% 2.39/2.77
% 2.39/2.77 % add.comm_monoid_axioms
% 2.39/2.77 thf(fact_2553_add_Ocomm__monoid__axioms,axiom,
% 2.39/2.77 comm_monoid_rat @ plus_plus_rat @ zero_zero_rat ).
% 2.39/2.77
% 2.39/2.77 % add.comm_monoid_axioms
% 2.39/2.77 thf(fact_2554_add_Ocomm__monoid__axioms,axiom,
% 2.39/2.77 comm_m1654649897431166824nteger @ plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger ).
% 2.39/2.77
% 2.39/2.77 % add.comm_monoid_axioms
% 2.39/2.77 thf(fact_2555_add_Ocomm__monoid__axioms,axiom,
% 2.39/2.77 comm_m478245049187884339atural @ plus_p4538020629002901425atural @ zero_z2226904508553997617atural ).
% 2.39/2.77
% 2.39/2.77 % add.comm_monoid_axioms
% 2.39/2.77 thf(fact_2556_add_Omonoid__axioms,axiom,
% 2.39/2.77 monoid_nat @ plus_plus_nat @ zero_zero_nat ).
% 2.39/2.77
% 2.39/2.77 % add.monoid_axioms
% 2.39/2.77 thf(fact_2557_add_Omonoid__axioms,axiom,
% 2.39/2.77 monoid_int @ plus_plus_int @ zero_zero_int ).
% 2.39/2.77
% 2.39/2.77 % add.monoid_axioms
% 2.39/2.77 thf(fact_2558_add_Omonoid__axioms,axiom,
% 2.39/2.77 monoid_rat @ plus_plus_rat @ zero_zero_rat ).
% 2.39/2.77
% 2.39/2.77 % add.monoid_axioms
% 2.39/2.77 thf(fact_2559_add_Omonoid__axioms,axiom,
% 2.39/2.77 monoid_Code_integer @ plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger ).
% 2.39/2.77
% 2.39/2.77 % add.monoid_axioms
% 2.39/2.77 thf(fact_2560_add_Omonoid__axioms,axiom,
% 2.39/2.77 monoid_Code_natural @ plus_p4538020629002901425atural @ zero_z2226904508553997617atural ).
% 2.39/2.77
% 2.39/2.77 % add.monoid_axioms
% 2.39/2.77 thf(fact_2561_dbl__inc__def,axiom,
% 2.39/2.77 ( neg_nu5831290666863070958nteger
% 2.39/2.77 = ( ^ [X2: code_integer] : ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ X2 @ X2 ) @ one_one_Code_integer ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % dbl_inc_def
% 2.39/2.77 thf(fact_2562_dbl__inc__def,axiom,
% 2.39/2.77 ( neg_nu5219082963157363817nc_rat
% 2.39/2.77 = ( ^ [X2: rat] : ( plus_plus_rat @ ( plus_plus_rat @ X2 @ X2 ) @ one_one_rat ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % dbl_inc_def
% 2.39/2.77 thf(fact_2563_dbl__inc__def,axiom,
% 2.39/2.77 ( neg_nu5851722552734809277nc_int
% 2.39/2.77 = ( ^ [X2: int] : ( plus_plus_int @ ( plus_plus_int @ X2 @ X2 ) @ one_one_int ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % dbl_inc_def
% 2.39/2.77 thf(fact_2564_add__neg__nonpos,axiom,
% 2.39/2.77 ! [A: code_natural,B: code_natural] :
% 2.39/2.77 ( ( ord_le5570908160329646204atural @ A @ zero_z2226904508553997617atural )
% 2.39/2.77 => ( ( ord_le1926595141338095240atural @ B @ zero_z2226904508553997617atural )
% 2.39/2.77 => ( ord_le5570908160329646204atural @ ( plus_p4538020629002901425atural @ A @ B ) @ zero_z2226904508553997617atural ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % add_neg_nonpos
% 2.39/2.77 thf(fact_2565_add__neg__nonpos,axiom,
% 2.39/2.77 ! [A: code_integer,B: code_integer] :
% 2.39/2.77 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 2.39/2.77 => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 2.39/2.77 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % add_neg_nonpos
% 2.39/2.77 thf(fact_2566_add__neg__nonpos,axiom,
% 2.39/2.77 ! [A: rat,B: rat] :
% 2.39/2.77 ( ( ord_less_rat @ A @ zero_zero_rat )
% 2.39/2.77 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 2.39/2.77 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % add_neg_nonpos
% 2.39/2.77 thf(fact_2567_add__neg__nonpos,axiom,
% 2.39/2.77 ! [A: nat,B: nat] :
% 2.39/2.77 ( ( ord_less_nat @ A @ zero_zero_nat )
% 2.39/2.77 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 2.39/2.77 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % add_neg_nonpos
% 2.39/2.77 thf(fact_2568_add__neg__nonpos,axiom,
% 2.39/2.77 ! [A: int,B: int] :
% 2.39/2.77 ( ( ord_less_int @ A @ zero_zero_int )
% 2.39/2.77 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 2.39/2.77 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % add_neg_nonpos
% 2.39/2.77 thf(fact_2569_add__nonneg__pos,axiom,
% 2.39/2.77 ! [A: code_natural,B: code_natural] :
% 2.39/2.77 ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 2.39/2.77 => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ B )
% 2.39/2.77 => ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ ( plus_p4538020629002901425atural @ A @ B ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % add_nonneg_pos
% 2.39/2.77 thf(fact_2570_add__nonneg__pos,axiom,
% 2.39/2.77 ! [A: code_integer,B: code_integer] :
% 2.39/2.77 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.77 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 2.39/2.77 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % add_nonneg_pos
% 2.39/2.77 thf(fact_2571_add__nonneg__pos,axiom,
% 2.39/2.77 ! [A: rat,B: rat] :
% 2.39/2.77 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 2.39/2.77 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 2.39/2.77 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % add_nonneg_pos
% 2.39/2.77 thf(fact_2572_add__nonneg__pos,axiom,
% 2.39/2.77 ! [A: nat,B: nat] :
% 2.39/2.77 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 2.39/2.77 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 2.39/2.77 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % add_nonneg_pos
% 2.39/2.77 thf(fact_2573_add__nonneg__pos,axiom,
% 2.39/2.77 ! [A: int,B: int] :
% 2.39/2.77 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 2.39/2.77 => ( ( ord_less_int @ zero_zero_int @ B )
% 2.39/2.77 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % add_nonneg_pos
% 2.39/2.77 thf(fact_2574_add__nonpos__neg,axiom,
% 2.39/2.77 ! [A: code_natural,B: code_natural] :
% 2.39/2.77 ( ( ord_le1926595141338095240atural @ A @ zero_z2226904508553997617atural )
% 2.39/2.77 => ( ( ord_le5570908160329646204atural @ B @ zero_z2226904508553997617atural )
% 2.39/2.77 => ( ord_le5570908160329646204atural @ ( plus_p4538020629002901425atural @ A @ B ) @ zero_z2226904508553997617atural ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % add_nonpos_neg
% 2.39/2.77 thf(fact_2575_add__nonpos__neg,axiom,
% 2.39/2.77 ! [A: code_integer,B: code_integer] :
% 2.39/2.77 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 2.39/2.77 => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 2.39/2.77 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % add_nonpos_neg
% 2.39/2.77 thf(fact_2576_add__nonpos__neg,axiom,
% 2.39/2.77 ! [A: rat,B: rat] :
% 2.39/2.77 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 2.39/2.77 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 2.39/2.77 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % add_nonpos_neg
% 2.39/2.77 thf(fact_2577_add__nonpos__neg,axiom,
% 2.39/2.77 ! [A: nat,B: nat] :
% 2.39/2.77 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 2.39/2.77 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 2.39/2.77 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % add_nonpos_neg
% 2.39/2.77 thf(fact_2578_add__nonpos__neg,axiom,
% 2.39/2.77 ! [A: int,B: int] :
% 2.39/2.77 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 2.39/2.77 => ( ( ord_less_int @ B @ zero_zero_int )
% 2.39/2.77 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % add_nonpos_neg
% 2.39/2.77 thf(fact_2579_add__pos__nonneg,axiom,
% 2.39/2.77 ! [A: code_natural,B: code_natural] :
% 2.39/2.77 ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A )
% 2.39/2.77 => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ B )
% 2.39/2.77 => ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ ( plus_p4538020629002901425atural @ A @ B ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % add_pos_nonneg
% 2.39/2.77 thf(fact_2580_add__pos__nonneg,axiom,
% 2.39/2.77 ! [A: code_integer,B: code_integer] :
% 2.39/2.77 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.77 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 2.39/2.77 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % add_pos_nonneg
% 2.39/2.77 thf(fact_2581_add__pos__nonneg,axiom,
% 2.39/2.77 ! [A: rat,B: rat] :
% 2.39/2.77 ( ( ord_less_rat @ zero_zero_rat @ A )
% 2.39/2.77 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 2.39/2.77 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % add_pos_nonneg
% 2.39/2.77 thf(fact_2582_add__pos__nonneg,axiom,
% 2.39/2.77 ! [A: nat,B: nat] :
% 2.39/2.77 ( ( ord_less_nat @ zero_zero_nat @ A )
% 2.39/2.77 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 2.39/2.77 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % add_pos_nonneg
% 2.39/2.77 thf(fact_2583_add__pos__nonneg,axiom,
% 2.39/2.77 ! [A: int,B: int] :
% 2.39/2.77 ( ( ord_less_int @ zero_zero_int @ A )
% 2.39/2.77 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 2.39/2.77 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % add_pos_nonneg
% 2.39/2.77 thf(fact_2584_add__strict__increasing,axiom,
% 2.39/2.77 ! [A: code_natural,B: code_natural,C: code_natural] :
% 2.39/2.77 ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A )
% 2.39/2.77 => ( ( ord_le1926595141338095240atural @ B @ C )
% 2.39/2.77 => ( ord_le5570908160329646204atural @ B @ ( plus_p4538020629002901425atural @ A @ C ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % add_strict_increasing
% 2.39/2.77 thf(fact_2585_add__strict__increasing,axiom,
% 2.39/2.77 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.77 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.77 => ( ( ord_le3102999989581377725nteger @ B @ C )
% 2.39/2.77 => ( ord_le6747313008572928689nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % add_strict_increasing
% 2.39/2.77 thf(fact_2586_add__strict__increasing,axiom,
% 2.39/2.77 ! [A: rat,B: rat,C: rat] :
% 2.39/2.77 ( ( ord_less_rat @ zero_zero_rat @ A )
% 2.39/2.77 => ( ( ord_less_eq_rat @ B @ C )
% 2.39/2.77 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % add_strict_increasing
% 2.39/2.77 thf(fact_2587_add__strict__increasing,axiom,
% 2.39/2.77 ! [A: nat,B: nat,C: nat] :
% 2.39/2.77 ( ( ord_less_nat @ zero_zero_nat @ A )
% 2.39/2.77 => ( ( ord_less_eq_nat @ B @ C )
% 2.39/2.77 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % add_strict_increasing
% 2.39/2.77 thf(fact_2588_add__strict__increasing,axiom,
% 2.39/2.77 ! [A: int,B: int,C: int] :
% 2.39/2.77 ( ( ord_less_int @ zero_zero_int @ A )
% 2.39/2.77 => ( ( ord_less_eq_int @ B @ C )
% 2.39/2.77 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % add_strict_increasing
% 2.39/2.77 thf(fact_2589_add__strict__increasing2,axiom,
% 2.39/2.77 ! [A: code_natural,B: code_natural,C: code_natural] :
% 2.39/2.77 ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 2.39/2.77 => ( ( ord_le5570908160329646204atural @ B @ C )
% 2.39/2.77 => ( ord_le5570908160329646204atural @ B @ ( plus_p4538020629002901425atural @ A @ C ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % add_strict_increasing2
% 2.39/2.77 thf(fact_2590_add__strict__increasing2,axiom,
% 2.39/2.77 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.77 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.77 => ( ( ord_le6747313008572928689nteger @ B @ C )
% 2.39/2.77 => ( ord_le6747313008572928689nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % add_strict_increasing2
% 2.39/2.77 thf(fact_2591_add__strict__increasing2,axiom,
% 2.39/2.77 ! [A: rat,B: rat,C: rat] :
% 2.39/2.77 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 2.39/2.77 => ( ( ord_less_rat @ B @ C )
% 2.39/2.77 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % add_strict_increasing2
% 2.39/2.77 thf(fact_2592_add__strict__increasing2,axiom,
% 2.39/2.77 ! [A: nat,B: nat,C: nat] :
% 2.39/2.77 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 2.39/2.77 => ( ( ord_less_nat @ B @ C )
% 2.39/2.77 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % add_strict_increasing2
% 2.39/2.77 thf(fact_2593_add__strict__increasing2,axiom,
% 2.39/2.77 ! [A: int,B: int,C: int] :
% 2.39/2.77 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 2.39/2.77 => ( ( ord_less_int @ B @ C )
% 2.39/2.77 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % add_strict_increasing2
% 2.39/2.77 thf(fact_2594_sum__squares__ge__zero,axiom,
% 2.39/2.77 ! [X: code_integer,Y: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % sum_squares_ge_zero
% 2.39/2.77 thf(fact_2595_sum__squares__ge__zero,axiom,
% 2.39/2.77 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % sum_squares_ge_zero
% 2.39/2.77 thf(fact_2596_sum__squares__ge__zero,axiom,
% 2.39/2.77 ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % sum_squares_ge_zero
% 2.39/2.77 thf(fact_2597_not__sum__squares__lt__zero,axiom,
% 2.39/2.77 ! [X: code_integer,Y: code_integer] :
% 2.39/2.77 ~ ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) @ zero_z3403309356797280102nteger ) ).
% 2.39/2.77
% 2.39/2.77 % not_sum_squares_lt_zero
% 2.39/2.77 thf(fact_2598_not__sum__squares__lt__zero,axiom,
% 2.39/2.77 ! [X: rat,Y: rat] :
% 2.39/2.77 ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat ) ).
% 2.39/2.77
% 2.39/2.77 % not_sum_squares_lt_zero
% 2.39/2.77 thf(fact_2599_not__sum__squares__lt__zero,axiom,
% 2.39/2.77 ! [X: int,Y: int] :
% 2.39/2.77 ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int ) ).
% 2.39/2.77
% 2.39/2.77 % not_sum_squares_lt_zero
% 2.39/2.77 thf(fact_2600_zero__less__two,axiom,
% 2.39/2.77 ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ ( plus_p4538020629002901425atural @ one_one_Code_natural @ one_one_Code_natural ) ).
% 2.39/2.77
% 2.39/2.77 % zero_less_two
% 2.39/2.77 thf(fact_2601_zero__less__two,axiom,
% 2.39/2.77 ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ one_one_Code_integer ) ).
% 2.39/2.77
% 2.39/2.77 % zero_less_two
% 2.39/2.77 thf(fact_2602_zero__less__two,axiom,
% 2.39/2.77 ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 2.39/2.77
% 2.39/2.77 % zero_less_two
% 2.39/2.77 thf(fact_2603_zero__less__two,axiom,
% 2.39/2.77 ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 2.39/2.77
% 2.39/2.77 % zero_less_two
% 2.39/2.77 thf(fact_2604_zero__less__two,axiom,
% 2.39/2.77 ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 2.39/2.77
% 2.39/2.77 % zero_less_two
% 2.39/2.77 thf(fact_2605_sgn__1__pos,axiom,
% 2.39/2.77 ! [A: code_integer] :
% 2.39/2.77 ( ( ( sgn_sgn_Code_integer @ A )
% 2.39/2.77 = one_one_Code_integer )
% 2.39/2.77 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 2.39/2.77
% 2.39/2.77 % sgn_1_pos
% 2.39/2.77 thf(fact_2606_sgn__1__pos,axiom,
% 2.39/2.77 ! [A: rat] :
% 2.39/2.77 ( ( ( sgn_sgn_rat @ A )
% 2.39/2.77 = one_one_rat )
% 2.39/2.77 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 2.39/2.77
% 2.39/2.77 % sgn_1_pos
% 2.39/2.77 thf(fact_2607_sgn__1__pos,axiom,
% 2.39/2.77 ! [A: int] :
% 2.39/2.77 ( ( ( sgn_sgn_int @ A )
% 2.39/2.77 = one_one_int )
% 2.39/2.77 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 2.39/2.77
% 2.39/2.77 % sgn_1_pos
% 2.39/2.77 thf(fact_2608_convex__bound__le,axiom,
% 2.39/2.77 ! [X: code_integer,A: code_integer,Y: code_integer,U: code_integer,V2: code_integer] :
% 2.39/2.77 ( ( ord_le3102999989581377725nteger @ X @ A )
% 2.39/2.77 => ( ( ord_le3102999989581377725nteger @ Y @ A )
% 2.39/2.77 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ U )
% 2.39/2.77 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ V2 )
% 2.39/2.77 => ( ( ( plus_p5714425477246183910nteger @ U @ V2 )
% 2.39/2.77 = one_one_Code_integer )
% 2.39/2.77 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ U @ X ) @ ( times_3573771949741848930nteger @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % convex_bound_le
% 2.39/2.77 thf(fact_2609_convex__bound__le,axiom,
% 2.39/2.77 ! [X: rat,A: rat,Y: rat,U: rat,V2: rat] :
% 2.39/2.77 ( ( ord_less_eq_rat @ X @ A )
% 2.39/2.77 => ( ( ord_less_eq_rat @ Y @ A )
% 2.39/2.77 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 2.39/2.77 => ( ( ord_less_eq_rat @ zero_zero_rat @ V2 )
% 2.39/2.77 => ( ( ( plus_plus_rat @ U @ V2 )
% 2.39/2.77 = one_one_rat )
% 2.39/2.77 => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % convex_bound_le
% 2.39/2.77 thf(fact_2610_convex__bound__le,axiom,
% 2.39/2.77 ! [X: int,A: int,Y: int,U: int,V2: int] :
% 2.39/2.77 ( ( ord_less_eq_int @ X @ A )
% 2.39/2.77 => ( ( ord_less_eq_int @ Y @ A )
% 2.39/2.77 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 2.39/2.77 => ( ( ord_less_eq_int @ zero_zero_int @ V2 )
% 2.39/2.77 => ( ( ( plus_plus_int @ U @ V2 )
% 2.39/2.77 = one_one_int )
% 2.39/2.77 => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % convex_bound_le
% 2.39/2.77 thf(fact_2611_sgn__if,axiom,
% 2.39/2.77 ( sgn_sgn_int
% 2.39/2.77 = ( ^ [X2: int] : ( if_int @ ( X2 = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ X2 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % sgn_if
% 2.39/2.77 thf(fact_2612_sgn__if,axiom,
% 2.39/2.77 ( sgn_sgn_rat
% 2.39/2.77 = ( ^ [X2: rat] : ( if_rat @ ( X2 = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ X2 ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % sgn_if
% 2.39/2.77 thf(fact_2613_sgn__if,axiom,
% 2.39/2.77 ( sgn_sgn_Code_integer
% 2.39/2.77 = ( ^ [X2: code_integer] : ( if_Code_integer @ ( X2 = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ X2 ) @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % sgn_if
% 2.39/2.77 thf(fact_2614_sgn__1__neg,axiom,
% 2.39/2.77 ! [A: int] :
% 2.39/2.77 ( ( ( sgn_sgn_int @ A )
% 2.39/2.77 = ( uminus_uminus_int @ one_one_int ) )
% 2.39/2.77 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 2.39/2.77
% 2.39/2.77 % sgn_1_neg
% 2.39/2.77 thf(fact_2615_sgn__1__neg,axiom,
% 2.39/2.77 ! [A: rat] :
% 2.39/2.77 ( ( ( sgn_sgn_rat @ A )
% 2.39/2.77 = ( uminus_uminus_rat @ one_one_rat ) )
% 2.39/2.77 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 2.39/2.77
% 2.39/2.77 % sgn_1_neg
% 2.39/2.77 thf(fact_2616_sgn__1__neg,axiom,
% 2.39/2.77 ! [A: code_integer] :
% 2.39/2.77 ( ( ( sgn_sgn_Code_integer @ A )
% 2.39/2.77 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 2.39/2.77 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 2.39/2.77
% 2.39/2.77 % sgn_1_neg
% 2.39/2.77 thf(fact_2617_less__one,axiom,
% 2.39/2.77 ! [N: nat] :
% 2.39/2.77 ( ( ord_less_nat @ N @ one_one_nat )
% 2.39/2.77 = ( N = zero_zero_nat ) ) ).
% 2.39/2.77
% 2.39/2.77 % less_one
% 2.39/2.77 thf(fact_2618_discrete,axiom,
% 2.39/2.77 ( ord_le6747313008572928689nteger
% 2.39/2.77 = ( ^ [A2: code_integer] : ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A2 @ one_one_Code_integer ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % discrete
% 2.39/2.77 thf(fact_2619_discrete,axiom,
% 2.39/2.77 ( ord_less_nat
% 2.39/2.77 = ( ^ [A2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ one_one_nat ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % discrete
% 2.39/2.77 thf(fact_2620_discrete,axiom,
% 2.39/2.77 ( ord_less_int
% 2.39/2.77 = ( ^ [A2: int] : ( ord_less_eq_int @ ( plus_plus_int @ A2 @ one_one_int ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % discrete
% 2.39/2.77 thf(fact_2621_sum__squares__gt__zero__iff,axiom,
% 2.39/2.77 ! [X: code_integer,Y: code_integer] :
% 2.39/2.77 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) )
% 2.39/2.77 = ( ( X != zero_z3403309356797280102nteger )
% 2.39/2.77 | ( Y != zero_z3403309356797280102nteger ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % sum_squares_gt_zero_iff
% 2.39/2.77 thf(fact_2622_sum__squares__gt__zero__iff,axiom,
% 2.39/2.77 ! [X: rat,Y: rat] :
% 2.39/2.77 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) )
% 2.39/2.77 = ( ( X != zero_zero_rat )
% 2.39/2.77 | ( Y != zero_zero_rat ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % sum_squares_gt_zero_iff
% 2.39/2.77 thf(fact_2623_sum__squares__gt__zero__iff,axiom,
% 2.39/2.77 ! [X: int,Y: int] :
% 2.39/2.77 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) )
% 2.39/2.77 = ( ( X != zero_zero_int )
% 2.39/2.77 | ( Y != zero_zero_int ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % sum_squares_gt_zero_iff
% 2.39/2.77 thf(fact_2624_sum__squares__le__zero__iff,axiom,
% 2.39/2.77 ! [X: code_integer,Y: code_integer] :
% 2.39/2.77 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) @ zero_z3403309356797280102nteger )
% 2.39/2.77 = ( ( X = zero_z3403309356797280102nteger )
% 2.39/2.77 & ( Y = zero_z3403309356797280102nteger ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % sum_squares_le_zero_iff
% 2.39/2.77 thf(fact_2625_sum__squares__le__zero__iff,axiom,
% 2.39/2.77 ! [X: rat,Y: rat] :
% 2.39/2.77 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat )
% 2.39/2.77 = ( ( X = zero_zero_rat )
% 2.39/2.77 & ( Y = zero_zero_rat ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % sum_squares_le_zero_iff
% 2.39/2.77 thf(fact_2626_sum__squares__le__zero__iff,axiom,
% 2.39/2.77 ! [X: int,Y: int] :
% 2.39/2.77 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int )
% 2.39/2.77 = ( ( X = zero_zero_int )
% 2.39/2.77 & ( Y = zero_zero_int ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % sum_squares_le_zero_iff
% 2.39/2.77 thf(fact_2627_n__lists__Nil,axiom,
% 2.39/2.77 ! [N: nat] :
% 2.39/2.77 ( ( ( N = zero_zero_nat )
% 2.39/2.77 => ( ( n_list679713369942834879n_assn @ N @ nil_Pr5671120429643327159n_assn )
% 2.39/2.77 = ( cons_l2423627976422276333n_assn @ nil_Pr5671120429643327159n_assn @ nil_li5476096274760905021n_assn ) ) )
% 2.39/2.77 & ( ( N != zero_zero_nat )
% 2.39/2.77 => ( ( n_list679713369942834879n_assn @ N @ nil_Pr5671120429643327159n_assn )
% 2.39/2.77 = nil_li5476096274760905021n_assn ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % n_lists_Nil
% 2.39/2.77 thf(fact_2628_n__lists__Nil,axiom,
% 2.39/2.77 ! [N: nat] :
% 2.39/2.77 ( ( ( N = zero_zero_nat )
% 2.39/2.77 => ( ( n_lists_int @ N @ nil_int )
% 2.39/2.77 = ( cons_list_int @ nil_int @ nil_list_int ) ) )
% 2.39/2.77 & ( ( N != zero_zero_nat )
% 2.39/2.77 => ( ( n_lists_int @ N @ nil_int )
% 2.39/2.77 = nil_list_int ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % n_lists_Nil
% 2.39/2.77 thf(fact_2629_n__lists__Nil,axiom,
% 2.39/2.77 ! [N: nat] :
% 2.39/2.77 ( ( ( N = zero_zero_nat )
% 2.39/2.77 => ( ( n_lists_nat @ N @ nil_nat )
% 2.39/2.77 = ( cons_list_nat @ nil_nat @ nil_list_nat ) ) )
% 2.39/2.77 & ( ( N != zero_zero_nat )
% 2.39/2.77 => ( ( n_lists_nat @ N @ nil_nat )
% 2.39/2.77 = nil_list_nat ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % n_lists_Nil
% 2.39/2.77 thf(fact_2630_add__scale__eq__noteq,axiom,
% 2.39/2.77 ! [R2: rat,A: rat,B: rat,C: rat,D2: rat] :
% 2.39/2.77 ( ( R2 != zero_zero_rat )
% 2.39/2.77 => ( ( ( A = B )
% 2.39/2.77 & ( C != D2 ) )
% 2.39/2.77 => ( ( plus_plus_rat @ A @ ( times_times_rat @ R2 @ C ) )
% 2.39/2.77 != ( plus_plus_rat @ B @ ( times_times_rat @ R2 @ D2 ) ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % add_scale_eq_noteq
% 2.39/2.77 thf(fact_2631_add__scale__eq__noteq,axiom,
% 2.39/2.77 ! [R2: nat,A: nat,B: nat,C: nat,D2: nat] :
% 2.39/2.77 ( ( R2 != zero_zero_nat )
% 2.39/2.77 => ( ( ( A = B )
% 2.39/2.77 & ( C != D2 ) )
% 2.39/2.77 => ( ( plus_plus_nat @ A @ ( times_times_nat @ R2 @ C ) )
% 2.39/2.77 != ( plus_plus_nat @ B @ ( times_times_nat @ R2 @ D2 ) ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % add_scale_eq_noteq
% 2.39/2.77 thf(fact_2632_add__scale__eq__noteq,axiom,
% 2.39/2.77 ! [R2: int,A: int,B: int,C: int,D2: int] :
% 2.39/2.77 ( ( R2 != zero_zero_int )
% 2.39/2.77 => ( ( ( A = B )
% 2.39/2.77 & ( C != D2 ) )
% 2.39/2.77 => ( ( plus_plus_int @ A @ ( times_times_int @ R2 @ C ) )
% 2.39/2.77 != ( plus_plus_int @ B @ ( times_times_int @ R2 @ D2 ) ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % add_scale_eq_noteq
% 2.39/2.77 thf(fact_2633_add__scale__eq__noteq,axiom,
% 2.39/2.77 ! [R2: code_integer,A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 2.39/2.77 ( ( R2 != zero_z3403309356797280102nteger )
% 2.39/2.77 => ( ( ( A = B )
% 2.39/2.77 & ( C != D2 ) )
% 2.39/2.77 => ( ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ R2 @ C ) )
% 2.39/2.77 != ( plus_p5714425477246183910nteger @ B @ ( times_3573771949741848930nteger @ R2 @ D2 ) ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % add_scale_eq_noteq
% 2.39/2.77 thf(fact_2634_sum__squares__eq__zero__iff,axiom,
% 2.39/2.77 ! [X: rat,Y: rat] :
% 2.39/2.77 ( ( ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 2.39/2.77 = zero_zero_rat )
% 2.39/2.77 = ( ( X = zero_zero_rat )
% 2.39/2.77 & ( Y = zero_zero_rat ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % sum_squares_eq_zero_iff
% 2.39/2.77 thf(fact_2635_sum__squares__eq__zero__iff,axiom,
% 2.39/2.77 ! [X: int,Y: int] :
% 2.39/2.77 ( ( ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 2.39/2.77 = zero_zero_int )
% 2.39/2.77 = ( ( X = zero_zero_int )
% 2.39/2.77 & ( Y = zero_zero_int ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % sum_squares_eq_zero_iff
% 2.39/2.77 thf(fact_2636_sum__squares__eq__zero__iff,axiom,
% 2.39/2.77 ! [X: code_integer,Y: code_integer] :
% 2.39/2.77 ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) )
% 2.39/2.77 = zero_z3403309356797280102nteger )
% 2.39/2.77 = ( ( X = zero_z3403309356797280102nteger )
% 2.39/2.77 & ( Y = zero_z3403309356797280102nteger ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % sum_squares_eq_zero_iff
% 2.39/2.77 thf(fact_2637_n__lists_Osimps_I1_J,axiom,
% 2.39/2.77 ! [Xs: list_P8527749157015355191n_assn] :
% 2.39/2.77 ( ( n_list679713369942834879n_assn @ zero_zero_nat @ Xs )
% 2.39/2.77 = ( cons_l2423627976422276333n_assn @ nil_Pr5671120429643327159n_assn @ nil_li5476096274760905021n_assn ) ) ).
% 2.39/2.77
% 2.39/2.77 % n_lists.simps(1)
% 2.39/2.77 thf(fact_2638_n__lists_Osimps_I1_J,axiom,
% 2.39/2.77 ! [Xs: list_int] :
% 2.39/2.77 ( ( n_lists_int @ zero_zero_nat @ Xs )
% 2.39/2.77 = ( cons_list_int @ nil_int @ nil_list_int ) ) ).
% 2.39/2.77
% 2.39/2.77 % n_lists.simps(1)
% 2.39/2.77 thf(fact_2639_n__lists_Osimps_I1_J,axiom,
% 2.39/2.77 ! [Xs: list_nat] :
% 2.39/2.77 ( ( n_lists_nat @ zero_zero_nat @ Xs )
% 2.39/2.77 = ( cons_list_nat @ nil_nat @ nil_list_nat ) ) ).
% 2.39/2.77
% 2.39/2.77 % n_lists.simps(1)
% 2.39/2.77 thf(fact_2640_crossproduct__noteq,axiom,
% 2.39/2.77 ! [A: rat,B: rat,C: rat,D2: rat] :
% 2.39/2.77 ( ( ( A != B )
% 2.39/2.77 & ( C != D2 ) )
% 2.39/2.77 = ( ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) )
% 2.39/2.77 != ( plus_plus_rat @ ( times_times_rat @ A @ D2 ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % crossproduct_noteq
% 2.39/2.77 thf(fact_2641_crossproduct__noteq,axiom,
% 2.39/2.77 ! [A: nat,B: nat,C: nat,D2: nat] :
% 2.39/2.77 ( ( ( A != B )
% 2.39/2.77 & ( C != D2 ) )
% 2.39/2.77 = ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) )
% 2.39/2.77 != ( plus_plus_nat @ ( times_times_nat @ A @ D2 ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % crossproduct_noteq
% 2.39/2.77 thf(fact_2642_crossproduct__noteq,axiom,
% 2.39/2.77 ! [A: int,B: int,C: int,D2: int] :
% 2.39/2.77 ( ( ( A != B )
% 2.39/2.77 & ( C != D2 ) )
% 2.39/2.77 = ( ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) )
% 2.39/2.77 != ( plus_plus_int @ ( times_times_int @ A @ D2 ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % crossproduct_noteq
% 2.39/2.77 thf(fact_2643_crossproduct__noteq,axiom,
% 2.39/2.77 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 2.39/2.77 ( ( ( A != B )
% 2.39/2.77 & ( C != D2 ) )
% 2.39/2.77 = ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) )
% 2.39/2.77 != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ D2 ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % crossproduct_noteq
% 2.39/2.77 thf(fact_2644_crossproduct__eq,axiom,
% 2.39/2.77 ! [W: rat,Y: rat,X: rat,Z: rat] :
% 2.39/2.77 ( ( ( plus_plus_rat @ ( times_times_rat @ W @ Y ) @ ( times_times_rat @ X @ Z ) )
% 2.39/2.77 = ( plus_plus_rat @ ( times_times_rat @ W @ Z ) @ ( times_times_rat @ X @ Y ) ) )
% 2.39/2.77 = ( ( W = X )
% 2.39/2.77 | ( Y = Z ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % crossproduct_eq
% 2.39/2.77 thf(fact_2645_crossproduct__eq,axiom,
% 2.39/2.77 ! [W: nat,Y: nat,X: nat,Z: nat] :
% 2.39/2.77 ( ( ( plus_plus_nat @ ( times_times_nat @ W @ Y ) @ ( times_times_nat @ X @ Z ) )
% 2.39/2.77 = ( plus_plus_nat @ ( times_times_nat @ W @ Z ) @ ( times_times_nat @ X @ Y ) ) )
% 2.39/2.77 = ( ( W = X )
% 2.39/2.77 | ( Y = Z ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % crossproduct_eq
% 2.39/2.77 thf(fact_2646_crossproduct__eq,axiom,
% 2.39/2.77 ! [W: int,Y: int,X: int,Z: int] :
% 2.39/2.77 ( ( ( plus_plus_int @ ( times_times_int @ W @ Y ) @ ( times_times_int @ X @ Z ) )
% 2.39/2.77 = ( plus_plus_int @ ( times_times_int @ W @ Z ) @ ( times_times_int @ X @ Y ) ) )
% 2.39/2.77 = ( ( W = X )
% 2.39/2.77 | ( Y = Z ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % crossproduct_eq
% 2.39/2.77 thf(fact_2647_crossproduct__eq,axiom,
% 2.39/2.77 ! [W: code_integer,Y: code_integer,X: code_integer,Z: code_integer] :
% 2.39/2.77 ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ W @ Y ) @ ( times_3573771949741848930nteger @ X @ Z ) )
% 2.39/2.77 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ W @ Z ) @ ( times_3573771949741848930nteger @ X @ Y ) ) )
% 2.39/2.77 = ( ( W = X )
% 2.39/2.77 | ( Y = Z ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % crossproduct_eq
% 2.39/2.77 thf(fact_2648_nat__1__eq__mult__iff,axiom,
% 2.39/2.77 ! [M2: nat,N: nat] :
% 2.39/2.77 ( ( one_one_nat
% 2.39/2.77 = ( times_times_nat @ M2 @ N ) )
% 2.39/2.77 = ( ( M2 = one_one_nat )
% 2.39/2.77 & ( N = one_one_nat ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % nat_1_eq_mult_iff
% 2.39/2.77 thf(fact_2649_nat__mult__eq__1__iff,axiom,
% 2.39/2.77 ! [M2: nat,N: nat] :
% 2.39/2.77 ( ( ( times_times_nat @ M2 @ N )
% 2.39/2.77 = one_one_nat )
% 2.39/2.77 = ( ( M2 = one_one_nat )
% 2.39/2.77 & ( N = one_one_nat ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % nat_mult_eq_1_iff
% 2.39/2.77 thf(fact_2650_nat__mult__1,axiom,
% 2.39/2.77 ! [N: nat] :
% 2.39/2.77 ( ( times_times_nat @ one_one_nat @ N )
% 2.39/2.77 = N ) ).
% 2.39/2.77
% 2.39/2.77 % nat_mult_1
% 2.39/2.77 thf(fact_2651_nat__mult__1__right,axiom,
% 2.39/2.77 ! [N: nat] :
% 2.39/2.77 ( ( times_times_nat @ N @ one_one_nat )
% 2.39/2.77 = N ) ).
% 2.39/2.77
% 2.39/2.77 % nat_mult_1_right
% 2.39/2.77 thf(fact_2652_mult__eq__self__implies__10,axiom,
% 2.39/2.77 ! [M2: nat,N: nat] :
% 2.39/2.77 ( ( M2
% 2.39/2.77 = ( times_times_nat @ M2 @ N ) )
% 2.39/2.77 => ( ( N = one_one_nat )
% 2.39/2.77 | ( M2 = zero_zero_nat ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % mult_eq_self_implies_10
% 2.39/2.77 thf(fact_2653_product__lists_Osimps_I1_J,axiom,
% 2.39/2.77 ( ( produc1566369527784499744n_assn @ nil_li5476096274760905021n_assn )
% 2.39/2.77 = ( cons_l2423627976422276333n_assn @ nil_Pr5671120429643327159n_assn @ nil_li5476096274760905021n_assn ) ) ).
% 2.39/2.77
% 2.39/2.77 % product_lists.simps(1)
% 2.39/2.77 thf(fact_2654_product__lists_Osimps_I1_J,axiom,
% 2.39/2.77 ( ( product_lists_int @ nil_list_int )
% 2.39/2.77 = ( cons_list_int @ nil_int @ nil_list_int ) ) ).
% 2.39/2.77
% 2.39/2.77 % product_lists.simps(1)
% 2.39/2.77 thf(fact_2655_product__lists_Osimps_I1_J,axiom,
% 2.39/2.77 ( ( product_lists_nat @ nil_list_nat )
% 2.39/2.77 = ( cons_list_nat @ nil_nat @ nil_list_nat ) ) ).
% 2.39/2.77
% 2.39/2.77 % product_lists.simps(1)
% 2.39/2.77 thf(fact_2656_power__decreasing__iff,axiom,
% 2.39/2.77 ! [B: code_natural,M2: nat,N: nat] :
% 2.39/2.77 ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ B )
% 2.39/2.77 => ( ( ord_le5570908160329646204atural @ B @ one_one_Code_natural )
% 2.39/2.77 => ( ( ord_le1926595141338095240atural @ ( power_7079662738309270450atural @ B @ M2 ) @ ( power_7079662738309270450atural @ B @ N ) )
% 2.39/2.77 = ( ord_less_eq_nat @ N @ M2 ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_decreasing_iff
% 2.39/2.77 thf(fact_2657_power__decreasing__iff,axiom,
% 2.39/2.77 ! [B: code_integer,M2: nat,N: nat] :
% 2.39/2.77 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 2.39/2.77 => ( ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer )
% 2.39/2.77 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ B @ M2 ) @ ( power_8256067586552552935nteger @ B @ N ) )
% 2.39/2.77 = ( ord_less_eq_nat @ N @ M2 ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_decreasing_iff
% 2.39/2.77 thf(fact_2658_power__decreasing__iff,axiom,
% 2.39/2.77 ! [B: rat,M2: nat,N: nat] :
% 2.39/2.77 ( ( ord_less_rat @ zero_zero_rat @ B )
% 2.39/2.77 => ( ( ord_less_rat @ B @ one_one_rat )
% 2.39/2.77 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ M2 ) @ ( power_power_rat @ B @ N ) )
% 2.39/2.77 = ( ord_less_eq_nat @ N @ M2 ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_decreasing_iff
% 2.39/2.77 thf(fact_2659_power__decreasing__iff,axiom,
% 2.39/2.77 ! [B: nat,M2: nat,N: nat] :
% 2.39/2.77 ( ( ord_less_nat @ zero_zero_nat @ B )
% 2.39/2.77 => ( ( ord_less_nat @ B @ one_one_nat )
% 2.39/2.77 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M2 ) @ ( power_power_nat @ B @ N ) )
% 2.39/2.77 = ( ord_less_eq_nat @ N @ M2 ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_decreasing_iff
% 2.39/2.77 thf(fact_2660_power__decreasing__iff,axiom,
% 2.39/2.77 ! [B: int,M2: nat,N: nat] :
% 2.39/2.77 ( ( ord_less_int @ zero_zero_int @ B )
% 2.39/2.77 => ( ( ord_less_int @ B @ one_one_int )
% 2.39/2.77 => ( ( ord_less_eq_int @ ( power_power_int @ B @ M2 ) @ ( power_power_int @ B @ N ) )
% 2.39/2.77 = ( ord_less_eq_nat @ N @ M2 ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_decreasing_iff
% 2.39/2.77 thf(fact_2661_subseqs_Osimps_I1_J,axiom,
% 2.39/2.77 ( ( subseq184808802919281286n_assn @ nil_Pr5671120429643327159n_assn )
% 2.39/2.77 = ( cons_l2423627976422276333n_assn @ nil_Pr5671120429643327159n_assn @ nil_li5476096274760905021n_assn ) ) ).
% 2.39/2.77
% 2.39/2.77 % subseqs.simps(1)
% 2.39/2.77 thf(fact_2662_subseqs_Osimps_I1_J,axiom,
% 2.39/2.77 ( ( subseqs_int @ nil_int )
% 2.39/2.77 = ( cons_list_int @ nil_int @ nil_list_int ) ) ).
% 2.39/2.77
% 2.39/2.77 % subseqs.simps(1)
% 2.39/2.77 thf(fact_2663_subseqs_Osimps_I1_J,axiom,
% 2.39/2.77 ( ( subseqs_nat @ nil_nat )
% 2.39/2.77 = ( cons_list_nat @ nil_nat @ nil_list_nat ) ) ).
% 2.39/2.77
% 2.39/2.77 % subseqs.simps(1)
% 2.39/2.77 thf(fact_2664_le__minus__divide__eq,axiom,
% 2.39/2.77 ! [A: rat,B: rat,C: rat] :
% 2.39/2.77 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 2.39/2.77 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.77 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 2.39/2.77 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.77 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.77 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 2.39/2.77 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.77 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % le_minus_divide_eq
% 2.39/2.77 thf(fact_2665_minus__divide__le__eq,axiom,
% 2.39/2.77 ! [B: rat,C: rat,A: rat] :
% 2.39/2.77 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 2.39/2.77 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.77 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 2.39/2.77 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.77 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.77 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 2.39/2.77 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.77 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % minus_divide_le_eq
% 2.39/2.77 thf(fact_2666_neg__le__minus__divide__eq,axiom,
% 2.39/2.77 ! [C: rat,A: rat,B: rat] :
% 2.39/2.77 ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.77 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 2.39/2.77 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % neg_le_minus_divide_eq
% 2.39/2.77 thf(fact_2667_times__divide__eq__right,axiom,
% 2.39/2.77 ! [A: rat,B: rat,C: rat] :
% 2.39/2.77 ( ( times_times_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 2.39/2.77 = ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ C ) ) ).
% 2.39/2.77
% 2.39/2.77 % times_divide_eq_right
% 2.39/2.77 thf(fact_2668_divide__divide__eq__right,axiom,
% 2.39/2.77 ! [A: rat,B: rat,C: rat] :
% 2.39/2.77 ( ( divide_divide_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 2.39/2.77 = ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ B ) ) ).
% 2.39/2.77
% 2.39/2.77 % divide_divide_eq_right
% 2.39/2.77 thf(fact_2669_divide__divide__eq__left,axiom,
% 2.39/2.77 ! [A: rat,B: rat,C: rat] :
% 2.39/2.77 ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 2.39/2.77 = ( divide_divide_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % divide_divide_eq_left
% 2.39/2.77 thf(fact_2670_times__divide__eq__left,axiom,
% 2.39/2.77 ! [B: rat,C: rat,A: rat] :
% 2.39/2.77 ( ( times_times_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 2.39/2.77 = ( divide_divide_rat @ ( times_times_rat @ B @ A ) @ C ) ) ).
% 2.39/2.77
% 2.39/2.77 % times_divide_eq_left
% 2.39/2.77 thf(fact_2671_div__by__1,axiom,
% 2.39/2.77 ! [A: code_integer] :
% 2.39/2.77 ( ( divide6298287555418463151nteger @ A @ one_one_Code_integer )
% 2.39/2.77 = A ) ).
% 2.39/2.77
% 2.39/2.77 % div_by_1
% 2.39/2.77 thf(fact_2672_div__by__1,axiom,
% 2.39/2.77 ! [A: nat] :
% 2.39/2.77 ( ( divide_divide_nat @ A @ one_one_nat )
% 2.39/2.77 = A ) ).
% 2.39/2.77
% 2.39/2.77 % div_by_1
% 2.39/2.77 thf(fact_2673_div__by__1,axiom,
% 2.39/2.77 ! [A: int] :
% 2.39/2.77 ( ( divide_divide_int @ A @ one_one_int )
% 2.39/2.77 = A ) ).
% 2.39/2.77
% 2.39/2.77 % div_by_1
% 2.39/2.77 thf(fact_2674_div__by__1,axiom,
% 2.39/2.77 ! [A: rat] :
% 2.39/2.77 ( ( divide_divide_rat @ A @ one_one_rat )
% 2.39/2.77 = A ) ).
% 2.39/2.77
% 2.39/2.77 % div_by_1
% 2.39/2.77 thf(fact_2675_div__by__1,axiom,
% 2.39/2.77 ! [A: code_natural] :
% 2.39/2.77 ( ( divide5121882707175180666atural @ A @ one_one_Code_natural )
% 2.39/2.77 = A ) ).
% 2.39/2.77
% 2.39/2.77 % div_by_1
% 2.39/2.77 thf(fact_2676_power__one,axiom,
% 2.39/2.77 ! [N: nat] :
% 2.39/2.77 ( ( power_8256067586552552935nteger @ one_one_Code_integer @ N )
% 2.39/2.77 = one_one_Code_integer ) ).
% 2.39/2.77
% 2.39/2.77 % power_one
% 2.39/2.77 thf(fact_2677_power__one,axiom,
% 2.39/2.77 ! [N: nat] :
% 2.39/2.77 ( ( power_power_assn @ one_one_assn @ N )
% 2.39/2.77 = one_one_assn ) ).
% 2.39/2.77
% 2.39/2.77 % power_one
% 2.39/2.77 thf(fact_2678_power__one,axiom,
% 2.39/2.77 ! [N: nat] :
% 2.39/2.77 ( ( power_power_rat @ one_one_rat @ N )
% 2.39/2.77 = one_one_rat ) ).
% 2.39/2.77
% 2.39/2.77 % power_one
% 2.39/2.77 thf(fact_2679_power__one,axiom,
% 2.39/2.77 ! [N: nat] :
% 2.39/2.77 ( ( power_power_int @ one_one_int @ N )
% 2.39/2.77 = one_one_int ) ).
% 2.39/2.77
% 2.39/2.77 % power_one
% 2.39/2.77 thf(fact_2680_power__one,axiom,
% 2.39/2.77 ! [N: nat] :
% 2.39/2.77 ( ( power_power_nat @ one_one_nat @ N )
% 2.39/2.77 = one_one_nat ) ).
% 2.39/2.77
% 2.39/2.77 % power_one
% 2.39/2.77 thf(fact_2681_power__one__right,axiom,
% 2.39/2.77 ! [A: int] :
% 2.39/2.77 ( ( power_power_int @ A @ one_one_nat )
% 2.39/2.77 = A ) ).
% 2.39/2.77
% 2.39/2.77 % power_one_right
% 2.39/2.77 thf(fact_2682_power__one__right,axiom,
% 2.39/2.77 ! [A: nat] :
% 2.39/2.77 ( ( power_power_nat @ A @ one_one_nat )
% 2.39/2.77 = A ) ).
% 2.39/2.77
% 2.39/2.77 % power_one_right
% 2.39/2.77 thf(fact_2683_nonzero__mult__divide__mult__cancel__right2,axiom,
% 2.39/2.77 ! [C: rat,A: rat,B: rat] :
% 2.39/2.77 ( ( C != zero_zero_rat )
% 2.39/2.77 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ C @ B ) )
% 2.39/2.77 = ( divide_divide_rat @ A @ B ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % nonzero_mult_divide_mult_cancel_right2
% 2.39/2.77 thf(fact_2684_nonzero__mult__divide__mult__cancel__right,axiom,
% 2.39/2.77 ! [C: rat,A: rat,B: rat] :
% 2.39/2.77 ( ( C != zero_zero_rat )
% 2.39/2.77 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 2.39/2.77 = ( divide_divide_rat @ A @ B ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % nonzero_mult_divide_mult_cancel_right
% 2.39/2.77 thf(fact_2685_nonzero__mult__divide__mult__cancel__left2,axiom,
% 2.39/2.77 ! [C: rat,A: rat,B: rat] :
% 2.39/2.77 ( ( C != zero_zero_rat )
% 2.39/2.77 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ B @ C ) )
% 2.39/2.77 = ( divide_divide_rat @ A @ B ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % nonzero_mult_divide_mult_cancel_left2
% 2.39/2.77 thf(fact_2686_nonzero__mult__divide__mult__cancel__left,axiom,
% 2.39/2.77 ! [C: rat,A: rat,B: rat] :
% 2.39/2.77 ( ( C != zero_zero_rat )
% 2.39/2.77 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 2.39/2.77 = ( divide_divide_rat @ A @ B ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % nonzero_mult_divide_mult_cancel_left
% 2.39/2.77 thf(fact_2687_mult__divide__mult__cancel__left__if,axiom,
% 2.39/2.77 ! [C: rat,A: rat,B: rat] :
% 2.39/2.77 ( ( ( C = zero_zero_rat )
% 2.39/2.77 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 2.39/2.77 = zero_zero_rat ) )
% 2.39/2.77 & ( ( C != zero_zero_rat )
% 2.39/2.77 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 2.39/2.77 = ( divide_divide_rat @ A @ B ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % mult_divide_mult_cancel_left_if
% 2.39/2.77 thf(fact_2688_nonzero__mult__div__cancel__right,axiom,
% 2.39/2.77 ! [B: code_integer,A: code_integer] :
% 2.39/2.77 ( ( B != zero_z3403309356797280102nteger )
% 2.39/2.77 => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ B )
% 2.39/2.77 = A ) ) ).
% 2.39/2.77
% 2.39/2.77 % nonzero_mult_div_cancel_right
% 2.39/2.77 thf(fact_2689_nonzero__mult__div__cancel__right,axiom,
% 2.39/2.77 ! [B: nat,A: nat] :
% 2.39/2.77 ( ( B != zero_zero_nat )
% 2.39/2.77 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ B )
% 2.39/2.77 = A ) ) ).
% 2.39/2.77
% 2.39/2.77 % nonzero_mult_div_cancel_right
% 2.39/2.77 thf(fact_2690_nonzero__mult__div__cancel__right,axiom,
% 2.39/2.77 ! [B: int,A: int] :
% 2.39/2.77 ( ( B != zero_zero_int )
% 2.39/2.77 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ B )
% 2.39/2.77 = A ) ) ).
% 2.39/2.77
% 2.39/2.77 % nonzero_mult_div_cancel_right
% 2.39/2.77 thf(fact_2691_nonzero__mult__div__cancel__right,axiom,
% 2.39/2.77 ! [B: rat,A: rat] :
% 2.39/2.77 ( ( B != zero_zero_rat )
% 2.39/2.77 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ B )
% 2.39/2.77 = A ) ) ).
% 2.39/2.77
% 2.39/2.77 % nonzero_mult_div_cancel_right
% 2.39/2.77 thf(fact_2692_nonzero__mult__div__cancel__right,axiom,
% 2.39/2.77 ! [B: code_natural,A: code_natural] :
% 2.39/2.77 ( ( B != zero_z2226904508553997617atural )
% 2.39/2.77 => ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ B ) @ B )
% 2.39/2.77 = A ) ) ).
% 2.39/2.77
% 2.39/2.77 % nonzero_mult_div_cancel_right
% 2.39/2.77 thf(fact_2693_nonzero__mult__div__cancel__left,axiom,
% 2.39/2.77 ! [A: code_integer,B: code_integer] :
% 2.39/2.77 ( ( A != zero_z3403309356797280102nteger )
% 2.39/2.77 => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ A )
% 2.39/2.77 = B ) ) ).
% 2.39/2.77
% 2.39/2.77 % nonzero_mult_div_cancel_left
% 2.39/2.77 thf(fact_2694_nonzero__mult__div__cancel__left,axiom,
% 2.39/2.77 ! [A: nat,B: nat] :
% 2.39/2.77 ( ( A != zero_zero_nat )
% 2.39/2.77 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
% 2.39/2.77 = B ) ) ).
% 2.39/2.77
% 2.39/2.77 % nonzero_mult_div_cancel_left
% 2.39/2.77 thf(fact_2695_nonzero__mult__div__cancel__left,axiom,
% 2.39/2.77 ! [A: int,B: int] :
% 2.39/2.77 ( ( A != zero_zero_int )
% 2.39/2.77 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ A )
% 2.39/2.77 = B ) ) ).
% 2.39/2.77
% 2.39/2.77 % nonzero_mult_div_cancel_left
% 2.39/2.77 thf(fact_2696_nonzero__mult__div__cancel__left,axiom,
% 2.39/2.77 ! [A: rat,B: rat] :
% 2.39/2.77 ( ( A != zero_zero_rat )
% 2.39/2.77 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ A )
% 2.39/2.77 = B ) ) ).
% 2.39/2.77
% 2.39/2.77 % nonzero_mult_div_cancel_left
% 2.39/2.77 thf(fact_2697_nonzero__mult__div__cancel__left,axiom,
% 2.39/2.77 ! [A: code_natural,B: code_natural] :
% 2.39/2.77 ( ( A != zero_z2226904508553997617atural )
% 2.39/2.77 => ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ B ) @ A )
% 2.39/2.77 = B ) ) ).
% 2.39/2.77
% 2.39/2.77 % nonzero_mult_div_cancel_left
% 2.39/2.77 thf(fact_2698_zero__eq__1__divide__iff,axiom,
% 2.39/2.77 ! [A: rat] :
% 2.39/2.77 ( ( zero_zero_rat
% 2.39/2.77 = ( divide_divide_rat @ one_one_rat @ A ) )
% 2.39/2.77 = ( A = zero_zero_rat ) ) ).
% 2.39/2.77
% 2.39/2.77 % zero_eq_1_divide_iff
% 2.39/2.77 thf(fact_2699_one__divide__eq__0__iff,axiom,
% 2.39/2.77 ! [A: rat] :
% 2.39/2.77 ( ( ( divide_divide_rat @ one_one_rat @ A )
% 2.39/2.77 = zero_zero_rat )
% 2.39/2.77 = ( A = zero_zero_rat ) ) ).
% 2.39/2.77
% 2.39/2.77 % one_divide_eq_0_iff
% 2.39/2.77 thf(fact_2700_eq__divide__eq__1,axiom,
% 2.39/2.77 ! [B: rat,A: rat] :
% 2.39/2.77 ( ( one_one_rat
% 2.39/2.77 = ( divide_divide_rat @ B @ A ) )
% 2.39/2.77 = ( ( A != zero_zero_rat )
% 2.39/2.77 & ( A = B ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % eq_divide_eq_1
% 2.39/2.77 thf(fact_2701_divide__eq__eq__1,axiom,
% 2.39/2.77 ! [B: rat,A: rat] :
% 2.39/2.77 ( ( ( divide_divide_rat @ B @ A )
% 2.39/2.77 = one_one_rat )
% 2.39/2.77 = ( ( A != zero_zero_rat )
% 2.39/2.77 & ( A = B ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % divide_eq_eq_1
% 2.39/2.77 thf(fact_2702_divide__self__if,axiom,
% 2.39/2.77 ! [A: rat] :
% 2.39/2.77 ( ( ( A = zero_zero_rat )
% 2.39/2.77 => ( ( divide_divide_rat @ A @ A )
% 2.39/2.77 = zero_zero_rat ) )
% 2.39/2.77 & ( ( A != zero_zero_rat )
% 2.39/2.77 => ( ( divide_divide_rat @ A @ A )
% 2.39/2.77 = one_one_rat ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % divide_self_if
% 2.39/2.77 thf(fact_2703_divide__self,axiom,
% 2.39/2.77 ! [A: rat] :
% 2.39/2.77 ( ( A != zero_zero_rat )
% 2.39/2.77 => ( ( divide_divide_rat @ A @ A )
% 2.39/2.77 = one_one_rat ) ) ).
% 2.39/2.77
% 2.39/2.77 % divide_self
% 2.39/2.77 thf(fact_2704_one__eq__divide__iff,axiom,
% 2.39/2.77 ! [A: rat,B: rat] :
% 2.39/2.77 ( ( one_one_rat
% 2.39/2.77 = ( divide_divide_rat @ A @ B ) )
% 2.39/2.77 = ( ( B != zero_zero_rat )
% 2.39/2.77 & ( A = B ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % one_eq_divide_iff
% 2.39/2.77 thf(fact_2705_divide__eq__1__iff,axiom,
% 2.39/2.77 ! [A: rat,B: rat] :
% 2.39/2.77 ( ( ( divide_divide_rat @ A @ B )
% 2.39/2.77 = one_one_rat )
% 2.39/2.77 = ( ( B != zero_zero_rat )
% 2.39/2.77 & ( A = B ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % divide_eq_1_iff
% 2.39/2.77 thf(fact_2706_div__self,axiom,
% 2.39/2.77 ! [A: code_integer] :
% 2.39/2.77 ( ( A != zero_z3403309356797280102nteger )
% 2.39/2.77 => ( ( divide6298287555418463151nteger @ A @ A )
% 2.39/2.77 = one_one_Code_integer ) ) ).
% 2.39/2.77
% 2.39/2.77 % div_self
% 2.39/2.77 thf(fact_2707_div__self,axiom,
% 2.39/2.77 ! [A: nat] :
% 2.39/2.77 ( ( A != zero_zero_nat )
% 2.39/2.77 => ( ( divide_divide_nat @ A @ A )
% 2.39/2.77 = one_one_nat ) ) ).
% 2.39/2.77
% 2.39/2.77 % div_self
% 2.39/2.77 thf(fact_2708_div__self,axiom,
% 2.39/2.77 ! [A: int] :
% 2.39/2.77 ( ( A != zero_zero_int )
% 2.39/2.77 => ( ( divide_divide_int @ A @ A )
% 2.39/2.77 = one_one_int ) ) ).
% 2.39/2.77
% 2.39/2.77 % div_self
% 2.39/2.77 thf(fact_2709_div__self,axiom,
% 2.39/2.77 ! [A: rat] :
% 2.39/2.77 ( ( A != zero_zero_rat )
% 2.39/2.77 => ( ( divide_divide_rat @ A @ A )
% 2.39/2.77 = one_one_rat ) ) ).
% 2.39/2.77
% 2.39/2.77 % div_self
% 2.39/2.77 thf(fact_2710_div__self,axiom,
% 2.39/2.77 ! [A: code_natural] :
% 2.39/2.77 ( ( A != zero_z2226904508553997617atural )
% 2.39/2.77 => ( ( divide5121882707175180666atural @ A @ A )
% 2.39/2.77 = one_one_Code_natural ) ) ).
% 2.39/2.77
% 2.39/2.77 % div_self
% 2.39/2.77 thf(fact_2711_power__inject__exp,axiom,
% 2.39/2.77 ! [A: code_integer,M2: nat,N: nat] :
% 2.39/2.77 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 2.39/2.77 => ( ( ( power_8256067586552552935nteger @ A @ M2 )
% 2.39/2.77 = ( power_8256067586552552935nteger @ A @ N ) )
% 2.39/2.77 = ( M2 = N ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_inject_exp
% 2.39/2.77 thf(fact_2712_power__inject__exp,axiom,
% 2.39/2.77 ! [A: rat,M2: nat,N: nat] :
% 2.39/2.77 ( ( ord_less_rat @ one_one_rat @ A )
% 2.39/2.77 => ( ( ( power_power_rat @ A @ M2 )
% 2.39/2.77 = ( power_power_rat @ A @ N ) )
% 2.39/2.77 = ( M2 = N ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_inject_exp
% 2.39/2.77 thf(fact_2713_power__inject__exp,axiom,
% 2.39/2.77 ! [A: nat,M2: nat,N: nat] :
% 2.39/2.77 ( ( ord_less_nat @ one_one_nat @ A )
% 2.39/2.77 => ( ( ( power_power_nat @ A @ M2 )
% 2.39/2.77 = ( power_power_nat @ A @ N ) )
% 2.39/2.77 = ( M2 = N ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_inject_exp
% 2.39/2.77 thf(fact_2714_power__inject__exp,axiom,
% 2.39/2.77 ! [A: int,M2: nat,N: nat] :
% 2.39/2.77 ( ( ord_less_int @ one_one_int @ A )
% 2.39/2.77 => ( ( ( power_power_int @ A @ M2 )
% 2.39/2.77 = ( power_power_int @ A @ N ) )
% 2.39/2.77 = ( M2 = N ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_inject_exp
% 2.39/2.77 thf(fact_2715_divide__minus1,axiom,
% 2.39/2.77 ! [X: rat] :
% 2.39/2.77 ( ( divide_divide_rat @ X @ ( uminus_uminus_rat @ one_one_rat ) )
% 2.39/2.77 = ( uminus_uminus_rat @ X ) ) ).
% 2.39/2.77
% 2.39/2.77 % divide_minus1
% 2.39/2.77 thf(fact_2716_divide__sgn,axiom,
% 2.39/2.77 ! [A: rat,B: rat] :
% 2.39/2.77 ( ( divide_divide_rat @ A @ ( sgn_sgn_rat @ B ) )
% 2.39/2.77 = ( times_times_rat @ A @ ( sgn_sgn_rat @ B ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % divide_sgn
% 2.39/2.77 thf(fact_2717_zero__le__divide__1__iff,axiom,
% 2.39/2.77 ! [A: rat] :
% 2.39/2.77 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 2.39/2.77 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 2.39/2.77
% 2.39/2.77 % zero_le_divide_1_iff
% 2.39/2.77 thf(fact_2718_divide__le__0__1__iff,axiom,
% 2.39/2.77 ! [A: rat] :
% 2.39/2.77 ( ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 2.39/2.77 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 2.39/2.77
% 2.39/2.77 % divide_le_0_1_iff
% 2.39/2.77 thf(fact_2719_zero__less__divide__1__iff,axiom,
% 2.39/2.77 ! [A: rat] :
% 2.39/2.77 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 2.39/2.77 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 2.39/2.77
% 2.39/2.77 % zero_less_divide_1_iff
% 2.39/2.77 thf(fact_2720_less__divide__eq__1__pos,axiom,
% 2.39/2.77 ! [A: rat,B: rat] :
% 2.39/2.77 ( ( ord_less_rat @ zero_zero_rat @ A )
% 2.39/2.77 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 2.39/2.77 = ( ord_less_rat @ A @ B ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % less_divide_eq_1_pos
% 2.39/2.77 thf(fact_2721_less__divide__eq__1__neg,axiom,
% 2.39/2.77 ! [A: rat,B: rat] :
% 2.39/2.77 ( ( ord_less_rat @ A @ zero_zero_rat )
% 2.39/2.77 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 2.39/2.77 = ( ord_less_rat @ B @ A ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % less_divide_eq_1_neg
% 2.39/2.77 thf(fact_2722_divide__less__eq__1__pos,axiom,
% 2.39/2.77 ! [A: rat,B: rat] :
% 2.39/2.77 ( ( ord_less_rat @ zero_zero_rat @ A )
% 2.39/2.77 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 2.39/2.77 = ( ord_less_rat @ B @ A ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % divide_less_eq_1_pos
% 2.39/2.77 thf(fact_2723_divide__less__eq__1__neg,axiom,
% 2.39/2.77 ! [A: rat,B: rat] :
% 2.39/2.77 ( ( ord_less_rat @ A @ zero_zero_rat )
% 2.39/2.77 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 2.39/2.77 = ( ord_less_rat @ A @ B ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % divide_less_eq_1_neg
% 2.39/2.77 thf(fact_2724_divide__less__0__1__iff,axiom,
% 2.39/2.77 ! [A: rat] :
% 2.39/2.77 ( ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 2.39/2.77 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 2.39/2.77
% 2.39/2.77 % divide_less_0_1_iff
% 2.39/2.77 thf(fact_2725_nonzero__divide__mult__cancel__right,axiom,
% 2.39/2.77 ! [B: rat,A: rat] :
% 2.39/2.77 ( ( B != zero_zero_rat )
% 2.39/2.77 => ( ( divide_divide_rat @ B @ ( times_times_rat @ A @ B ) )
% 2.39/2.77 = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % nonzero_divide_mult_cancel_right
% 2.39/2.77 thf(fact_2726_nonzero__divide__mult__cancel__left,axiom,
% 2.39/2.77 ! [A: rat,B: rat] :
% 2.39/2.77 ( ( A != zero_zero_rat )
% 2.39/2.77 => ( ( divide_divide_rat @ A @ ( times_times_rat @ A @ B ) )
% 2.39/2.77 = ( divide_divide_rat @ one_one_rat @ B ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % nonzero_divide_mult_cancel_left
% 2.39/2.77 thf(fact_2727_power__strict__increasing__iff,axiom,
% 2.39/2.77 ! [B: code_integer,X: nat,Y: nat] :
% 2.39/2.77 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B )
% 2.39/2.77 => ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ B @ X ) @ ( power_8256067586552552935nteger @ B @ Y ) )
% 2.39/2.77 = ( ord_less_nat @ X @ Y ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_strict_increasing_iff
% 2.39/2.77 thf(fact_2728_power__strict__increasing__iff,axiom,
% 2.39/2.77 ! [B: rat,X: nat,Y: nat] :
% 2.39/2.77 ( ( ord_less_rat @ one_one_rat @ B )
% 2.39/2.77 => ( ( ord_less_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y ) )
% 2.39/2.77 = ( ord_less_nat @ X @ Y ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_strict_increasing_iff
% 2.39/2.77 thf(fact_2729_power__strict__increasing__iff,axiom,
% 2.39/2.77 ! [B: nat,X: nat,Y: nat] :
% 2.39/2.77 ( ( ord_less_nat @ one_one_nat @ B )
% 2.39/2.77 => ( ( ord_less_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y ) )
% 2.39/2.77 = ( ord_less_nat @ X @ Y ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_strict_increasing_iff
% 2.39/2.77 thf(fact_2730_power__strict__increasing__iff,axiom,
% 2.39/2.77 ! [B: int,X: nat,Y: nat] :
% 2.39/2.77 ( ( ord_less_int @ one_one_int @ B )
% 2.39/2.77 => ( ( ord_less_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y ) )
% 2.39/2.77 = ( ord_less_nat @ X @ Y ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_strict_increasing_iff
% 2.39/2.77 thf(fact_2731_left__minus__one__mult__self,axiom,
% 2.39/2.77 ! [N: nat,A: int] :
% 2.39/2.77 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ A ) )
% 2.39/2.77 = A ) ).
% 2.39/2.77
% 2.39/2.77 % left_minus_one_mult_self
% 2.39/2.77 thf(fact_2732_left__minus__one__mult__self,axiom,
% 2.39/2.77 ! [N: nat,A: rat] :
% 2.39/2.77 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ A ) )
% 2.39/2.77 = A ) ).
% 2.39/2.77
% 2.39/2.77 % left_minus_one_mult_self
% 2.39/2.77 thf(fact_2733_left__minus__one__mult__self,axiom,
% 2.39/2.77 ! [N: nat,A: code_integer] :
% 2.39/2.77 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ A ) )
% 2.39/2.77 = A ) ).
% 2.39/2.77
% 2.39/2.77 % left_minus_one_mult_self
% 2.39/2.77 thf(fact_2734_minus__one__mult__self,axiom,
% 2.39/2.77 ! [N: nat] :
% 2.39/2.77 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) )
% 2.39/2.77 = one_one_int ) ).
% 2.39/2.77
% 2.39/2.77 % minus_one_mult_self
% 2.39/2.77 thf(fact_2735_minus__one__mult__self,axiom,
% 2.39/2.77 ! [N: nat] :
% 2.39/2.77 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) )
% 2.39/2.77 = one_one_rat ) ).
% 2.39/2.77
% 2.39/2.77 % minus_one_mult_self
% 2.39/2.77 thf(fact_2736_minus__one__mult__self,axiom,
% 2.39/2.77 ! [N: nat] :
% 2.39/2.77 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) )
% 2.39/2.77 = one_one_Code_integer ) ).
% 2.39/2.77
% 2.39/2.77 % minus_one_mult_self
% 2.39/2.77 thf(fact_2737_le__divide__eq__1__pos,axiom,
% 2.39/2.77 ! [A: rat,B: rat] :
% 2.39/2.77 ( ( ord_less_rat @ zero_zero_rat @ A )
% 2.39/2.77 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 2.39/2.77 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % le_divide_eq_1_pos
% 2.39/2.77 thf(fact_2738_le__divide__eq__1__neg,axiom,
% 2.39/2.77 ! [A: rat,B: rat] :
% 2.39/2.77 ( ( ord_less_rat @ A @ zero_zero_rat )
% 2.39/2.77 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 2.39/2.77 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % le_divide_eq_1_neg
% 2.39/2.77 thf(fact_2739_divide__le__eq__1__pos,axiom,
% 2.39/2.77 ! [A: rat,B: rat] :
% 2.39/2.77 ( ( ord_less_rat @ zero_zero_rat @ A )
% 2.39/2.77 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 2.39/2.77 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % divide_le_eq_1_pos
% 2.39/2.77 thf(fact_2740_divide__le__eq__1__neg,axiom,
% 2.39/2.77 ! [A: rat,B: rat] :
% 2.39/2.77 ( ( ord_less_rat @ A @ zero_zero_rat )
% 2.39/2.77 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 2.39/2.77 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % divide_le_eq_1_neg
% 2.39/2.77 thf(fact_2741_power__strict__decreasing__iff,axiom,
% 2.39/2.77 ! [B: code_natural,M2: nat,N: nat] :
% 2.39/2.77 ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ B )
% 2.39/2.77 => ( ( ord_le5570908160329646204atural @ B @ one_one_Code_natural )
% 2.39/2.77 => ( ( ord_le5570908160329646204atural @ ( power_7079662738309270450atural @ B @ M2 ) @ ( power_7079662738309270450atural @ B @ N ) )
% 2.39/2.77 = ( ord_less_nat @ N @ M2 ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_strict_decreasing_iff
% 2.39/2.77 thf(fact_2742_power__strict__decreasing__iff,axiom,
% 2.39/2.77 ! [B: code_integer,M2: nat,N: nat] :
% 2.39/2.77 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 2.39/2.77 => ( ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer )
% 2.39/2.77 => ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ B @ M2 ) @ ( power_8256067586552552935nteger @ B @ N ) )
% 2.39/2.77 = ( ord_less_nat @ N @ M2 ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_strict_decreasing_iff
% 2.39/2.77 thf(fact_2743_power__strict__decreasing__iff,axiom,
% 2.39/2.77 ! [B: rat,M2: nat,N: nat] :
% 2.39/2.77 ( ( ord_less_rat @ zero_zero_rat @ B )
% 2.39/2.77 => ( ( ord_less_rat @ B @ one_one_rat )
% 2.39/2.77 => ( ( ord_less_rat @ ( power_power_rat @ B @ M2 ) @ ( power_power_rat @ B @ N ) )
% 2.39/2.77 = ( ord_less_nat @ N @ M2 ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_strict_decreasing_iff
% 2.39/2.77 thf(fact_2744_power__strict__decreasing__iff,axiom,
% 2.39/2.77 ! [B: nat,M2: nat,N: nat] :
% 2.39/2.77 ( ( ord_less_nat @ zero_zero_nat @ B )
% 2.39/2.77 => ( ( ord_less_nat @ B @ one_one_nat )
% 2.39/2.77 => ( ( ord_less_nat @ ( power_power_nat @ B @ M2 ) @ ( power_power_nat @ B @ N ) )
% 2.39/2.77 = ( ord_less_nat @ N @ M2 ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_strict_decreasing_iff
% 2.39/2.77 thf(fact_2745_power__strict__decreasing__iff,axiom,
% 2.39/2.77 ! [B: int,M2: nat,N: nat] :
% 2.39/2.77 ( ( ord_less_int @ zero_zero_int @ B )
% 2.39/2.77 => ( ( ord_less_int @ B @ one_one_int )
% 2.39/2.77 => ( ( ord_less_int @ ( power_power_int @ B @ M2 ) @ ( power_power_int @ B @ N ) )
% 2.39/2.77 = ( ord_less_nat @ N @ M2 ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_strict_decreasing_iff
% 2.39/2.77 thf(fact_2746_power__increasing__iff,axiom,
% 2.39/2.77 ! [B: code_integer,X: nat,Y: nat] :
% 2.39/2.77 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B )
% 2.39/2.77 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ B @ X ) @ ( power_8256067586552552935nteger @ B @ Y ) )
% 2.39/2.77 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_increasing_iff
% 2.39/2.77 thf(fact_2747_power__increasing__iff,axiom,
% 2.39/2.77 ! [B: rat,X: nat,Y: nat] :
% 2.39/2.77 ( ( ord_less_rat @ one_one_rat @ B )
% 2.39/2.77 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y ) )
% 2.39/2.77 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_increasing_iff
% 2.39/2.77 thf(fact_2748_power__increasing__iff,axiom,
% 2.39/2.77 ! [B: nat,X: nat,Y: nat] :
% 2.39/2.77 ( ( ord_less_nat @ one_one_nat @ B )
% 2.39/2.77 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y ) )
% 2.39/2.77 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_increasing_iff
% 2.39/2.77 thf(fact_2749_power__increasing__iff,axiom,
% 2.39/2.77 ! [B: int,X: nat,Y: nat] :
% 2.39/2.77 ( ( ord_less_int @ one_one_int @ B )
% 2.39/2.77 => ( ( ord_less_eq_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y ) )
% 2.39/2.77 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_increasing_iff
% 2.39/2.77 thf(fact_2750_power__one__over,axiom,
% 2.39/2.77 ! [A: rat,N: nat] :
% 2.39/2.77 ( ( power_power_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ N )
% 2.39/2.77 = ( divide_divide_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_one_over
% 2.39/2.77 thf(fact_2751_power__add,axiom,
% 2.39/2.77 ! [A: assn,M2: nat,N: nat] :
% 2.39/2.77 ( ( power_power_assn @ A @ ( plus_plus_nat @ M2 @ N ) )
% 2.39/2.77 = ( times_times_assn @ ( power_power_assn @ A @ M2 ) @ ( power_power_assn @ A @ N ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_add
% 2.39/2.77 thf(fact_2752_power__add,axiom,
% 2.39/2.77 ! [A: nat,M2: nat,N: nat] :
% 2.39/2.77 ( ( power_power_nat @ A @ ( plus_plus_nat @ M2 @ N ) )
% 2.39/2.77 = ( times_times_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_add
% 2.39/2.77 thf(fact_2753_power__add,axiom,
% 2.39/2.77 ! [A: int,M2: nat,N: nat] :
% 2.39/2.77 ( ( power_power_int @ A @ ( plus_plus_nat @ M2 @ N ) )
% 2.39/2.77 = ( times_times_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_add
% 2.39/2.77 thf(fact_2754_power__add,axiom,
% 2.39/2.77 ! [A: code_integer,M2: nat,N: nat] :
% 2.39/2.77 ( ( power_8256067586552552935nteger @ A @ ( plus_plus_nat @ M2 @ N ) )
% 2.39/2.77 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ M2 ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_add
% 2.39/2.77 thf(fact_2755_power__add,axiom,
% 2.39/2.77 ! [A: code_natural,M2: nat,N: nat] :
% 2.39/2.77 ( ( power_7079662738309270450atural @ A @ ( plus_plus_nat @ M2 @ N ) )
% 2.39/2.77 = ( times_2397367101498566445atural @ ( power_7079662738309270450atural @ A @ M2 ) @ ( power_7079662738309270450atural @ A @ N ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_add
% 2.39/2.77 thf(fact_2756_power__commuting__commutes,axiom,
% 2.39/2.77 ! [X: assn,Y: assn,N: nat] :
% 2.39/2.77 ( ( ( times_times_assn @ X @ Y )
% 2.39/2.77 = ( times_times_assn @ Y @ X ) )
% 2.39/2.77 => ( ( times_times_assn @ ( power_power_assn @ X @ N ) @ Y )
% 2.39/2.77 = ( times_times_assn @ Y @ ( power_power_assn @ X @ N ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_commuting_commutes
% 2.39/2.77 thf(fact_2757_power__commuting__commutes,axiom,
% 2.39/2.77 ! [X: nat,Y: nat,N: nat] :
% 2.39/2.77 ( ( ( times_times_nat @ X @ Y )
% 2.39/2.77 = ( times_times_nat @ Y @ X ) )
% 2.39/2.77 => ( ( times_times_nat @ ( power_power_nat @ X @ N ) @ Y )
% 2.39/2.77 = ( times_times_nat @ Y @ ( power_power_nat @ X @ N ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_commuting_commutes
% 2.39/2.77 thf(fact_2758_power__commuting__commutes,axiom,
% 2.39/2.77 ! [X: int,Y: int,N: nat] :
% 2.39/2.77 ( ( ( times_times_int @ X @ Y )
% 2.39/2.77 = ( times_times_int @ Y @ X ) )
% 2.39/2.77 => ( ( times_times_int @ ( power_power_int @ X @ N ) @ Y )
% 2.39/2.77 = ( times_times_int @ Y @ ( power_power_int @ X @ N ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_commuting_commutes
% 2.39/2.77 thf(fact_2759_power__commuting__commutes,axiom,
% 2.39/2.77 ! [X: code_integer,Y: code_integer,N: nat] :
% 2.39/2.77 ( ( ( times_3573771949741848930nteger @ X @ Y )
% 2.39/2.77 = ( times_3573771949741848930nteger @ Y @ X ) )
% 2.39/2.77 => ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ X @ N ) @ Y )
% 2.39/2.77 = ( times_3573771949741848930nteger @ Y @ ( power_8256067586552552935nteger @ X @ N ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_commuting_commutes
% 2.39/2.77 thf(fact_2760_power__commuting__commutes,axiom,
% 2.39/2.77 ! [X: code_natural,Y: code_natural,N: nat] :
% 2.39/2.77 ( ( ( times_2397367101498566445atural @ X @ Y )
% 2.39/2.77 = ( times_2397367101498566445atural @ Y @ X ) )
% 2.39/2.77 => ( ( times_2397367101498566445atural @ ( power_7079662738309270450atural @ X @ N ) @ Y )
% 2.39/2.77 = ( times_2397367101498566445atural @ Y @ ( power_7079662738309270450atural @ X @ N ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_commuting_commutes
% 2.39/2.77 thf(fact_2761_power__mult__distrib,axiom,
% 2.39/2.77 ! [A: assn,B: assn,N: nat] :
% 2.39/2.77 ( ( power_power_assn @ ( times_times_assn @ A @ B ) @ N )
% 2.39/2.77 = ( times_times_assn @ ( power_power_assn @ A @ N ) @ ( power_power_assn @ B @ N ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_mult_distrib
% 2.39/2.77 thf(fact_2762_power__mult__distrib,axiom,
% 2.39/2.77 ! [A: nat,B: nat,N: nat] :
% 2.39/2.77 ( ( power_power_nat @ ( times_times_nat @ A @ B ) @ N )
% 2.39/2.77 = ( times_times_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_mult_distrib
% 2.39/2.77 thf(fact_2763_power__mult__distrib,axiom,
% 2.39/2.77 ! [A: int,B: int,N: nat] :
% 2.39/2.77 ( ( power_power_int @ ( times_times_int @ A @ B ) @ N )
% 2.39/2.77 = ( times_times_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_mult_distrib
% 2.39/2.77 thf(fact_2764_power__mult__distrib,axiom,
% 2.39/2.77 ! [A: code_integer,B: code_integer,N: nat] :
% 2.39/2.77 ( ( power_8256067586552552935nteger @ ( times_3573771949741848930nteger @ A @ B ) @ N )
% 2.39/2.77 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_mult_distrib
% 2.39/2.77 thf(fact_2765_power__mult__distrib,axiom,
% 2.39/2.77 ! [A: code_natural,B: code_natural,N: nat] :
% 2.39/2.77 ( ( power_7079662738309270450atural @ ( times_2397367101498566445atural @ A @ B ) @ N )
% 2.39/2.77 = ( times_2397367101498566445atural @ ( power_7079662738309270450atural @ A @ N ) @ ( power_7079662738309270450atural @ B @ N ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_mult_distrib
% 2.39/2.77 thf(fact_2766_power__commutes,axiom,
% 2.39/2.77 ! [A: assn,N: nat] :
% 2.39/2.77 ( ( times_times_assn @ ( power_power_assn @ A @ N ) @ A )
% 2.39/2.77 = ( times_times_assn @ A @ ( power_power_assn @ A @ N ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_commutes
% 2.39/2.77 thf(fact_2767_power__commutes,axiom,
% 2.39/2.77 ! [A: nat,N: nat] :
% 2.39/2.77 ( ( times_times_nat @ ( power_power_nat @ A @ N ) @ A )
% 2.39/2.77 = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_commutes
% 2.39/2.77 thf(fact_2768_power__commutes,axiom,
% 2.39/2.77 ! [A: int,N: nat] :
% 2.39/2.77 ( ( times_times_int @ ( power_power_int @ A @ N ) @ A )
% 2.39/2.77 = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_commutes
% 2.39/2.77 thf(fact_2769_power__commutes,axiom,
% 2.39/2.77 ! [A: code_integer,N: nat] :
% 2.39/2.77 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ N ) @ A )
% 2.39/2.77 = ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_commutes
% 2.39/2.77 thf(fact_2770_power__commutes,axiom,
% 2.39/2.77 ! [A: code_natural,N: nat] :
% 2.39/2.77 ( ( times_2397367101498566445atural @ ( power_7079662738309270450atural @ A @ N ) @ A )
% 2.39/2.77 = ( times_2397367101498566445atural @ A @ ( power_7079662738309270450atural @ A @ N ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_commutes
% 2.39/2.77 thf(fact_2771_divide__divide__eq__left_H,axiom,
% 2.39/2.77 ! [A: rat,B: rat,C: rat] :
% 2.39/2.77 ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 2.39/2.77 = ( divide_divide_rat @ A @ ( times_times_rat @ C @ B ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % divide_divide_eq_left'
% 2.39/2.77 thf(fact_2772_divide__divide__times__eq,axiom,
% 2.39/2.77 ! [X: rat,Y: rat,Z: rat,W: rat] :
% 2.39/2.77 ( ( divide_divide_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ Z @ W ) )
% 2.39/2.77 = ( divide_divide_rat @ ( times_times_rat @ X @ W ) @ ( times_times_rat @ Y @ Z ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % divide_divide_times_eq
% 2.39/2.77 thf(fact_2773_times__divide__times__eq,axiom,
% 2.39/2.77 ! [X: rat,Y: rat,Z: rat,W: rat] :
% 2.39/2.77 ( ( times_times_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ Z @ W ) )
% 2.39/2.77 = ( divide_divide_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y @ W ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % times_divide_times_eq
% 2.39/2.77 thf(fact_2774_one__le__power,axiom,
% 2.39/2.77 ! [A: code_integer,N: nat] :
% 2.39/2.77 ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A )
% 2.39/2.77 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % one_le_power
% 2.39/2.77 thf(fact_2775_one__le__power,axiom,
% 2.39/2.77 ! [A: rat,N: nat] :
% 2.39/2.77 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 2.39/2.77 => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % one_le_power
% 2.39/2.77 thf(fact_2776_one__le__power,axiom,
% 2.39/2.77 ! [A: nat,N: nat] :
% 2.39/2.77 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 2.39/2.77 => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % one_le_power
% 2.39/2.77 thf(fact_2777_one__le__power,axiom,
% 2.39/2.77 ! [A: int,N: nat] :
% 2.39/2.77 ( ( ord_less_eq_int @ one_one_int @ A )
% 2.39/2.77 => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % one_le_power
% 2.39/2.77 thf(fact_2778_left__right__inverse__power,axiom,
% 2.39/2.77 ! [X: rat,Y: rat,N: nat] :
% 2.39/2.77 ( ( ( times_times_rat @ X @ Y )
% 2.39/2.77 = one_one_rat )
% 2.39/2.77 => ( ( times_times_rat @ ( power_power_rat @ X @ N ) @ ( power_power_rat @ Y @ N ) )
% 2.39/2.77 = one_one_rat ) ) ).
% 2.39/2.77
% 2.39/2.77 % left_right_inverse_power
% 2.39/2.77 thf(fact_2779_left__right__inverse__power,axiom,
% 2.39/2.77 ! [X: assn,Y: assn,N: nat] :
% 2.39/2.77 ( ( ( times_times_assn @ X @ Y )
% 2.39/2.77 = one_one_assn )
% 2.39/2.77 => ( ( times_times_assn @ ( power_power_assn @ X @ N ) @ ( power_power_assn @ Y @ N ) )
% 2.39/2.77 = one_one_assn ) ) ).
% 2.39/2.77
% 2.39/2.77 % left_right_inverse_power
% 2.39/2.77 thf(fact_2780_left__right__inverse__power,axiom,
% 2.39/2.77 ! [X: nat,Y: nat,N: nat] :
% 2.39/2.77 ( ( ( times_times_nat @ X @ Y )
% 2.39/2.77 = one_one_nat )
% 2.39/2.77 => ( ( times_times_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y @ N ) )
% 2.39/2.77 = one_one_nat ) ) ).
% 2.39/2.77
% 2.39/2.77 % left_right_inverse_power
% 2.39/2.77 thf(fact_2781_left__right__inverse__power,axiom,
% 2.39/2.77 ! [X: int,Y: int,N: nat] :
% 2.39/2.77 ( ( ( times_times_int @ X @ Y )
% 2.39/2.77 = one_one_int )
% 2.39/2.77 => ( ( times_times_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y @ N ) )
% 2.39/2.77 = one_one_int ) ) ).
% 2.39/2.77
% 2.39/2.77 % left_right_inverse_power
% 2.39/2.77 thf(fact_2782_left__right__inverse__power,axiom,
% 2.39/2.77 ! [X: code_integer,Y: code_integer,N: nat] :
% 2.39/2.77 ( ( ( times_3573771949741848930nteger @ X @ Y )
% 2.39/2.77 = one_one_Code_integer )
% 2.39/2.77 => ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ X @ N ) @ ( power_8256067586552552935nteger @ Y @ N ) )
% 2.39/2.77 = one_one_Code_integer ) ) ).
% 2.39/2.77
% 2.39/2.77 % left_right_inverse_power
% 2.39/2.77 thf(fact_2783_left__right__inverse__power,axiom,
% 2.39/2.77 ! [X: code_natural,Y: code_natural,N: nat] :
% 2.39/2.77 ( ( ( times_2397367101498566445atural @ X @ Y )
% 2.39/2.77 = one_one_Code_natural )
% 2.39/2.77 => ( ( times_2397367101498566445atural @ ( power_7079662738309270450atural @ X @ N ) @ ( power_7079662738309270450atural @ Y @ N ) )
% 2.39/2.77 = one_one_Code_natural ) ) ).
% 2.39/2.77
% 2.39/2.77 % left_right_inverse_power
% 2.39/2.77 thf(fact_2784_nonzero__eq__divide__eq,axiom,
% 2.39/2.77 ! [C: rat,A: rat,B: rat] :
% 2.39/2.77 ( ( C != zero_zero_rat )
% 2.39/2.77 => ( ( A
% 2.39/2.77 = ( divide_divide_rat @ B @ C ) )
% 2.39/2.77 = ( ( times_times_rat @ A @ C )
% 2.39/2.77 = B ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % nonzero_eq_divide_eq
% 2.39/2.77 thf(fact_2785_nonzero__divide__eq__eq,axiom,
% 2.39/2.77 ! [C: rat,B: rat,A: rat] :
% 2.39/2.77 ( ( C != zero_zero_rat )
% 2.39/2.77 => ( ( ( divide_divide_rat @ B @ C )
% 2.39/2.77 = A )
% 2.39/2.77 = ( B
% 2.39/2.77 = ( times_times_rat @ A @ C ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % nonzero_divide_eq_eq
% 2.39/2.77 thf(fact_2786_eq__divide__imp,axiom,
% 2.39/2.77 ! [C: rat,A: rat,B: rat] :
% 2.39/2.77 ( ( C != zero_zero_rat )
% 2.39/2.77 => ( ( ( times_times_rat @ A @ C )
% 2.39/2.77 = B )
% 2.39/2.77 => ( A
% 2.39/2.77 = ( divide_divide_rat @ B @ C ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % eq_divide_imp
% 2.39/2.77 thf(fact_2787_divide__eq__imp,axiom,
% 2.39/2.77 ! [C: rat,B: rat,A: rat] :
% 2.39/2.77 ( ( C != zero_zero_rat )
% 2.39/2.77 => ( ( B
% 2.39/2.77 = ( times_times_rat @ A @ C ) )
% 2.39/2.77 => ( ( divide_divide_rat @ B @ C )
% 2.39/2.77 = A ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % divide_eq_imp
% 2.39/2.77 thf(fact_2788_eq__divide__eq,axiom,
% 2.39/2.77 ! [A: rat,B: rat,C: rat] :
% 2.39/2.77 ( ( A
% 2.39/2.77 = ( divide_divide_rat @ B @ C ) )
% 2.39/2.77 = ( ( ( C != zero_zero_rat )
% 2.39/2.77 => ( ( times_times_rat @ A @ C )
% 2.39/2.77 = B ) )
% 2.39/2.77 & ( ( C = zero_zero_rat )
% 2.39/2.77 => ( A = zero_zero_rat ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % eq_divide_eq
% 2.39/2.77 thf(fact_2789_divide__eq__eq,axiom,
% 2.39/2.77 ! [B: rat,C: rat,A: rat] :
% 2.39/2.77 ( ( ( divide_divide_rat @ B @ C )
% 2.39/2.77 = A )
% 2.39/2.77 = ( ( ( C != zero_zero_rat )
% 2.39/2.77 => ( B
% 2.39/2.77 = ( times_times_rat @ A @ C ) ) )
% 2.39/2.77 & ( ( C = zero_zero_rat )
% 2.39/2.77 => ( A = zero_zero_rat ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % divide_eq_eq
% 2.39/2.77 thf(fact_2790_frac__eq__eq,axiom,
% 2.39/2.77 ! [Y: rat,Z: rat,X: rat,W: rat] :
% 2.39/2.77 ( ( Y != zero_zero_rat )
% 2.39/2.77 => ( ( Z != zero_zero_rat )
% 2.39/2.77 => ( ( ( divide_divide_rat @ X @ Y )
% 2.39/2.77 = ( divide_divide_rat @ W @ Z ) )
% 2.39/2.77 = ( ( times_times_rat @ X @ Z )
% 2.39/2.77 = ( times_times_rat @ W @ Y ) ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % frac_eq_eq
% 2.39/2.77 thf(fact_2791_right__inverse__eq,axiom,
% 2.39/2.77 ! [B: rat,A: rat] :
% 2.39/2.77 ( ( B != zero_zero_rat )
% 2.39/2.77 => ( ( ( divide_divide_rat @ A @ B )
% 2.39/2.77 = one_one_rat )
% 2.39/2.77 = ( A = B ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % right_inverse_eq
% 2.39/2.77 thf(fact_2792_power__0,axiom,
% 2.39/2.77 ! [A: code_integer] :
% 2.39/2.77 ( ( power_8256067586552552935nteger @ A @ zero_zero_nat )
% 2.39/2.77 = one_one_Code_integer ) ).
% 2.39/2.77
% 2.39/2.77 % power_0
% 2.39/2.77 thf(fact_2793_power__0,axiom,
% 2.39/2.77 ! [A: assn] :
% 2.39/2.77 ( ( power_power_assn @ A @ zero_zero_nat )
% 2.39/2.77 = one_one_assn ) ).
% 2.39/2.77
% 2.39/2.77 % power_0
% 2.39/2.77 thf(fact_2794_power__0,axiom,
% 2.39/2.77 ! [A: rat] :
% 2.39/2.77 ( ( power_power_rat @ A @ zero_zero_nat )
% 2.39/2.77 = one_one_rat ) ).
% 2.39/2.77
% 2.39/2.77 % power_0
% 2.39/2.77 thf(fact_2795_power__0,axiom,
% 2.39/2.77 ! [A: int] :
% 2.39/2.77 ( ( power_power_int @ A @ zero_zero_nat )
% 2.39/2.77 = one_one_int ) ).
% 2.39/2.77
% 2.39/2.77 % power_0
% 2.39/2.77 thf(fact_2796_power__0,axiom,
% 2.39/2.77 ! [A: nat] :
% 2.39/2.77 ( ( power_power_nat @ A @ zero_zero_nat )
% 2.39/2.77 = one_one_nat ) ).
% 2.39/2.77
% 2.39/2.77 % power_0
% 2.39/2.77 thf(fact_2797_power__le__one,axiom,
% 2.39/2.77 ! [A: code_integer,N: nat] :
% 2.39/2.77 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.77 => ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 2.39/2.77 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ one_one_Code_integer ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_le_one
% 2.39/2.77 thf(fact_2798_power__le__one,axiom,
% 2.39/2.77 ! [A: code_natural,N: nat] :
% 2.39/2.77 ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 2.39/2.77 => ( ( ord_le1926595141338095240atural @ A @ one_one_Code_natural )
% 2.39/2.77 => ( ord_le1926595141338095240atural @ ( power_7079662738309270450atural @ A @ N ) @ one_one_Code_natural ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_le_one
% 2.39/2.77 thf(fact_2799_power__le__one,axiom,
% 2.39/2.77 ! [A: rat,N: nat] :
% 2.39/2.77 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 2.39/2.77 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 2.39/2.77 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ one_one_rat ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_le_one
% 2.39/2.77 thf(fact_2800_power__le__one,axiom,
% 2.39/2.77 ! [A: nat,N: nat] :
% 2.39/2.77 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 2.39/2.77 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 2.39/2.77 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ one_one_nat ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_le_one
% 2.39/2.77 thf(fact_2801_power__le__one,axiom,
% 2.39/2.77 ! [A: int,N: nat] :
% 2.39/2.77 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 2.39/2.77 => ( ( ord_less_eq_int @ A @ one_one_int )
% 2.39/2.77 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ one_one_int ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_le_one
% 2.39/2.77 thf(fact_2802_power__less__power__Suc,axiom,
% 2.39/2.77 ! [A: code_natural,N: nat] :
% 2.39/2.77 ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ A )
% 2.39/2.77 => ( ord_le5570908160329646204atural @ ( power_7079662738309270450atural @ A @ N ) @ ( times_2397367101498566445atural @ A @ ( power_7079662738309270450atural @ A @ N ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_less_power_Suc
% 2.39/2.77 thf(fact_2803_power__less__power__Suc,axiom,
% 2.39/2.77 ! [A: code_integer,N: nat] :
% 2.39/2.77 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 2.39/2.77 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_less_power_Suc
% 2.39/2.77 thf(fact_2804_power__less__power__Suc,axiom,
% 2.39/2.77 ! [A: rat,N: nat] :
% 2.39/2.77 ( ( ord_less_rat @ one_one_rat @ A )
% 2.39/2.77 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_less_power_Suc
% 2.39/2.77 thf(fact_2805_power__less__power__Suc,axiom,
% 2.39/2.77 ! [A: nat,N: nat] :
% 2.39/2.77 ( ( ord_less_nat @ one_one_nat @ A )
% 2.39/2.77 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_less_power_Suc
% 2.39/2.77 thf(fact_2806_power__less__power__Suc,axiom,
% 2.39/2.77 ! [A: int,N: nat] :
% 2.39/2.77 ( ( ord_less_int @ one_one_int @ A )
% 2.39/2.77 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_less_power_Suc
% 2.39/2.77 thf(fact_2807_power__gt1__lemma,axiom,
% 2.39/2.77 ! [A: code_natural,N: nat] :
% 2.39/2.77 ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ A )
% 2.39/2.77 => ( ord_le5570908160329646204atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ A @ ( power_7079662738309270450atural @ A @ N ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_gt1_lemma
% 2.39/2.77 thf(fact_2808_power__gt1__lemma,axiom,
% 2.39/2.77 ! [A: code_integer,N: nat] :
% 2.39/2.77 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 2.39/2.77 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_gt1_lemma
% 2.39/2.77 thf(fact_2809_power__gt1__lemma,axiom,
% 2.39/2.77 ! [A: rat,N: nat] :
% 2.39/2.77 ( ( ord_less_rat @ one_one_rat @ A )
% 2.39/2.77 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_gt1_lemma
% 2.39/2.77 thf(fact_2810_power__gt1__lemma,axiom,
% 2.39/2.77 ! [A: nat,N: nat] :
% 2.39/2.77 ( ( ord_less_nat @ one_one_nat @ A )
% 2.39/2.77 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_gt1_lemma
% 2.39/2.77 thf(fact_2811_power__gt1__lemma,axiom,
% 2.39/2.77 ! [A: int,N: nat] :
% 2.39/2.77 ( ( ord_less_int @ one_one_int @ A )
% 2.39/2.77 => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_gt1_lemma
% 2.39/2.77 thf(fact_2812_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 2.39/2.77 ! [C: code_integer,A: code_integer,B: code_integer] :
% 2.39/2.77 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 2.39/2.77 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 2.39/2.77 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 2.39/2.77 thf(fact_2813_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 2.39/2.77 ! [C: nat,A: nat,B: nat] :
% 2.39/2.77 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 2.39/2.77 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 2.39/2.77 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 2.39/2.77 thf(fact_2814_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 2.39/2.77 ! [C: int,A: int,B: int] :
% 2.39/2.77 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 2.39/2.77 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 2.39/2.77 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 2.39/2.77 thf(fact_2815_divide__strict__left__mono__neg,axiom,
% 2.39/2.77 ! [A: rat,B: rat,C: rat] :
% 2.39/2.77 ( ( ord_less_rat @ A @ B )
% 2.39/2.77 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.77 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 2.39/2.77 => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % divide_strict_left_mono_neg
% 2.39/2.77 thf(fact_2816_divide__strict__left__mono,axiom,
% 2.39/2.77 ! [B: rat,A: rat,C: rat] :
% 2.39/2.77 ( ( ord_less_rat @ B @ A )
% 2.39/2.77 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.77 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 2.39/2.77 => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % divide_strict_left_mono
% 2.39/2.77 thf(fact_2817_mult__imp__less__div__pos,axiom,
% 2.39/2.77 ! [Y: rat,Z: rat,X: rat] :
% 2.39/2.77 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 2.39/2.77 => ( ( ord_less_rat @ ( times_times_rat @ Z @ Y ) @ X )
% 2.39/2.77 => ( ord_less_rat @ Z @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % mult_imp_less_div_pos
% 2.39/2.77 thf(fact_2818_mult__imp__div__pos__less,axiom,
% 2.39/2.77 ! [Y: rat,X: rat,Z: rat] :
% 2.39/2.77 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 2.39/2.77 => ( ( ord_less_rat @ X @ ( times_times_rat @ Z @ Y ) )
% 2.39/2.77 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ Z ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % mult_imp_div_pos_less
% 2.39/2.77 thf(fact_2819_pos__less__divide__eq,axiom,
% 2.39/2.77 ! [C: rat,A: rat,B: rat] :
% 2.39/2.77 ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.77 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 2.39/2.77 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % pos_less_divide_eq
% 2.39/2.77 thf(fact_2820_pos__divide__less__eq,axiom,
% 2.39/2.77 ! [C: rat,B: rat,A: rat] :
% 2.39/2.77 ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.77 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 2.39/2.77 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % pos_divide_less_eq
% 2.39/2.77 thf(fact_2821_neg__less__divide__eq,axiom,
% 2.39/2.77 ! [C: rat,A: rat,B: rat] :
% 2.39/2.77 ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.77 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 2.39/2.77 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % neg_less_divide_eq
% 2.39/2.77 thf(fact_2822_neg__divide__less__eq,axiom,
% 2.39/2.77 ! [C: rat,B: rat,A: rat] :
% 2.39/2.77 ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.77 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 2.39/2.77 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % neg_divide_less_eq
% 2.39/2.77 thf(fact_2823_less__divide__eq,axiom,
% 2.39/2.77 ! [A: rat,B: rat,C: rat] :
% 2.39/2.77 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 2.39/2.77 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.77 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 2.39/2.77 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.77 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.77 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 2.39/2.77 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.77 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % less_divide_eq
% 2.39/2.77 thf(fact_2824_divide__less__eq,axiom,
% 2.39/2.77 ! [B: rat,C: rat,A: rat] :
% 2.39/2.77 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 2.39/2.77 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.77 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 2.39/2.77 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.77 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.77 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 2.39/2.77 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.77 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % divide_less_eq
% 2.39/2.77 thf(fact_2825_power__0__left,axiom,
% 2.39/2.77 ! [N: nat] :
% 2.39/2.77 ( ( ( N = zero_zero_nat )
% 2.39/2.77 => ( ( power_power_rat @ zero_zero_rat @ N )
% 2.39/2.77 = one_one_rat ) )
% 2.39/2.77 & ( ( N != zero_zero_nat )
% 2.39/2.77 => ( ( power_power_rat @ zero_zero_rat @ N )
% 2.39/2.77 = zero_zero_rat ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_0_left
% 2.39/2.77 thf(fact_2826_power__0__left,axiom,
% 2.39/2.77 ! [N: nat] :
% 2.39/2.77 ( ( ( N = zero_zero_nat )
% 2.39/2.77 => ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ N )
% 2.39/2.77 = one_one_Code_integer ) )
% 2.39/2.77 & ( ( N != zero_zero_nat )
% 2.39/2.77 => ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ N )
% 2.39/2.77 = zero_z3403309356797280102nteger ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_0_left
% 2.39/2.77 thf(fact_2827_power__0__left,axiom,
% 2.39/2.77 ! [N: nat] :
% 2.39/2.77 ( ( ( N = zero_zero_nat )
% 2.39/2.77 => ( ( power_7079662738309270450atural @ zero_z2226904508553997617atural @ N )
% 2.39/2.77 = one_one_Code_natural ) )
% 2.39/2.77 & ( ( N != zero_zero_nat )
% 2.39/2.77 => ( ( power_7079662738309270450atural @ zero_z2226904508553997617atural @ N )
% 2.39/2.77 = zero_z2226904508553997617atural ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_0_left
% 2.39/2.77 thf(fact_2828_power__0__left,axiom,
% 2.39/2.77 ! [N: nat] :
% 2.39/2.77 ( ( ( N = zero_zero_nat )
% 2.39/2.77 => ( ( power_power_int @ zero_zero_int @ N )
% 2.39/2.77 = one_one_int ) )
% 2.39/2.77 & ( ( N != zero_zero_nat )
% 2.39/2.77 => ( ( power_power_int @ zero_zero_int @ N )
% 2.39/2.77 = zero_zero_int ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_0_left
% 2.39/2.77 thf(fact_2829_power__0__left,axiom,
% 2.39/2.77 ! [N: nat] :
% 2.39/2.77 ( ( ( N = zero_zero_nat )
% 2.39/2.77 => ( ( power_power_nat @ zero_zero_nat @ N )
% 2.39/2.77 = one_one_nat ) )
% 2.39/2.77 & ( ( N != zero_zero_nat )
% 2.39/2.77 => ( ( power_power_nat @ zero_zero_nat @ N )
% 2.39/2.77 = zero_zero_nat ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_0_left
% 2.39/2.77 thf(fact_2830_less__divide__eq__1,axiom,
% 2.39/2.77 ! [B: rat,A: rat] :
% 2.39/2.77 ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 2.39/2.77 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 2.39/2.77 & ( ord_less_rat @ A @ B ) )
% 2.39/2.77 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 2.39/2.77 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % less_divide_eq_1
% 2.39/2.77 thf(fact_2831_divide__less__eq__1,axiom,
% 2.39/2.77 ! [B: rat,A: rat] :
% 2.39/2.77 ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 2.39/2.77 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 2.39/2.77 & ( ord_less_rat @ B @ A ) )
% 2.39/2.77 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 2.39/2.77 & ( ord_less_rat @ A @ B ) )
% 2.39/2.77 | ( A = zero_zero_rat ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % divide_less_eq_1
% 2.39/2.77 thf(fact_2832_divide__add__eq__iff,axiom,
% 2.39/2.77 ! [Z: rat,X: rat,Y: rat] :
% 2.39/2.77 ( ( Z != zero_zero_rat )
% 2.39/2.77 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Z ) @ Y )
% 2.39/2.77 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % divide_add_eq_iff
% 2.39/2.77 thf(fact_2833_add__divide__eq__iff,axiom,
% 2.39/2.77 ! [Z: rat,X: rat,Y: rat] :
% 2.39/2.77 ( ( Z != zero_zero_rat )
% 2.39/2.77 => ( ( plus_plus_rat @ X @ ( divide_divide_rat @ Y @ Z ) )
% 2.39/2.77 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % add_divide_eq_iff
% 2.39/2.77 thf(fact_2834_add__num__frac,axiom,
% 2.39/2.77 ! [Y: rat,Z: rat,X: rat] :
% 2.39/2.77 ( ( Y != zero_zero_rat )
% 2.39/2.77 => ( ( plus_plus_rat @ Z @ ( divide_divide_rat @ X @ Y ) )
% 2.39/2.77 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z @ Y ) ) @ Y ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % add_num_frac
% 2.39/2.77 thf(fact_2835_add__frac__num,axiom,
% 2.39/2.77 ! [Y: rat,X: rat,Z: rat] :
% 2.39/2.77 ( ( Y != zero_zero_rat )
% 2.39/2.77 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y ) @ Z )
% 2.39/2.77 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z @ Y ) ) @ Y ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % add_frac_num
% 2.39/2.77 thf(fact_2836_add__frac__eq,axiom,
% 2.39/2.77 ! [Y: rat,Z: rat,X: rat,W: rat] :
% 2.39/2.77 ( ( Y != zero_zero_rat )
% 2.39/2.77 => ( ( Z != zero_zero_rat )
% 2.39/2.77 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 2.39/2.77 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % add_frac_eq
% 2.39/2.77 thf(fact_2837_add__divide__eq__if__simps_I1_J,axiom,
% 2.39/2.77 ! [Z: rat,A: rat,B: rat] :
% 2.39/2.77 ( ( ( Z = zero_zero_rat )
% 2.39/2.77 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 2.39/2.77 = A ) )
% 2.39/2.77 & ( ( Z != zero_zero_rat )
% 2.39/2.77 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 2.39/2.77 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % add_divide_eq_if_simps(1)
% 2.39/2.77 thf(fact_2838_add__divide__eq__if__simps_I2_J,axiom,
% 2.39/2.77 ! [Z: rat,A: rat,B: rat] :
% 2.39/2.77 ( ( ( Z = zero_zero_rat )
% 2.39/2.77 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 2.39/2.77 = B ) )
% 2.39/2.77 & ( ( Z != zero_zero_rat )
% 2.39/2.77 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 2.39/2.77 = ( divide_divide_rat @ ( plus_plus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % add_divide_eq_if_simps(2)
% 2.39/2.77 thf(fact_2839_power__strict__increasing,axiom,
% 2.39/2.77 ! [N: nat,N2: nat,A: code_integer] :
% 2.39/2.77 ( ( ord_less_nat @ N @ N2 )
% 2.39/2.77 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 2.39/2.77 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_strict_increasing
% 2.39/2.77 thf(fact_2840_power__strict__increasing,axiom,
% 2.39/2.77 ! [N: nat,N2: nat,A: rat] :
% 2.39/2.77 ( ( ord_less_nat @ N @ N2 )
% 2.39/2.77 => ( ( ord_less_rat @ one_one_rat @ A )
% 2.39/2.77 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_strict_increasing
% 2.39/2.77 thf(fact_2841_power__strict__increasing,axiom,
% 2.39/2.77 ! [N: nat,N2: nat,A: nat] :
% 2.39/2.77 ( ( ord_less_nat @ N @ N2 )
% 2.39/2.77 => ( ( ord_less_nat @ one_one_nat @ A )
% 2.39/2.77 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_strict_increasing
% 2.39/2.77 thf(fact_2842_power__strict__increasing,axiom,
% 2.39/2.77 ! [N: nat,N2: nat,A: int] :
% 2.39/2.77 ( ( ord_less_nat @ N @ N2 )
% 2.39/2.77 => ( ( ord_less_int @ one_one_int @ A )
% 2.39/2.77 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_strict_increasing
% 2.39/2.77 thf(fact_2843_power__less__imp__less__exp,axiom,
% 2.39/2.77 ! [A: code_integer,M2: nat,N: nat] :
% 2.39/2.77 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 2.39/2.77 => ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ M2 ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 2.39/2.77 => ( ord_less_nat @ M2 @ N ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_less_imp_less_exp
% 2.39/2.77 thf(fact_2844_power__less__imp__less__exp,axiom,
% 2.39/2.77 ! [A: rat,M2: nat,N: nat] :
% 2.39/2.77 ( ( ord_less_rat @ one_one_rat @ A )
% 2.39/2.77 => ( ( ord_less_rat @ ( power_power_rat @ A @ M2 ) @ ( power_power_rat @ A @ N ) )
% 2.39/2.77 => ( ord_less_nat @ M2 @ N ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_less_imp_less_exp
% 2.39/2.77 thf(fact_2845_power__less__imp__less__exp,axiom,
% 2.39/2.77 ! [A: nat,M2: nat,N: nat] :
% 2.39/2.77 ( ( ord_less_nat @ one_one_nat @ A )
% 2.39/2.77 => ( ( ord_less_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N ) )
% 2.39/2.77 => ( ord_less_nat @ M2 @ N ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_less_imp_less_exp
% 2.39/2.77 thf(fact_2846_power__less__imp__less__exp,axiom,
% 2.39/2.77 ! [A: int,M2: nat,N: nat] :
% 2.39/2.77 ( ( ord_less_int @ one_one_int @ A )
% 2.39/2.77 => ( ( ord_less_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N ) )
% 2.39/2.77 => ( ord_less_nat @ M2 @ N ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_less_imp_less_exp
% 2.39/2.77 thf(fact_2847_power__minus,axiom,
% 2.39/2.77 ! [A: int,N: nat] :
% 2.39/2.77 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 2.39/2.77 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ A @ N ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_minus
% 2.39/2.77 thf(fact_2848_power__minus,axiom,
% 2.39/2.77 ! [A: rat,N: nat] :
% 2.39/2.77 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 2.39/2.77 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ A @ N ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_minus
% 2.39/2.77 thf(fact_2849_power__minus,axiom,
% 2.39/2.77 ! [A: code_integer,N: nat] :
% 2.39/2.77 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 2.39/2.77 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_minus
% 2.39/2.77 thf(fact_2850_power__increasing,axiom,
% 2.39/2.77 ! [N: nat,N2: nat,A: code_integer] :
% 2.39/2.77 ( ( ord_less_eq_nat @ N @ N2 )
% 2.39/2.77 => ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A )
% 2.39/2.77 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_increasing
% 2.39/2.77 thf(fact_2851_power__increasing,axiom,
% 2.39/2.77 ! [N: nat,N2: nat,A: rat] :
% 2.39/2.77 ( ( ord_less_eq_nat @ N @ N2 )
% 2.39/2.77 => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 2.39/2.77 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_increasing
% 2.39/2.77 thf(fact_2852_power__increasing,axiom,
% 2.39/2.77 ! [N: nat,N2: nat,A: nat] :
% 2.39/2.77 ( ( ord_less_eq_nat @ N @ N2 )
% 2.39/2.77 => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 2.39/2.77 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_increasing
% 2.39/2.77 thf(fact_2853_power__increasing,axiom,
% 2.39/2.77 ! [N: nat,N2: nat,A: int] :
% 2.39/2.77 ( ( ord_less_eq_nat @ N @ N2 )
% 2.39/2.77 => ( ( ord_less_eq_int @ one_one_int @ A )
% 2.39/2.77 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_increasing
% 2.39/2.77 thf(fact_2854_less__half__sum,axiom,
% 2.39/2.77 ! [A: rat,B: rat] :
% 2.39/2.77 ( ( ord_less_rat @ A @ B )
% 2.39/2.77 => ( ord_less_rat @ A @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % less_half_sum
% 2.39/2.77 thf(fact_2855_gt__half__sum,axiom,
% 2.39/2.77 ! [A: rat,B: rat] :
% 2.39/2.77 ( ( ord_less_rat @ A @ B )
% 2.39/2.77 => ( ord_less_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) @ B ) ) ).
% 2.39/2.77
% 2.39/2.77 % gt_half_sum
% 2.39/2.77 thf(fact_2856_nonzero__neg__divide__eq__eq2,axiom,
% 2.39/2.77 ! [B: rat,C: rat,A: rat] :
% 2.39/2.77 ( ( B != zero_zero_rat )
% 2.39/2.77 => ( ( C
% 2.39/2.77 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) )
% 2.39/2.77 = ( ( times_times_rat @ C @ B )
% 2.39/2.77 = ( uminus_uminus_rat @ A ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % nonzero_neg_divide_eq_eq2
% 2.39/2.77 thf(fact_2857_nonzero__neg__divide__eq__eq,axiom,
% 2.39/2.77 ! [B: rat,A: rat,C: rat] :
% 2.39/2.77 ( ( B != zero_zero_rat )
% 2.39/2.77 => ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 2.39/2.77 = C )
% 2.39/2.77 = ( ( uminus_uminus_rat @ A )
% 2.39/2.77 = ( times_times_rat @ C @ B ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % nonzero_neg_divide_eq_eq
% 2.39/2.77 thf(fact_2858_minus__divide__eq__eq,axiom,
% 2.39/2.77 ! [B: rat,C: rat,A: rat] :
% 2.39/2.77 ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) )
% 2.39/2.77 = A )
% 2.39/2.77 = ( ( ( C != zero_zero_rat )
% 2.39/2.77 => ( ( uminus_uminus_rat @ B )
% 2.39/2.77 = ( times_times_rat @ A @ C ) ) )
% 2.39/2.77 & ( ( C = zero_zero_rat )
% 2.39/2.77 => ( A = zero_zero_rat ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % minus_divide_eq_eq
% 2.39/2.77 thf(fact_2859_eq__minus__divide__eq,axiom,
% 2.39/2.77 ! [A: rat,B: rat,C: rat] :
% 2.39/2.77 ( ( A
% 2.39/2.77 = ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 2.39/2.77 = ( ( ( C != zero_zero_rat )
% 2.39/2.77 => ( ( times_times_rat @ A @ C )
% 2.39/2.77 = ( uminus_uminus_rat @ B ) ) )
% 2.39/2.77 & ( ( C = zero_zero_rat )
% 2.39/2.77 => ( A = zero_zero_rat ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % eq_minus_divide_eq
% 2.39/2.77 thf(fact_2860_divide__eq__minus__1__iff,axiom,
% 2.39/2.77 ! [A: rat,B: rat] :
% 2.39/2.77 ( ( ( divide_divide_rat @ A @ B )
% 2.39/2.77 = ( uminus_uminus_rat @ one_one_rat ) )
% 2.39/2.77 = ( ( B != zero_zero_rat )
% 2.39/2.77 & ( A
% 2.39/2.77 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % divide_eq_minus_1_iff
% 2.39/2.77 thf(fact_2861_power__Suc__less,axiom,
% 2.39/2.77 ! [A: code_natural,N: nat] :
% 2.39/2.77 ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A )
% 2.39/2.77 => ( ( ord_le5570908160329646204atural @ A @ one_one_Code_natural )
% 2.39/2.77 => ( ord_le5570908160329646204atural @ ( times_2397367101498566445atural @ A @ ( power_7079662738309270450atural @ A @ N ) ) @ ( power_7079662738309270450atural @ A @ N ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_Suc_less
% 2.39/2.77 thf(fact_2862_power__Suc__less,axiom,
% 2.39/2.77 ! [A: code_integer,N: nat] :
% 2.39/2.77 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.77 => ( ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer )
% 2.39/2.77 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_Suc_less
% 2.39/2.77 thf(fact_2863_power__Suc__less,axiom,
% 2.39/2.77 ! [A: rat,N: nat] :
% 2.39/2.77 ( ( ord_less_rat @ zero_zero_rat @ A )
% 2.39/2.77 => ( ( ord_less_rat @ A @ one_one_rat )
% 2.39/2.77 => ( ord_less_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) @ ( power_power_rat @ A @ N ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_Suc_less
% 2.39/2.77 thf(fact_2864_power__Suc__less,axiom,
% 2.39/2.77 ! [A: nat,N: nat] :
% 2.39/2.77 ( ( ord_less_nat @ zero_zero_nat @ A )
% 2.39/2.77 => ( ( ord_less_nat @ A @ one_one_nat )
% 2.39/2.77 => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) @ ( power_power_nat @ A @ N ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_Suc_less
% 2.39/2.77 thf(fact_2865_power__Suc__less,axiom,
% 2.39/2.77 ! [A: int,N: nat] :
% 2.39/2.77 ( ( ord_less_int @ zero_zero_int @ A )
% 2.39/2.77 => ( ( ord_less_int @ A @ one_one_int )
% 2.39/2.77 => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) @ ( power_power_int @ A @ N ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_Suc_less
% 2.39/2.77 thf(fact_2866_divide__left__mono__neg,axiom,
% 2.39/2.77 ! [A: rat,B: rat,C: rat] :
% 2.39/2.77 ( ( ord_less_eq_rat @ A @ B )
% 2.39/2.77 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 2.39/2.77 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 2.39/2.77 => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % divide_left_mono_neg
% 2.39/2.77 thf(fact_2867_mult__imp__le__div__pos,axiom,
% 2.39/2.77 ! [Y: rat,Z: rat,X: rat] :
% 2.39/2.77 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 2.39/2.77 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ Y ) @ X )
% 2.39/2.77 => ( ord_less_eq_rat @ Z @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % mult_imp_le_div_pos
% 2.39/2.77 thf(fact_2868_mult__imp__div__pos__le,axiom,
% 2.39/2.77 ! [Y: rat,X: rat,Z: rat] :
% 2.39/2.77 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 2.39/2.77 => ( ( ord_less_eq_rat @ X @ ( times_times_rat @ Z @ Y ) )
% 2.39/2.77 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ Z ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % mult_imp_div_pos_le
% 2.39/2.77 thf(fact_2869_pos__le__divide__eq,axiom,
% 2.39/2.77 ! [C: rat,A: rat,B: rat] :
% 2.39/2.77 ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.77 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 2.39/2.77 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % pos_le_divide_eq
% 2.39/2.77 thf(fact_2870_pos__divide__le__eq,axiom,
% 2.39/2.77 ! [C: rat,B: rat,A: rat] :
% 2.39/2.77 ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.77 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 2.39/2.77 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % pos_divide_le_eq
% 2.39/2.77 thf(fact_2871_neg__le__divide__eq,axiom,
% 2.39/2.77 ! [C: rat,A: rat,B: rat] :
% 2.39/2.77 ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.77 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 2.39/2.77 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % neg_le_divide_eq
% 2.39/2.77 thf(fact_2872_neg__divide__le__eq,axiom,
% 2.39/2.77 ! [C: rat,B: rat,A: rat] :
% 2.39/2.77 ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.77 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 2.39/2.77 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % neg_divide_le_eq
% 2.39/2.77 thf(fact_2873_divide__left__mono,axiom,
% 2.39/2.77 ! [B: rat,A: rat,C: rat] :
% 2.39/2.77 ( ( ord_less_eq_rat @ B @ A )
% 2.39/2.77 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 2.39/2.77 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 2.39/2.77 => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % divide_left_mono
% 2.39/2.77 thf(fact_2874_le__divide__eq,axiom,
% 2.39/2.77 ! [A: rat,B: rat,C: rat] :
% 2.39/2.77 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 2.39/2.77 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.77 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 2.39/2.77 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.77 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.77 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 2.39/2.77 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.77 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % le_divide_eq
% 2.39/2.77 thf(fact_2875_divide__le__eq,axiom,
% 2.39/2.77 ! [B: rat,C: rat,A: rat] :
% 2.39/2.77 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 2.39/2.77 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.77 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 2.39/2.77 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.77 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.77 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 2.39/2.77 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.77 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % divide_le_eq
% 2.39/2.77 thf(fact_2876_le__divide__eq__1,axiom,
% 2.39/2.77 ! [B: rat,A: rat] :
% 2.39/2.77 ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 2.39/2.77 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 2.39/2.77 & ( ord_less_eq_rat @ A @ B ) )
% 2.39/2.77 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 2.39/2.77 & ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % le_divide_eq_1
% 2.39/2.77 thf(fact_2877_divide__le__eq__1,axiom,
% 2.39/2.77 ! [B: rat,A: rat] :
% 2.39/2.77 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 2.39/2.77 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 2.39/2.77 & ( ord_less_eq_rat @ B @ A ) )
% 2.39/2.77 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 2.39/2.77 & ( ord_less_eq_rat @ A @ B ) )
% 2.39/2.77 | ( A = zero_zero_rat ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % divide_le_eq_1
% 2.39/2.77 thf(fact_2878_power__strict__decreasing,axiom,
% 2.39/2.77 ! [N: nat,N2: nat,A: code_natural] :
% 2.39/2.77 ( ( ord_less_nat @ N @ N2 )
% 2.39/2.77 => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A )
% 2.39/2.77 => ( ( ord_le5570908160329646204atural @ A @ one_one_Code_natural )
% 2.39/2.77 => ( ord_le5570908160329646204atural @ ( power_7079662738309270450atural @ A @ N2 ) @ ( power_7079662738309270450atural @ A @ N ) ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_strict_decreasing
% 2.39/2.77 thf(fact_2879_power__strict__decreasing,axiom,
% 2.39/2.77 ! [N: nat,N2: nat,A: code_integer] :
% 2.39/2.77 ( ( ord_less_nat @ N @ N2 )
% 2.39/2.77 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.77 => ( ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer )
% 2.39/2.77 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_strict_decreasing
% 2.39/2.77 thf(fact_2880_power__strict__decreasing,axiom,
% 2.39/2.77 ! [N: nat,N2: nat,A: rat] :
% 2.39/2.77 ( ( ord_less_nat @ N @ N2 )
% 2.39/2.77 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 2.39/2.77 => ( ( ord_less_rat @ A @ one_one_rat )
% 2.39/2.77 => ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_strict_decreasing
% 2.39/2.77 thf(fact_2881_power__strict__decreasing,axiom,
% 2.39/2.77 ! [N: nat,N2: nat,A: nat] :
% 2.39/2.77 ( ( ord_less_nat @ N @ N2 )
% 2.39/2.77 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 2.39/2.77 => ( ( ord_less_nat @ A @ one_one_nat )
% 2.39/2.77 => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_strict_decreasing
% 2.39/2.77 thf(fact_2882_power__strict__decreasing,axiom,
% 2.39/2.77 ! [N: nat,N2: nat,A: int] :
% 2.39/2.77 ( ( ord_less_nat @ N @ N2 )
% 2.39/2.77 => ( ( ord_less_int @ zero_zero_int @ A )
% 2.39/2.77 => ( ( ord_less_int @ A @ one_one_int )
% 2.39/2.77 => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_strict_decreasing
% 2.39/2.77 thf(fact_2883_power__decreasing,axiom,
% 2.39/2.77 ! [N: nat,N2: nat,A: code_integer] :
% 2.39/2.77 ( ( ord_less_eq_nat @ N @ N2 )
% 2.39/2.77 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.77 => ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 2.39/2.77 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_decreasing
% 2.39/2.77 thf(fact_2884_power__decreasing,axiom,
% 2.39/2.77 ! [N: nat,N2: nat,A: code_natural] :
% 2.39/2.77 ( ( ord_less_eq_nat @ N @ N2 )
% 2.39/2.77 => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 2.39/2.77 => ( ( ord_le1926595141338095240atural @ A @ one_one_Code_natural )
% 2.39/2.77 => ( ord_le1926595141338095240atural @ ( power_7079662738309270450atural @ A @ N2 ) @ ( power_7079662738309270450atural @ A @ N ) ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_decreasing
% 2.39/2.77 thf(fact_2885_power__decreasing,axiom,
% 2.39/2.77 ! [N: nat,N2: nat,A: rat] :
% 2.39/2.77 ( ( ord_less_eq_nat @ N @ N2 )
% 2.39/2.77 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 2.39/2.77 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 2.39/2.77 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_decreasing
% 2.39/2.77 thf(fact_2886_power__decreasing,axiom,
% 2.39/2.77 ! [N: nat,N2: nat,A: nat] :
% 2.39/2.77 ( ( ord_less_eq_nat @ N @ N2 )
% 2.39/2.77 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 2.39/2.77 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 2.39/2.77 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_decreasing
% 2.39/2.77 thf(fact_2887_power__decreasing,axiom,
% 2.39/2.77 ! [N: nat,N2: nat,A: int] :
% 2.39/2.77 ( ( ord_less_eq_nat @ N @ N2 )
% 2.39/2.77 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 2.39/2.77 => ( ( ord_less_eq_int @ A @ one_one_int )
% 2.39/2.77 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_decreasing
% 2.39/2.77 thf(fact_2888_power__le__imp__le__exp,axiom,
% 2.39/2.77 ! [A: code_integer,M2: nat,N: nat] :
% 2.39/2.77 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 2.39/2.77 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ M2 ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 2.39/2.77 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_le_imp_le_exp
% 2.39/2.77 thf(fact_2889_power__le__imp__le__exp,axiom,
% 2.39/2.77 ! [A: rat,M2: nat,N: nat] :
% 2.39/2.77 ( ( ord_less_rat @ one_one_rat @ A )
% 2.39/2.77 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M2 ) @ ( power_power_rat @ A @ N ) )
% 2.39/2.77 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_le_imp_le_exp
% 2.39/2.77 thf(fact_2890_power__le__imp__le__exp,axiom,
% 2.39/2.77 ! [A: nat,M2: nat,N: nat] :
% 2.39/2.77 ( ( ord_less_nat @ one_one_nat @ A )
% 2.39/2.77 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N ) )
% 2.39/2.77 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_le_imp_le_exp
% 2.39/2.77 thf(fact_2891_power__le__imp__le__exp,axiom,
% 2.39/2.77 ! [A: int,M2: nat,N: nat] :
% 2.39/2.77 ( ( ord_less_int @ one_one_int @ A )
% 2.39/2.77 => ( ( ord_less_eq_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N ) )
% 2.39/2.77 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % power_le_imp_le_exp
% 2.39/2.77 thf(fact_2892_self__le__power,axiom,
% 2.39/2.77 ! [A: code_integer,N: nat] :
% 2.39/2.77 ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A )
% 2.39/2.77 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.39/2.77 => ( ord_le3102999989581377725nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % self_le_power
% 2.39/2.77 thf(fact_2893_self__le__power,axiom,
% 2.39/2.77 ! [A: rat,N: nat] :
% 2.39/2.77 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 2.39/2.77 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.39/2.77 => ( ord_less_eq_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % self_le_power
% 2.39/2.77 thf(fact_2894_self__le__power,axiom,
% 2.39/2.77 ! [A: nat,N: nat] :
% 2.39/2.77 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 2.39/2.77 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.39/2.77 => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % self_le_power
% 2.39/2.77 thf(fact_2895_self__le__power,axiom,
% 2.39/2.77 ! [A: int,N: nat] :
% 2.39/2.77 ( ( ord_less_eq_int @ one_one_int @ A )
% 2.39/2.77 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.39/2.77 => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % self_le_power
% 2.39/2.77 thf(fact_2896_pos__minus__divide__less__eq,axiom,
% 2.39/2.77 ! [C: rat,B: rat,A: rat] :
% 2.39/2.77 ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.77 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 2.39/2.77 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % pos_minus_divide_less_eq
% 2.39/2.77 thf(fact_2897_pos__less__minus__divide__eq,axiom,
% 2.39/2.77 ! [C: rat,A: rat,B: rat] :
% 2.39/2.77 ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.77 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 2.39/2.77 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % pos_less_minus_divide_eq
% 2.39/2.77 thf(fact_2898_neg__minus__divide__less__eq,axiom,
% 2.39/2.77 ! [C: rat,B: rat,A: rat] :
% 2.39/2.77 ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.77 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 2.39/2.77 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % neg_minus_divide_less_eq
% 2.39/2.77 thf(fact_2899_neg__less__minus__divide__eq,axiom,
% 2.39/2.77 ! [C: rat,A: rat,B: rat] :
% 2.39/2.77 ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.77 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 2.39/2.77 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % neg_less_minus_divide_eq
% 2.39/2.77 thf(fact_2900_minus__divide__less__eq,axiom,
% 2.39/2.77 ! [B: rat,C: rat,A: rat] :
% 2.39/2.77 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 2.39/2.77 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.77 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 2.39/2.77 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.77 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.77 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 2.39/2.77 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.77 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % minus_divide_less_eq
% 2.39/2.77 thf(fact_2901_less__minus__divide__eq,axiom,
% 2.39/2.77 ! [A: rat,B: rat,C: rat] :
% 2.39/2.77 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 2.39/2.77 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.77 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 2.39/2.77 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.77 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.77 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 2.39/2.77 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.77 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % less_minus_divide_eq
% 2.39/2.77 thf(fact_2902_one__less__power,axiom,
% 2.39/2.77 ! [A: code_integer,N: nat] :
% 2.39/2.77 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 2.39/2.77 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.39/2.77 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % one_less_power
% 2.39/2.77 thf(fact_2903_one__less__power,axiom,
% 2.39/2.77 ! [A: rat,N: nat] :
% 2.39/2.77 ( ( ord_less_rat @ one_one_rat @ A )
% 2.39/2.77 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.39/2.77 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % one_less_power
% 2.39/2.77 thf(fact_2904_one__less__power,axiom,
% 2.39/2.77 ! [A: nat,N: nat] :
% 2.39/2.77 ( ( ord_less_nat @ one_one_nat @ A )
% 2.39/2.77 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.39/2.77 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % one_less_power
% 2.39/2.77 thf(fact_2905_one__less__power,axiom,
% 2.39/2.77 ! [A: int,N: nat] :
% 2.39/2.77 ( ( ord_less_int @ one_one_int @ A )
% 2.39/2.77 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.39/2.77 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % one_less_power
% 2.39/2.77 thf(fact_2906_minus__divide__add__eq__iff,axiom,
% 2.39/2.77 ! [Z: rat,X: rat,Y: rat] :
% 2.39/2.77 ( ( Z != zero_zero_rat )
% 2.39/2.77 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z ) ) @ Y )
% 2.39/2.77 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % minus_divide_add_eq_iff
% 2.39/2.77 thf(fact_2907_add__divide__eq__if__simps_I3_J,axiom,
% 2.39/2.77 ! [Z: rat,A: rat,B: rat] :
% 2.39/2.77 ( ( ( Z = zero_zero_rat )
% 2.39/2.77 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 2.39/2.77 = B ) )
% 2.39/2.77 & ( ( Z != zero_zero_rat )
% 2.39/2.77 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 2.39/2.77 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % add_divide_eq_if_simps(3)
% 2.39/2.77 thf(fact_2908_pos__minus__divide__le__eq,axiom,
% 2.39/2.77 ! [C: rat,B: rat,A: rat] :
% 2.39/2.77 ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.77 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 2.39/2.77 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % pos_minus_divide_le_eq
% 2.39/2.77 thf(fact_2909_pos__le__minus__divide__eq,axiom,
% 2.39/2.77 ! [C: rat,A: rat,B: rat] :
% 2.39/2.77 ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.77 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 2.39/2.77 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % pos_le_minus_divide_eq
% 2.39/2.77 thf(fact_2910_neg__minus__divide__le__eq,axiom,
% 2.39/2.77 ! [C: rat,B: rat,A: rat] :
% 2.39/2.77 ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.77 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 2.39/2.77 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % neg_minus_divide_le_eq
% 2.39/2.77 thf(fact_2911_div__mult__self4,axiom,
% 2.39/2.77 ! [B: code_integer,C: code_integer,A: code_integer] :
% 2.39/2.77 ( ( B != zero_z3403309356797280102nteger )
% 2.39/2.77 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ C ) @ A ) @ B )
% 2.39/2.77 = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % div_mult_self4
% 2.39/2.77 thf(fact_2912_div__mult__self4,axiom,
% 2.39/2.77 ! [B: nat,C: nat,A: nat] :
% 2.39/2.77 ( ( B != zero_zero_nat )
% 2.39/2.77 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 2.39/2.77 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % div_mult_self4
% 2.39/2.77 thf(fact_2913_div__mult__self4,axiom,
% 2.39/2.77 ! [B: int,C: int,A: int] :
% 2.39/2.77 ( ( B != zero_zero_int )
% 2.39/2.77 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 2.39/2.77 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % div_mult_self4
% 2.39/2.77 thf(fact_2914_div__mult__self4,axiom,
% 2.39/2.77 ! [B: code_natural,C: code_natural,A: code_natural] :
% 2.39/2.77 ( ( B != zero_z2226904508553997617atural )
% 2.39/2.77 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ C ) @ A ) @ B )
% 2.39/2.77 = ( plus_p4538020629002901425atural @ C @ ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % div_mult_self4
% 2.39/2.77 thf(fact_2915_div__mult__self3,axiom,
% 2.39/2.77 ! [B: code_integer,C: code_integer,A: code_integer] :
% 2.39/2.77 ( ( B != zero_z3403309356797280102nteger )
% 2.39/2.77 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ B ) @ A ) @ B )
% 2.39/2.77 = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % div_mult_self3
% 2.39/2.77 thf(fact_2916_div__mult__self3,axiom,
% 2.39/2.77 ! [B: nat,C: nat,A: nat] :
% 2.39/2.77 ( ( B != zero_zero_nat )
% 2.39/2.77 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 2.39/2.77 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % div_mult_self3
% 2.39/2.77 thf(fact_2917_div__mult__self3,axiom,
% 2.39/2.77 ! [B: int,C: int,A: int] :
% 2.39/2.77 ( ( B != zero_zero_int )
% 2.39/2.77 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 2.39/2.77 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % div_mult_self3
% 2.39/2.77 thf(fact_2918_div__mult__self3,axiom,
% 2.39/2.77 ! [B: code_natural,C: code_natural,A: code_natural] :
% 2.39/2.77 ( ( B != zero_z2226904508553997617atural )
% 2.39/2.77 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ C @ B ) @ A ) @ B )
% 2.39/2.77 = ( plus_p4538020629002901425atural @ C @ ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % div_mult_self3
% 2.39/2.77 thf(fact_2919_div__mult__self2,axiom,
% 2.39/2.77 ! [B: code_integer,A: code_integer,C: code_integer] :
% 2.39/2.77 ( ( B != zero_z3403309356797280102nteger )
% 2.39/2.77 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) @ B )
% 2.39/2.77 = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % div_mult_self2
% 2.39/2.77 thf(fact_2920_div__mult__self2,axiom,
% 2.39/2.77 ! [B: nat,A: nat,C: nat] :
% 2.39/2.77 ( ( B != zero_zero_nat )
% 2.39/2.77 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 2.39/2.77 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % div_mult_self2
% 2.39/2.77 thf(fact_2921_div__mult__self2,axiom,
% 2.39/2.77 ! [B: int,A: int,C: int] :
% 2.39/2.77 ( ( B != zero_zero_int )
% 2.39/2.77 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 2.39/2.77 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % div_mult_self2
% 2.39/2.77 thf(fact_2922_div__mult__self2,axiom,
% 2.39/2.77 ! [B: code_natural,A: code_natural,C: code_natural] :
% 2.39/2.77 ( ( B != zero_z2226904508553997617atural )
% 2.39/2.77 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ B @ C ) ) @ B )
% 2.39/2.77 = ( plus_p4538020629002901425atural @ C @ ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % div_mult_self2
% 2.39/2.77 thf(fact_2923_div__mult__self1,axiom,
% 2.39/2.77 ! [B: code_integer,A: code_integer,C: code_integer] :
% 2.39/2.77 ( ( B != zero_z3403309356797280102nteger )
% 2.39/2.77 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ B ) ) @ B )
% 2.39/2.77 = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % div_mult_self1
% 2.39/2.77 thf(fact_2924_div__mult__self1,axiom,
% 2.39/2.77 ! [B: nat,A: nat,C: nat] :
% 2.39/2.77 ( ( B != zero_zero_nat )
% 2.39/2.77 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 2.39/2.77 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % div_mult_self1
% 2.39/2.77 thf(fact_2925_div__mult__self1,axiom,
% 2.39/2.77 ! [B: int,A: int,C: int] :
% 2.39/2.77 ( ( B != zero_zero_int )
% 2.39/2.77 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 2.39/2.77 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % div_mult_self1
% 2.39/2.77 thf(fact_2926_div__mult__self1,axiom,
% 2.39/2.77 ! [B: code_natural,A: code_natural,C: code_natural] :
% 2.39/2.77 ( ( B != zero_z2226904508553997617atural )
% 2.39/2.77 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ C @ B ) ) @ B )
% 2.39/2.77 = ( plus_p4538020629002901425atural @ C @ ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % div_mult_self1
% 2.39/2.77 thf(fact_2927_div__minus1__right,axiom,
% 2.39/2.77 ! [A: int] :
% 2.39/2.77 ( ( divide_divide_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 2.39/2.77 = ( uminus_uminus_int @ A ) ) ).
% 2.39/2.77
% 2.39/2.77 % div_minus1_right
% 2.39/2.77 thf(fact_2928_div__minus1__right,axiom,
% 2.39/2.77 ! [A: code_integer] :
% 2.39/2.77 ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 2.39/2.77 = ( uminus1351360451143612070nteger @ A ) ) ).
% 2.39/2.77
% 2.39/2.77 % div_minus1_right
% 2.39/2.77 thf(fact_2929_div__mult__mult1__if,axiom,
% 2.39/2.77 ! [C: code_integer,A: code_integer,B: code_integer] :
% 2.39/2.77 ( ( ( C = zero_z3403309356797280102nteger )
% 2.39/2.77 => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 2.39/2.77 = zero_z3403309356797280102nteger ) )
% 2.39/2.77 & ( ( C != zero_z3403309356797280102nteger )
% 2.39/2.77 => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 2.39/2.77 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % div_mult_mult1_if
% 2.39/2.77 thf(fact_2930_div__mult__mult1__if,axiom,
% 2.39/2.77 ! [C: nat,A: nat,B: nat] :
% 2.39/2.77 ( ( ( C = zero_zero_nat )
% 2.39/2.77 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 2.39/2.77 = zero_zero_nat ) )
% 2.39/2.77 & ( ( C != zero_zero_nat )
% 2.39/2.77 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 2.39/2.77 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % div_mult_mult1_if
% 2.39/2.77 thf(fact_2931_div__mult__mult1__if,axiom,
% 2.39/2.77 ! [C: int,A: int,B: int] :
% 2.39/2.77 ( ( ( C = zero_zero_int )
% 2.39/2.77 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 2.39/2.77 = zero_zero_int ) )
% 2.39/2.77 & ( ( C != zero_zero_int )
% 2.39/2.77 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 2.39/2.77 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % div_mult_mult1_if
% 2.39/2.77 thf(fact_2932_div__mult__mult1__if,axiom,
% 2.39/2.77 ! [C: code_natural,A: code_natural,B: code_natural] :
% 2.39/2.77 ( ( ( C = zero_z2226904508553997617atural )
% 2.39/2.77 => ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ C @ A ) @ ( times_2397367101498566445atural @ C @ B ) )
% 2.39/2.77 = zero_z2226904508553997617atural ) )
% 2.39/2.77 & ( ( C != zero_z2226904508553997617atural )
% 2.39/2.77 => ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ C @ A ) @ ( times_2397367101498566445atural @ C @ B ) )
% 2.39/2.77 = ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % div_mult_mult1_if
% 2.39/2.77 thf(fact_2933_div__mult__mult2,axiom,
% 2.39/2.77 ! [C: code_integer,A: code_integer,B: code_integer] :
% 2.39/2.77 ( ( C != zero_z3403309356797280102nteger )
% 2.39/2.77 => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 2.39/2.77 = ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % div_mult_mult2
% 2.39/2.77 thf(fact_2934_div__mult__mult2,axiom,
% 2.39/2.77 ! [C: nat,A: nat,B: nat] :
% 2.39/2.77 ( ( C != zero_zero_nat )
% 2.39/2.77 => ( ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 2.39/2.77 = ( divide_divide_nat @ A @ B ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % div_mult_mult2
% 2.39/2.77 thf(fact_2935_div__mult__mult2,axiom,
% 2.39/2.77 ! [C: int,A: int,B: int] :
% 2.39/2.77 ( ( C != zero_zero_int )
% 2.39/2.77 => ( ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 2.39/2.77 = ( divide_divide_int @ A @ B ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % div_mult_mult2
% 2.39/2.77 thf(fact_2936_div__mult__mult2,axiom,
% 2.39/2.77 ! [C: code_natural,A: code_natural,B: code_natural] :
% 2.39/2.77 ( ( C != zero_z2226904508553997617atural )
% 2.39/2.77 => ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ C ) )
% 2.39/2.77 = ( divide5121882707175180666atural @ A @ B ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % div_mult_mult2
% 2.39/2.77 thf(fact_2937_div__mult__mult1,axiom,
% 2.39/2.77 ! [C: code_integer,A: code_integer,B: code_integer] :
% 2.39/2.77 ( ( C != zero_z3403309356797280102nteger )
% 2.39/2.77 => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 2.39/2.77 = ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % div_mult_mult1
% 2.39/2.77 thf(fact_2938_div__mult__mult1,axiom,
% 2.39/2.77 ! [C: nat,A: nat,B: nat] :
% 2.39/2.77 ( ( C != zero_zero_nat )
% 2.39/2.77 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 2.39/2.77 = ( divide_divide_nat @ A @ B ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % div_mult_mult1
% 2.39/2.77 thf(fact_2939_div__mult__mult1,axiom,
% 2.39/2.77 ! [C: int,A: int,B: int] :
% 2.39/2.77 ( ( C != zero_zero_int )
% 2.39/2.77 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 2.39/2.77 = ( divide_divide_int @ A @ B ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % div_mult_mult1
% 2.39/2.77 thf(fact_2940_div__mult__mult1,axiom,
% 2.39/2.77 ! [C: code_natural,A: code_natural,B: code_natural] :
% 2.39/2.77 ( ( C != zero_z2226904508553997617atural )
% 2.39/2.77 => ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ C @ A ) @ ( times_2397367101498566445atural @ C @ B ) )
% 2.39/2.77 = ( divide5121882707175180666atural @ A @ B ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % div_mult_mult1
% 2.39/2.77 thf(fact_2941_bits__div__by__1,axiom,
% 2.39/2.77 ! [A: code_integer] :
% 2.39/2.77 ( ( divide6298287555418463151nteger @ A @ one_one_Code_integer )
% 2.39/2.77 = A ) ).
% 2.39/2.77
% 2.39/2.77 % bits_div_by_1
% 2.39/2.77 thf(fact_2942_bits__div__by__1,axiom,
% 2.39/2.77 ! [A: nat] :
% 2.39/2.77 ( ( divide_divide_nat @ A @ one_one_nat )
% 2.39/2.77 = A ) ).
% 2.39/2.77
% 2.39/2.77 % bits_div_by_1
% 2.39/2.77 thf(fact_2943_bits__div__by__1,axiom,
% 2.39/2.77 ! [A: int] :
% 2.39/2.77 ( ( divide_divide_int @ A @ one_one_int )
% 2.39/2.77 = A ) ).
% 2.39/2.77
% 2.39/2.77 % bits_div_by_1
% 2.39/2.77 thf(fact_2944_bits__div__by__1,axiom,
% 2.39/2.77 ! [A: code_natural] :
% 2.39/2.77 ( ( divide5121882707175180666atural @ A @ one_one_Code_natural )
% 2.39/2.77 = A ) ).
% 2.39/2.77
% 2.39/2.77 % bits_div_by_1
% 2.39/2.77 thf(fact_2945_div__less__dividend,axiom,
% 2.39/2.77 ! [N: nat,M2: nat] :
% 2.39/2.77 ( ( ord_less_nat @ one_one_nat @ N )
% 2.39/2.77 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 2.39/2.77 => ( ord_less_nat @ ( divide_divide_nat @ M2 @ N ) @ M2 ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % div_less_dividend
% 2.39/2.77 thf(fact_2946_div__eq__dividend__iff,axiom,
% 2.39/2.77 ! [M2: nat,N: nat] :
% 2.39/2.77 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 2.39/2.77 => ( ( ( divide_divide_nat @ M2 @ N )
% 2.39/2.77 = M2 )
% 2.39/2.77 = ( N = one_one_nat ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % div_eq_dividend_iff
% 2.39/2.77 thf(fact_2947_div__add__self1,axiom,
% 2.39/2.77 ! [B: code_integer,A: code_integer] :
% 2.39/2.77 ( ( B != zero_z3403309356797280102nteger )
% 2.39/2.77 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 2.39/2.77 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % div_add_self1
% 2.39/2.77 thf(fact_2948_div__add__self1,axiom,
% 2.39/2.77 ! [B: nat,A: nat] :
% 2.39/2.77 ( ( B != zero_zero_nat )
% 2.39/2.77 => ( ( divide_divide_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 2.39/2.77 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % div_add_self1
% 2.39/2.77 thf(fact_2949_div__add__self1,axiom,
% 2.39/2.77 ! [B: int,A: int] :
% 2.39/2.77 ( ( B != zero_zero_int )
% 2.39/2.77 => ( ( divide_divide_int @ ( plus_plus_int @ B @ A ) @ B )
% 2.39/2.77 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % div_add_self1
% 2.39/2.77 thf(fact_2950_div__add__self1,axiom,
% 2.39/2.77 ! [B: code_natural,A: code_natural] :
% 2.39/2.77 ( ( B != zero_z2226904508553997617atural )
% 2.39/2.77 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ B @ A ) @ B )
% 2.39/2.77 = ( plus_p4538020629002901425atural @ ( divide5121882707175180666atural @ A @ B ) @ one_one_Code_natural ) ) ) ).
% 2.39/2.77
% 2.39/2.77 % div_add_self1
% 2.39/2.77 thf(fact_2951_div__add__self2,axiom,
% 2.39/2.78 ! [B: code_integer,A: code_integer] :
% 2.39/2.78 ( ( B != zero_z3403309356797280102nteger )
% 2.39/2.78 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 2.39/2.78 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % div_add_self2
% 2.39/2.78 thf(fact_2952_div__add__self2,axiom,
% 2.39/2.78 ! [B: nat,A: nat] :
% 2.39/2.78 ( ( B != zero_zero_nat )
% 2.39/2.78 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 2.39/2.78 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % div_add_self2
% 2.39/2.78 thf(fact_2953_div__add__self2,axiom,
% 2.39/2.78 ! [B: int,A: int] :
% 2.39/2.78 ( ( B != zero_zero_int )
% 2.39/2.78 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ B )
% 2.39/2.78 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % div_add_self2
% 2.39/2.78 thf(fact_2954_div__add__self2,axiom,
% 2.39/2.78 ! [B: code_natural,A: code_natural] :
% 2.39/2.78 ( ( B != zero_z2226904508553997617atural )
% 2.39/2.78 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ B ) @ B )
% 2.39/2.78 = ( plus_p4538020629002901425atural @ ( divide5121882707175180666atural @ A @ B ) @ one_one_Code_natural ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % div_add_self2
% 2.39/2.78 thf(fact_2955_power__minus_H,axiom,
% 2.39/2.78 ! [X: int,N: nat] :
% 2.39/2.78 ( ( nO_MATCH_int_int @ one_one_int @ X )
% 2.39/2.78 => ( ( power_power_int @ ( uminus_uminus_int @ X ) @ N )
% 2.39/2.78 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ X @ N ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % power_minus'
% 2.39/2.78 thf(fact_2956_power__minus_H,axiom,
% 2.39/2.78 ! [X: rat,N: nat] :
% 2.39/2.78 ( ( nO_MATCH_rat_rat @ one_one_rat @ X )
% 2.39/2.78 => ( ( power_power_rat @ ( uminus_uminus_rat @ X ) @ N )
% 2.39/2.78 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ X @ N ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % power_minus'
% 2.39/2.78 thf(fact_2957_power__minus_H,axiom,
% 2.39/2.78 ! [X: code_integer,N: nat] :
% 2.39/2.78 ( ( nO_MAT8252062027627875367nteger @ one_one_Code_integer @ X )
% 2.39/2.78 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X ) @ N )
% 2.39/2.78 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ X @ N ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % power_minus'
% 2.39/2.78 thf(fact_2958_divide__le__eq__numeral_I2_J,axiom,
% 2.39/2.78 ! [B: rat,C: rat,W: num] :
% 2.39/2.78 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 2.39/2.78 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.78 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 2.39/2.78 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.78 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.78 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 2.39/2.78 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.78 => ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % divide_le_eq_numeral(2)
% 2.39/2.78 thf(fact_2959_le__divide__eq__numeral_I2_J,axiom,
% 2.39/2.78 ! [W: num,B: rat,C: rat] :
% 2.39/2.78 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 2.39/2.78 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.78 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 2.39/2.78 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.78 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.78 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 2.39/2.78 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.78 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % le_divide_eq_numeral(2)
% 2.39/2.78 thf(fact_2960_count__list_Osimps_I2_J,axiom,
% 2.39/2.78 ! [X: int,Y: int,Xs: list_int] :
% 2.39/2.78 ( ( ( X = Y )
% 2.39/2.78 => ( ( count_list_int @ ( cons_int @ X @ Xs ) @ Y )
% 2.39/2.78 = ( plus_plus_nat @ ( count_list_int @ Xs @ Y ) @ one_one_nat ) ) )
% 2.39/2.78 & ( ( X != Y )
% 2.39/2.78 => ( ( count_list_int @ ( cons_int @ X @ Xs ) @ Y )
% 2.39/2.78 = ( count_list_int @ Xs @ Y ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % count_list.simps(2)
% 2.39/2.78 thf(fact_2961_count__list_Osimps_I2_J,axiom,
% 2.39/2.78 ! [X: nat,Y: nat,Xs: list_nat] :
% 2.39/2.78 ( ( ( X = Y )
% 2.39/2.78 => ( ( count_list_nat @ ( cons_nat @ X @ Xs ) @ Y )
% 2.39/2.78 = ( plus_plus_nat @ ( count_list_nat @ Xs @ Y ) @ one_one_nat ) ) )
% 2.39/2.78 & ( ( X != Y )
% 2.39/2.78 => ( ( count_list_nat @ ( cons_nat @ X @ Xs ) @ Y )
% 2.39/2.78 = ( count_list_nat @ Xs @ Y ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % count_list.simps(2)
% 2.39/2.78 thf(fact_2962_distrib__right__NO__MATCH,axiom,
% 2.39/2.78 ! [X: nat,Y: nat,C: rat,A: rat,B: rat] :
% 2.39/2.78 ( ( nO_MATCH_nat_rat @ ( divide_divide_nat @ X @ Y ) @ C )
% 2.39/2.78 => ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 2.39/2.78 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % distrib_right_NO_MATCH
% 2.39/2.78 thf(fact_2963_distrib__right__NO__MATCH,axiom,
% 2.39/2.78 ! [X: nat,Y: nat,C: nat,A: nat,B: nat] :
% 2.39/2.78 ( ( nO_MATCH_nat_nat @ ( divide_divide_nat @ X @ Y ) @ C )
% 2.39/2.78 => ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 2.39/2.78 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % distrib_right_NO_MATCH
% 2.39/2.78 thf(fact_2964_distrib__right__NO__MATCH,axiom,
% 2.39/2.78 ! [X: nat,Y: nat,C: int,A: int,B: int] :
% 2.39/2.78 ( ( nO_MATCH_nat_int @ ( divide_divide_nat @ X @ Y ) @ C )
% 2.39/2.78 => ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 2.39/2.78 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % distrib_right_NO_MATCH
% 2.39/2.78 thf(fact_2965_distrib__right__NO__MATCH,axiom,
% 2.39/2.78 ! [X: nat,Y: nat,C: code_integer,A: code_integer,B: code_integer] :
% 2.39/2.78 ( ( nO_MAT8694959213317031834nteger @ ( divide_divide_nat @ X @ Y ) @ C )
% 2.39/2.78 => ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 2.39/2.78 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % distrib_right_NO_MATCH
% 2.39/2.78 thf(fact_2966_distrib__right__NO__MATCH,axiom,
% 2.39/2.78 ! [X: nat,Y: nat,C: code_natural,A: code_natural,B: code_natural] :
% 2.39/2.78 ( ( nO_MAT7518554365073749349atural @ ( divide_divide_nat @ X @ Y ) @ C )
% 2.39/2.78 => ( ( times_2397367101498566445atural @ ( plus_p4538020629002901425atural @ A @ B ) @ C )
% 2.39/2.78 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ C ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % distrib_right_NO_MATCH
% 2.39/2.78 thf(fact_2967_distrib__right__NO__MATCH,axiom,
% 2.39/2.78 ! [X: int,Y: int,C: rat,A: rat,B: rat] :
% 2.39/2.78 ( ( nO_MATCH_int_rat @ ( divide_divide_int @ X @ Y ) @ C )
% 2.39/2.78 => ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 2.39/2.78 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % distrib_right_NO_MATCH
% 2.39/2.78 thf(fact_2968_distrib__right__NO__MATCH,axiom,
% 2.39/2.78 ! [X: int,Y: int,C: nat,A: nat,B: nat] :
% 2.39/2.78 ( ( nO_MATCH_int_nat @ ( divide_divide_int @ X @ Y ) @ C )
% 2.39/2.78 => ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 2.39/2.78 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % distrib_right_NO_MATCH
% 2.39/2.78 thf(fact_2969_distrib__right__NO__MATCH,axiom,
% 2.39/2.78 ! [X: int,Y: int,C: int,A: int,B: int] :
% 2.39/2.78 ( ( nO_MATCH_int_int @ ( divide_divide_int @ X @ Y ) @ C )
% 2.39/2.78 => ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 2.39/2.78 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % distrib_right_NO_MATCH
% 2.39/2.78 thf(fact_2970_distrib__right__NO__MATCH,axiom,
% 2.39/2.78 ! [X: int,Y: int,C: code_integer,A: code_integer,B: code_integer] :
% 2.39/2.78 ( ( nO_MAT9066612773553876470nteger @ ( divide_divide_int @ X @ Y ) @ C )
% 2.39/2.78 => ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 2.39/2.78 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % distrib_right_NO_MATCH
% 2.39/2.78 thf(fact_2971_distrib__right__NO__MATCH,axiom,
% 2.39/2.78 ! [X: int,Y: int,C: code_natural,A: code_natural,B: code_natural] :
% 2.39/2.78 ( ( nO_MAT7890207925310593985atural @ ( divide_divide_int @ X @ Y ) @ C )
% 2.39/2.78 => ( ( times_2397367101498566445atural @ ( plus_p4538020629002901425atural @ A @ B ) @ C )
% 2.39/2.78 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ C ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % distrib_right_NO_MATCH
% 2.39/2.78 thf(fact_2972_distrib__left__NO__MATCH,axiom,
% 2.39/2.78 ! [X: nat,Y: nat,A: rat,B: rat,C: rat] :
% 2.39/2.78 ( ( nO_MATCH_nat_rat @ ( divide_divide_nat @ X @ Y ) @ A )
% 2.39/2.78 => ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 2.39/2.78 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % distrib_left_NO_MATCH
% 2.39/2.78 thf(fact_2973_distrib__left__NO__MATCH,axiom,
% 2.39/2.78 ! [X: nat,Y: nat,A: nat,B: nat,C: nat] :
% 2.39/2.78 ( ( nO_MATCH_nat_nat @ ( divide_divide_nat @ X @ Y ) @ A )
% 2.39/2.78 => ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 2.39/2.78 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % distrib_left_NO_MATCH
% 2.39/2.78 thf(fact_2974_distrib__left__NO__MATCH,axiom,
% 2.39/2.78 ! [X: nat,Y: nat,A: int,B: int,C: int] :
% 2.39/2.78 ( ( nO_MATCH_nat_int @ ( divide_divide_nat @ X @ Y ) @ A )
% 2.39/2.78 => ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 2.39/2.78 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % distrib_left_NO_MATCH
% 2.39/2.78 thf(fact_2975_distrib__left__NO__MATCH,axiom,
% 2.39/2.78 ! [X: nat,Y: nat,A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.78 ( ( nO_MAT8694959213317031834nteger @ ( divide_divide_nat @ X @ Y ) @ A )
% 2.39/2.78 => ( ( times_3573771949741848930nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 2.39/2.78 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % distrib_left_NO_MATCH
% 2.39/2.78 thf(fact_2976_distrib__left__NO__MATCH,axiom,
% 2.39/2.78 ! [X: nat,Y: nat,A: code_natural,B: code_natural,C: code_natural] :
% 2.39/2.78 ( ( nO_MAT7518554365073749349atural @ ( divide_divide_nat @ X @ Y ) @ A )
% 2.39/2.78 => ( ( times_2397367101498566445atural @ A @ ( plus_p4538020629002901425atural @ B @ C ) )
% 2.39/2.78 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ A @ B ) @ ( times_2397367101498566445atural @ A @ C ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % distrib_left_NO_MATCH
% 2.39/2.78 thf(fact_2977_distrib__left__NO__MATCH,axiom,
% 2.39/2.78 ! [X: int,Y: int,A: rat,B: rat,C: rat] :
% 2.39/2.78 ( ( nO_MATCH_int_rat @ ( divide_divide_int @ X @ Y ) @ A )
% 2.39/2.78 => ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 2.39/2.78 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % distrib_left_NO_MATCH
% 2.39/2.78 thf(fact_2978_distrib__left__NO__MATCH,axiom,
% 2.39/2.78 ! [X: int,Y: int,A: nat,B: nat,C: nat] :
% 2.39/2.78 ( ( nO_MATCH_int_nat @ ( divide_divide_int @ X @ Y ) @ A )
% 2.39/2.78 => ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 2.39/2.78 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % distrib_left_NO_MATCH
% 2.39/2.78 thf(fact_2979_distrib__left__NO__MATCH,axiom,
% 2.39/2.78 ! [X: int,Y: int,A: int,B: int,C: int] :
% 2.39/2.78 ( ( nO_MATCH_int_int @ ( divide_divide_int @ X @ Y ) @ A )
% 2.39/2.78 => ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 2.39/2.78 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % distrib_left_NO_MATCH
% 2.39/2.78 thf(fact_2980_distrib__left__NO__MATCH,axiom,
% 2.39/2.78 ! [X: int,Y: int,A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.78 ( ( nO_MAT9066612773553876470nteger @ ( divide_divide_int @ X @ Y ) @ A )
% 2.39/2.78 => ( ( times_3573771949741848930nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 2.39/2.78 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % distrib_left_NO_MATCH
% 2.39/2.78 thf(fact_2981_distrib__left__NO__MATCH,axiom,
% 2.39/2.78 ! [X: int,Y: int,A: code_natural,B: code_natural,C: code_natural] :
% 2.39/2.78 ( ( nO_MAT7890207925310593985atural @ ( divide_divide_int @ X @ Y ) @ A )
% 2.39/2.78 => ( ( times_2397367101498566445atural @ A @ ( plus_p4538020629002901425atural @ B @ C ) )
% 2.39/2.78 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ A @ B ) @ ( times_2397367101498566445atural @ A @ C ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % distrib_left_NO_MATCH
% 2.39/2.78 thf(fact_2982_power__minus__mult,axiom,
% 2.39/2.78 ! [N: nat,A: assn] :
% 2.39/2.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.39/2.78 => ( ( times_times_assn @ ( power_power_assn @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 2.39/2.78 = ( power_power_assn @ A @ N ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % power_minus_mult
% 2.39/2.78 thf(fact_2983_power__minus__mult,axiom,
% 2.39/2.78 ! [N: nat,A: nat] :
% 2.39/2.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.39/2.78 => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 2.39/2.78 = ( power_power_nat @ A @ N ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % power_minus_mult
% 2.39/2.78 thf(fact_2984_power__minus__mult,axiom,
% 2.39/2.78 ! [N: nat,A: int] :
% 2.39/2.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.39/2.78 => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 2.39/2.78 = ( power_power_int @ A @ N ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % power_minus_mult
% 2.39/2.78 thf(fact_2985_power__minus__mult,axiom,
% 2.39/2.78 ! [N: nat,A: code_integer] :
% 2.39/2.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.39/2.78 => ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 2.39/2.78 = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % power_minus_mult
% 2.39/2.78 thf(fact_2986_power__minus__mult,axiom,
% 2.39/2.78 ! [N: nat,A: code_natural] :
% 2.39/2.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.39/2.78 => ( ( times_2397367101498566445atural @ ( power_7079662738309270450atural @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 2.39/2.78 = ( power_7079662738309270450atural @ A @ N ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % power_minus_mult
% 2.39/2.78 thf(fact_2987_diff__self,axiom,
% 2.39/2.78 ! [A: rat] :
% 2.39/2.78 ( ( minus_minus_rat @ A @ A )
% 2.39/2.78 = zero_zero_rat ) ).
% 2.39/2.78
% 2.39/2.78 % diff_self
% 2.39/2.78 thf(fact_2988_diff__self,axiom,
% 2.39/2.78 ! [A: int] :
% 2.39/2.78 ( ( minus_minus_int @ A @ A )
% 2.39/2.78 = zero_zero_int ) ).
% 2.39/2.78
% 2.39/2.78 % diff_self
% 2.39/2.78 thf(fact_2989_diff__self,axiom,
% 2.39/2.78 ! [A: code_integer] :
% 2.39/2.78 ( ( minus_8373710615458151222nteger @ A @ A )
% 2.39/2.78 = zero_z3403309356797280102nteger ) ).
% 2.39/2.78
% 2.39/2.78 % diff_self
% 2.39/2.78 thf(fact_2990_diff__0__right,axiom,
% 2.39/2.78 ! [A: rat] :
% 2.39/2.78 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 2.39/2.78 = A ) ).
% 2.39/2.78
% 2.39/2.78 % diff_0_right
% 2.39/2.78 thf(fact_2991_diff__0__right,axiom,
% 2.39/2.78 ! [A: int] :
% 2.39/2.78 ( ( minus_minus_int @ A @ zero_zero_int )
% 2.39/2.78 = A ) ).
% 2.39/2.78
% 2.39/2.78 % diff_0_right
% 2.39/2.78 thf(fact_2992_diff__0__right,axiom,
% 2.39/2.78 ! [A: code_integer] :
% 2.39/2.78 ( ( minus_8373710615458151222nteger @ A @ zero_z3403309356797280102nteger )
% 2.39/2.78 = A ) ).
% 2.39/2.78
% 2.39/2.78 % diff_0_right
% 2.39/2.78 thf(fact_2993_zero__diff,axiom,
% 2.39/2.78 ! [A: nat] :
% 2.39/2.78 ( ( minus_minus_nat @ zero_zero_nat @ A )
% 2.39/2.78 = zero_zero_nat ) ).
% 2.39/2.78
% 2.39/2.78 % zero_diff
% 2.39/2.78 thf(fact_2994_zero__diff,axiom,
% 2.39/2.78 ! [A: code_natural] :
% 2.39/2.78 ( ( minus_7197305767214868737atural @ zero_z2226904508553997617atural @ A )
% 2.39/2.78 = zero_z2226904508553997617atural ) ).
% 2.39/2.78
% 2.39/2.78 % zero_diff
% 2.39/2.78 thf(fact_2995_diff__zero,axiom,
% 2.39/2.78 ! [A: rat] :
% 2.39/2.78 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 2.39/2.78 = A ) ).
% 2.39/2.78
% 2.39/2.78 % diff_zero
% 2.39/2.78 thf(fact_2996_diff__zero,axiom,
% 2.39/2.78 ! [A: nat] :
% 2.39/2.78 ( ( minus_minus_nat @ A @ zero_zero_nat )
% 2.39/2.78 = A ) ).
% 2.39/2.78
% 2.39/2.78 % diff_zero
% 2.39/2.78 thf(fact_2997_diff__zero,axiom,
% 2.39/2.78 ! [A: int] :
% 2.39/2.78 ( ( minus_minus_int @ A @ zero_zero_int )
% 2.39/2.78 = A ) ).
% 2.39/2.78
% 2.39/2.78 % diff_zero
% 2.39/2.78 thf(fact_2998_diff__zero,axiom,
% 2.39/2.78 ! [A: code_integer] :
% 2.39/2.78 ( ( minus_8373710615458151222nteger @ A @ zero_z3403309356797280102nteger )
% 2.39/2.78 = A ) ).
% 2.39/2.78
% 2.39/2.78 % diff_zero
% 2.39/2.78 thf(fact_2999_diff__zero,axiom,
% 2.39/2.78 ! [A: code_natural] :
% 2.39/2.78 ( ( minus_7197305767214868737atural @ A @ zero_z2226904508553997617atural )
% 2.39/2.78 = A ) ).
% 2.39/2.78
% 2.39/2.78 % diff_zero
% 2.39/2.78 thf(fact_3000_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 2.39/2.78 ! [A: rat] :
% 2.39/2.78 ( ( minus_minus_rat @ A @ A )
% 2.39/2.78 = zero_zero_rat ) ).
% 2.39/2.78
% 2.39/2.78 % cancel_comm_monoid_add_class.diff_cancel
% 2.39/2.78 thf(fact_3001_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 2.39/2.78 ! [A: nat] :
% 2.39/2.78 ( ( minus_minus_nat @ A @ A )
% 2.39/2.78 = zero_zero_nat ) ).
% 2.39/2.78
% 2.39/2.78 % cancel_comm_monoid_add_class.diff_cancel
% 2.39/2.78 thf(fact_3002_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 2.39/2.78 ! [A: int] :
% 2.39/2.78 ( ( minus_minus_int @ A @ A )
% 2.39/2.78 = zero_zero_int ) ).
% 2.39/2.78
% 2.39/2.78 % cancel_comm_monoid_add_class.diff_cancel
% 2.39/2.78 thf(fact_3003_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 2.39/2.78 ! [A: code_integer] :
% 2.39/2.78 ( ( minus_8373710615458151222nteger @ A @ A )
% 2.39/2.78 = zero_z3403309356797280102nteger ) ).
% 2.39/2.78
% 2.39/2.78 % cancel_comm_monoid_add_class.diff_cancel
% 2.39/2.78 thf(fact_3004_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 2.39/2.78 ! [A: code_natural] :
% 2.39/2.78 ( ( minus_7197305767214868737atural @ A @ A )
% 2.39/2.78 = zero_z2226904508553997617atural ) ).
% 2.39/2.78
% 2.39/2.78 % cancel_comm_monoid_add_class.diff_cancel
% 2.39/2.78 thf(fact_3005_mult__numeral__left__semiring__numeral,axiom,
% 2.39/2.78 ! [V2: num,W: num,Z: nat] :
% 2.39/2.78 ( ( times_times_nat @ ( numeral_numeral_nat @ V2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 2.39/2.78 = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V2 @ W ) ) @ Z ) ) ).
% 2.39/2.78
% 2.39/2.78 % mult_numeral_left_semiring_numeral
% 2.39/2.78 thf(fact_3006_mult__numeral__left__semiring__numeral,axiom,
% 2.39/2.78 ! [V2: num,W: num,Z: int] :
% 2.39/2.78 ( ( times_times_int @ ( numeral_numeral_int @ V2 ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 2.39/2.78 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V2 @ W ) ) @ Z ) ) ).
% 2.39/2.78
% 2.39/2.78 % mult_numeral_left_semiring_numeral
% 2.39/2.78 thf(fact_3007_mult__numeral__left__semiring__numeral,axiom,
% 2.39/2.78 ! [V2: num,W: num,Z: rat] :
% 2.39/2.78 ( ( times_times_rat @ ( numeral_numeral_rat @ V2 ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 2.39/2.78 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V2 @ W ) ) @ Z ) ) ).
% 2.39/2.78
% 2.39/2.78 % mult_numeral_left_semiring_numeral
% 2.39/2.78 thf(fact_3008_mult__numeral__left__semiring__numeral,axiom,
% 2.39/2.78 ! [V2: num,W: num,Z: code_integer] :
% 2.39/2.78 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V2 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ Z ) )
% 2.39/2.78 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V2 @ W ) ) @ Z ) ) ).
% 2.39/2.78
% 2.39/2.78 % mult_numeral_left_semiring_numeral
% 2.39/2.78 thf(fact_3009_mult__numeral__left__semiring__numeral,axiom,
% 2.39/2.78 ! [V2: num,W: num,Z: code_natural] :
% 2.39/2.78 ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ V2 ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ W ) @ Z ) )
% 2.39/2.78 = ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( times_times_num @ V2 @ W ) ) @ Z ) ) ).
% 2.39/2.78
% 2.39/2.78 % mult_numeral_left_semiring_numeral
% 2.39/2.78 thf(fact_3010_numeral__times__numeral,axiom,
% 2.39/2.78 ! [M2: num,N: num] :
% 2.39/2.78 ( ( times_times_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 2.39/2.78 = ( numeral_numeral_nat @ ( times_times_num @ M2 @ N ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % numeral_times_numeral
% 2.39/2.78 thf(fact_3011_numeral__times__numeral,axiom,
% 2.39/2.78 ! [M2: num,N: num] :
% 2.39/2.78 ( ( times_times_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) )
% 2.39/2.78 = ( numeral_numeral_int @ ( times_times_num @ M2 @ N ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % numeral_times_numeral
% 2.39/2.78 thf(fact_3012_numeral__times__numeral,axiom,
% 2.39/2.78 ! [M2: num,N: num] :
% 2.39/2.78 ( ( times_times_rat @ ( numeral_numeral_rat @ M2 ) @ ( numeral_numeral_rat @ N ) )
% 2.39/2.78 = ( numeral_numeral_rat @ ( times_times_num @ M2 @ N ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % numeral_times_numeral
% 2.39/2.78 thf(fact_3013_numeral__times__numeral,axiom,
% 2.39/2.78 ! [M2: num,N: num] :
% 2.39/2.78 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( numera6620942414471956472nteger @ N ) )
% 2.39/2.78 = ( numera6620942414471956472nteger @ ( times_times_num @ M2 @ N ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % numeral_times_numeral
% 2.39/2.78 thf(fact_3014_numeral__times__numeral,axiom,
% 2.39/2.78 ! [M2: num,N: num] :
% 2.39/2.78 ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ M2 ) @ ( numera5444537566228673987atural @ N ) )
% 2.39/2.78 = ( numera5444537566228673987atural @ ( times_times_num @ M2 @ N ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % numeral_times_numeral
% 2.39/2.78 thf(fact_3015_add__diff__cancel,axiom,
% 2.39/2.78 ! [A: rat,B: rat] :
% 2.39/2.78 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 2.39/2.78 = A ) ).
% 2.39/2.78
% 2.39/2.78 % add_diff_cancel
% 2.39/2.78 thf(fact_3016_add__diff__cancel,axiom,
% 2.39/2.78 ! [A: int,B: int] :
% 2.39/2.78 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 2.39/2.78 = A ) ).
% 2.39/2.78
% 2.39/2.78 % add_diff_cancel
% 2.39/2.78 thf(fact_3017_add__diff__cancel,axiom,
% 2.39/2.78 ! [A: code_integer,B: code_integer] :
% 2.39/2.78 ( ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 2.39/2.78 = A ) ).
% 2.39/2.78
% 2.39/2.78 % add_diff_cancel
% 2.39/2.78 thf(fact_3018_diff__add__cancel,axiom,
% 2.39/2.78 ! [A: rat,B: rat] :
% 2.39/2.78 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 2.39/2.78 = A ) ).
% 2.39/2.78
% 2.39/2.78 % diff_add_cancel
% 2.39/2.78 thf(fact_3019_diff__add__cancel,axiom,
% 2.39/2.78 ! [A: int,B: int] :
% 2.39/2.78 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 2.39/2.78 = A ) ).
% 2.39/2.78
% 2.39/2.78 % diff_add_cancel
% 2.39/2.78 thf(fact_3020_diff__add__cancel,axiom,
% 2.39/2.78 ! [A: code_integer,B: code_integer] :
% 2.39/2.78 ( ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ B )
% 2.39/2.78 = A ) ).
% 2.39/2.78
% 2.39/2.78 % diff_add_cancel
% 2.39/2.78 thf(fact_3021_add__diff__cancel__left,axiom,
% 2.39/2.78 ! [C: rat,A: rat,B: rat] :
% 2.39/2.78 ( ( minus_minus_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 2.39/2.78 = ( minus_minus_rat @ A @ B ) ) ).
% 2.39/2.78
% 2.39/2.78 % add_diff_cancel_left
% 2.39/2.78 thf(fact_3022_add__diff__cancel__left,axiom,
% 2.39/2.78 ! [C: nat,A: nat,B: nat] :
% 2.39/2.78 ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 2.39/2.78 = ( minus_minus_nat @ A @ B ) ) ).
% 2.39/2.78
% 2.39/2.78 % add_diff_cancel_left
% 2.39/2.78 thf(fact_3023_add__diff__cancel__left,axiom,
% 2.39/2.78 ! [C: int,A: int,B: int] :
% 2.39/2.78 ( ( minus_minus_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 2.39/2.78 = ( minus_minus_int @ A @ B ) ) ).
% 2.39/2.78
% 2.39/2.78 % add_diff_cancel_left
% 2.39/2.78 thf(fact_3024_add__diff__cancel__left,axiom,
% 2.39/2.78 ! [C: code_integer,A: code_integer,B: code_integer] :
% 2.39/2.78 ( ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ C @ A ) @ ( plus_p5714425477246183910nteger @ C @ B ) )
% 2.39/2.78 = ( minus_8373710615458151222nteger @ A @ B ) ) ).
% 2.39/2.78
% 2.39/2.78 % add_diff_cancel_left
% 2.39/2.78 thf(fact_3025_add__diff__cancel__left,axiom,
% 2.39/2.78 ! [C: code_natural,A: code_natural,B: code_natural] :
% 2.39/2.78 ( ( minus_7197305767214868737atural @ ( plus_p4538020629002901425atural @ C @ A ) @ ( plus_p4538020629002901425atural @ C @ B ) )
% 2.39/2.78 = ( minus_7197305767214868737atural @ A @ B ) ) ).
% 2.39/2.78
% 2.39/2.78 % add_diff_cancel_left
% 2.39/2.78 thf(fact_3026_add__diff__cancel__left_H,axiom,
% 2.39/2.78 ! [A: rat,B: rat] :
% 2.39/2.78 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ A )
% 2.39/2.78 = B ) ).
% 2.39/2.78
% 2.39/2.78 % add_diff_cancel_left'
% 2.39/2.78 thf(fact_3027_add__diff__cancel__left_H,axiom,
% 2.39/2.78 ! [A: nat,B: nat] :
% 2.39/2.78 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 2.39/2.78 = B ) ).
% 2.39/2.78
% 2.39/2.78 % add_diff_cancel_left'
% 2.39/2.78 thf(fact_3028_add__diff__cancel__left_H,axiom,
% 2.39/2.78 ! [A: int,B: int] :
% 2.39/2.78 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
% 2.39/2.78 = B ) ).
% 2.39/2.78
% 2.39/2.78 % add_diff_cancel_left'
% 2.39/2.78 thf(fact_3029_add__diff__cancel__left_H,axiom,
% 2.39/2.78 ! [A: code_integer,B: code_integer] :
% 2.39/2.78 ( ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ A )
% 2.39/2.78 = B ) ).
% 2.39/2.78
% 2.39/2.78 % add_diff_cancel_left'
% 2.39/2.78 thf(fact_3030_add__diff__cancel__left_H,axiom,
% 2.39/2.78 ! [A: code_natural,B: code_natural] :
% 2.39/2.78 ( ( minus_7197305767214868737atural @ ( plus_p4538020629002901425atural @ A @ B ) @ A )
% 2.39/2.78 = B ) ).
% 2.39/2.78
% 2.39/2.78 % add_diff_cancel_left'
% 2.39/2.78 thf(fact_3031_add__diff__cancel__right,axiom,
% 2.39/2.78 ! [A: rat,C: rat,B: rat] :
% 2.39/2.78 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 2.39/2.78 = ( minus_minus_rat @ A @ B ) ) ).
% 2.39/2.78
% 2.39/2.78 % add_diff_cancel_right
% 2.39/2.78 thf(fact_3032_add__diff__cancel__right,axiom,
% 2.39/2.78 ! [A: nat,C: nat,B: nat] :
% 2.39/2.78 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 2.39/2.78 = ( minus_minus_nat @ A @ B ) ) ).
% 2.39/2.78
% 2.39/2.78 % add_diff_cancel_right
% 2.39/2.78 thf(fact_3033_add__diff__cancel__right,axiom,
% 2.39/2.78 ! [A: int,C: int,B: int] :
% 2.39/2.78 ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 2.39/2.78 = ( minus_minus_int @ A @ B ) ) ).
% 2.39/2.78
% 2.39/2.78 % add_diff_cancel_right
% 2.39/2.78 thf(fact_3034_add__diff__cancel__right,axiom,
% 2.39/2.78 ! [A: code_integer,C: code_integer,B: code_integer] :
% 2.39/2.78 ( ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 2.39/2.78 = ( minus_8373710615458151222nteger @ A @ B ) ) ).
% 2.39/2.78
% 2.39/2.78 % add_diff_cancel_right
% 2.39/2.78 thf(fact_3035_add__diff__cancel__right,axiom,
% 2.39/2.78 ! [A: code_natural,C: code_natural,B: code_natural] :
% 2.39/2.78 ( ( minus_7197305767214868737atural @ ( plus_p4538020629002901425atural @ A @ C ) @ ( plus_p4538020629002901425atural @ B @ C ) )
% 2.39/2.78 = ( minus_7197305767214868737atural @ A @ B ) ) ).
% 2.39/2.78
% 2.39/2.78 % add_diff_cancel_right
% 2.39/2.78 thf(fact_3036_add__diff__cancel__right_H,axiom,
% 2.39/2.78 ! [A: rat,B: rat] :
% 2.39/2.78 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 2.39/2.78 = A ) ).
% 2.39/2.78
% 2.39/2.78 % add_diff_cancel_right'
% 2.39/2.78 thf(fact_3037_add__diff__cancel__right_H,axiom,
% 2.39/2.78 ! [A: nat,B: nat] :
% 2.39/2.78 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 2.39/2.78 = A ) ).
% 2.39/2.78
% 2.39/2.78 % add_diff_cancel_right'
% 2.39/2.78 thf(fact_3038_add__diff__cancel__right_H,axiom,
% 2.39/2.78 ! [A: int,B: int] :
% 2.39/2.78 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 2.39/2.78 = A ) ).
% 2.39/2.78
% 2.39/2.78 % add_diff_cancel_right'
% 2.39/2.78 thf(fact_3039_add__diff__cancel__right_H,axiom,
% 2.39/2.78 ! [A: code_integer,B: code_integer] :
% 2.39/2.78 ( ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 2.39/2.78 = A ) ).
% 2.39/2.78
% 2.39/2.78 % add_diff_cancel_right'
% 2.39/2.78 thf(fact_3040_add__diff__cancel__right_H,axiom,
% 2.39/2.78 ! [A: code_natural,B: code_natural] :
% 2.39/2.78 ( ( minus_7197305767214868737atural @ ( plus_p4538020629002901425atural @ A @ B ) @ B )
% 2.39/2.78 = A ) ).
% 2.39/2.78
% 2.39/2.78 % add_diff_cancel_right'
% 2.39/2.78 thf(fact_3041_minus__diff__eq,axiom,
% 2.39/2.78 ! [A: int,B: int] :
% 2.39/2.78 ( ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) )
% 2.39/2.78 = ( minus_minus_int @ B @ A ) ) ).
% 2.39/2.78
% 2.39/2.78 % minus_diff_eq
% 2.39/2.78 thf(fact_3042_minus__diff__eq,axiom,
% 2.39/2.78 ! [A: rat,B: rat] :
% 2.39/2.78 ( ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) )
% 2.39/2.78 = ( minus_minus_rat @ B @ A ) ) ).
% 2.39/2.78
% 2.39/2.78 % minus_diff_eq
% 2.39/2.78 thf(fact_3043_minus__diff__eq,axiom,
% 2.39/2.78 ! [A: code_integer,B: code_integer] :
% 2.39/2.78 ( ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 2.39/2.78 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 2.39/2.78
% 2.39/2.78 % minus_diff_eq
% 2.39/2.78 thf(fact_3044_power__add__numeral2,axiom,
% 2.39/2.78 ! [A: assn,M2: num,N: num,B: assn] :
% 2.39/2.78 ( ( times_times_assn @ ( power_power_assn @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( times_times_assn @ ( power_power_assn @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 2.39/2.78 = ( times_times_assn @ ( power_power_assn @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) @ B ) ) ).
% 2.39/2.78
% 2.39/2.78 % power_add_numeral2
% 2.39/2.78 thf(fact_3045_power__add__numeral2,axiom,
% 2.39/2.78 ! [A: nat,M2: num,N: num,B: nat] :
% 2.39/2.78 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 2.39/2.78 = ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) @ B ) ) ).
% 2.39/2.78
% 2.39/2.78 % power_add_numeral2
% 2.39/2.78 thf(fact_3046_power__add__numeral2,axiom,
% 2.39/2.78 ! [A: int,M2: num,N: num,B: int] :
% 2.39/2.78 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 2.39/2.78 = ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) @ B ) ) ).
% 2.39/2.78
% 2.39/2.78 % power_add_numeral2
% 2.39/2.78 thf(fact_3047_power__add__numeral2,axiom,
% 2.39/2.78 ! [A: code_integer,M2: num,N: num,B: code_integer] :
% 2.39/2.78 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 2.39/2.78 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) @ B ) ) ).
% 2.39/2.78
% 2.39/2.78 % power_add_numeral2
% 2.39/2.78 thf(fact_3048_power__add__numeral2,axiom,
% 2.39/2.78 ! [A: code_natural,M2: num,N: num,B: code_natural] :
% 2.39/2.78 ( ( times_2397367101498566445atural @ ( power_7079662738309270450atural @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( times_2397367101498566445atural @ ( power_7079662738309270450atural @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 2.39/2.78 = ( times_2397367101498566445atural @ ( power_7079662738309270450atural @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) @ B ) ) ).
% 2.39/2.78
% 2.39/2.78 % power_add_numeral2
% 2.39/2.78 thf(fact_3049_power__add__numeral,axiom,
% 2.39/2.78 ! [A: assn,M2: num,N: num] :
% 2.39/2.78 ( ( times_times_assn @ ( power_power_assn @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( power_power_assn @ A @ ( numeral_numeral_nat @ N ) ) )
% 2.39/2.78 = ( power_power_assn @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % power_add_numeral
% 2.39/2.78 thf(fact_3050_power__add__numeral,axiom,
% 2.39/2.78 ! [A: nat,M2: num,N: num] :
% 2.39/2.78 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) )
% 2.39/2.78 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % power_add_numeral
% 2.39/2.78 thf(fact_3051_power__add__numeral,axiom,
% 2.39/2.78 ! [A: int,M2: num,N: num] :
% 2.39/2.78 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) )
% 2.39/2.78 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % power_add_numeral
% 2.39/2.78 thf(fact_3052_power__add__numeral,axiom,
% 2.39/2.78 ! [A: code_integer,M2: num,N: num] :
% 2.39/2.78 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ N ) ) )
% 2.39/2.78 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % power_add_numeral
% 2.39/2.78 thf(fact_3053_power__add__numeral,axiom,
% 2.39/2.78 ! [A: code_natural,M2: num,N: num] :
% 2.39/2.78 ( ( times_2397367101498566445atural @ ( power_7079662738309270450atural @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( power_7079662738309270450atural @ A @ ( numeral_numeral_nat @ N ) ) )
% 2.39/2.78 = ( power_7079662738309270450atural @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % power_add_numeral
% 2.39/2.78 thf(fact_3054_diff__ge__0__iff__ge,axiom,
% 2.39/2.78 ! [A: code_integer,B: code_integer] :
% 2.39/2.78 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 2.39/2.78 = ( ord_le3102999989581377725nteger @ B @ A ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_ge_0_iff_ge
% 2.39/2.78 thf(fact_3055_diff__ge__0__iff__ge,axiom,
% 2.39/2.78 ! [A: rat,B: rat] :
% 2.39/2.78 ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 2.39/2.78 = ( ord_less_eq_rat @ B @ A ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_ge_0_iff_ge
% 2.39/2.78 thf(fact_3056_diff__ge__0__iff__ge,axiom,
% 2.39/2.78 ! [A: int,B: int] :
% 2.39/2.78 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 2.39/2.78 = ( ord_less_eq_int @ B @ A ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_ge_0_iff_ge
% 2.39/2.78 thf(fact_3057_diff__gt__0__iff__gt,axiom,
% 2.39/2.78 ! [A: code_integer,B: code_integer] :
% 2.39/2.78 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 2.39/2.78 = ( ord_le6747313008572928689nteger @ B @ A ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_gt_0_iff_gt
% 2.39/2.78 thf(fact_3058_diff__gt__0__iff__gt,axiom,
% 2.39/2.78 ! [A: rat,B: rat] :
% 2.39/2.78 ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 2.39/2.78 = ( ord_less_rat @ B @ A ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_gt_0_iff_gt
% 2.39/2.78 thf(fact_3059_diff__gt__0__iff__gt,axiom,
% 2.39/2.78 ! [A: int,B: int] :
% 2.39/2.78 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 2.39/2.78 = ( ord_less_int @ B @ A ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_gt_0_iff_gt
% 2.39/2.78 thf(fact_3060_diff__add__zero,axiom,
% 2.39/2.78 ! [A: nat,B: nat] :
% 2.39/2.78 ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 2.39/2.78 = zero_zero_nat ) ).
% 2.39/2.78
% 2.39/2.78 % diff_add_zero
% 2.39/2.78 thf(fact_3061_diff__add__zero,axiom,
% 2.39/2.78 ! [A: code_natural,B: code_natural] :
% 2.39/2.78 ( ( minus_7197305767214868737atural @ A @ ( plus_p4538020629002901425atural @ A @ B ) )
% 2.39/2.78 = zero_z2226904508553997617atural ) ).
% 2.39/2.78
% 2.39/2.78 % diff_add_zero
% 2.39/2.78 thf(fact_3062_diff__numeral__special_I9_J,axiom,
% 2.39/2.78 ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 2.39/2.78 = zero_zero_rat ) ).
% 2.39/2.78
% 2.39/2.78 % diff_numeral_special(9)
% 2.39/2.78 thf(fact_3063_diff__numeral__special_I9_J,axiom,
% 2.39/2.78 ( ( minus_minus_int @ one_one_int @ one_one_int )
% 2.39/2.78 = zero_zero_int ) ).
% 2.39/2.78
% 2.39/2.78 % diff_numeral_special(9)
% 2.39/2.78 thf(fact_3064_diff__numeral__special_I9_J,axiom,
% 2.39/2.78 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ one_one_Code_integer )
% 2.39/2.78 = zero_z3403309356797280102nteger ) ).
% 2.39/2.78
% 2.39/2.78 % diff_numeral_special(9)
% 2.39/2.78 thf(fact_3065_distrib__right__numeral,axiom,
% 2.39/2.78 ! [A: nat,B: nat,V2: num] :
% 2.39/2.78 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V2 ) )
% 2.39/2.78 = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V2 ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V2 ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % distrib_right_numeral
% 2.39/2.78 thf(fact_3066_distrib__right__numeral,axiom,
% 2.39/2.78 ! [A: int,B: int,V2: num] :
% 2.39/2.78 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( numeral_numeral_int @ V2 ) )
% 2.39/2.78 = ( plus_plus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V2 ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V2 ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % distrib_right_numeral
% 2.39/2.78 thf(fact_3067_distrib__right__numeral,axiom,
% 2.39/2.78 ! [A: rat,B: rat,V2: num] :
% 2.39/2.78 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( numeral_numeral_rat @ V2 ) )
% 2.39/2.78 = ( plus_plus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V2 ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V2 ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % distrib_right_numeral
% 2.39/2.78 thf(fact_3068_distrib__right__numeral,axiom,
% 2.39/2.78 ! [A: code_integer,B: code_integer,V2: num] :
% 2.39/2.78 ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ ( numera6620942414471956472nteger @ V2 ) )
% 2.39/2.78 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ ( numera6620942414471956472nteger @ V2 ) ) @ ( times_3573771949741848930nteger @ B @ ( numera6620942414471956472nteger @ V2 ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % distrib_right_numeral
% 2.39/2.78 thf(fact_3069_distrib__right__numeral,axiom,
% 2.39/2.78 ! [A: code_natural,B: code_natural,V2: num] :
% 2.39/2.78 ( ( times_2397367101498566445atural @ ( plus_p4538020629002901425atural @ A @ B ) @ ( numera5444537566228673987atural @ V2 ) )
% 2.39/2.78 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ A @ ( numera5444537566228673987atural @ V2 ) ) @ ( times_2397367101498566445atural @ B @ ( numera5444537566228673987atural @ V2 ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % distrib_right_numeral
% 2.39/2.78 thf(fact_3070_distrib__left__numeral,axiom,
% 2.39/2.78 ! [V2: num,B: nat,C: nat] :
% 2.39/2.78 ( ( times_times_nat @ ( numeral_numeral_nat @ V2 ) @ ( plus_plus_nat @ B @ C ) )
% 2.39/2.78 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V2 ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V2 ) @ C ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % distrib_left_numeral
% 2.39/2.78 thf(fact_3071_distrib__left__numeral,axiom,
% 2.39/2.78 ! [V2: num,B: int,C: int] :
% 2.39/2.78 ( ( times_times_int @ ( numeral_numeral_int @ V2 ) @ ( plus_plus_int @ B @ C ) )
% 2.39/2.78 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ V2 ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V2 ) @ C ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % distrib_left_numeral
% 2.39/2.78 thf(fact_3072_distrib__left__numeral,axiom,
% 2.39/2.78 ! [V2: num,B: rat,C: rat] :
% 2.39/2.78 ( ( times_times_rat @ ( numeral_numeral_rat @ V2 ) @ ( plus_plus_rat @ B @ C ) )
% 2.39/2.78 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V2 ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V2 ) @ C ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % distrib_left_numeral
% 2.39/2.78 thf(fact_3073_distrib__left__numeral,axiom,
% 2.39/2.78 ! [V2: num,B: code_integer,C: code_integer] :
% 2.39/2.78 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V2 ) @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 2.39/2.78 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V2 ) @ B ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V2 ) @ C ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % distrib_left_numeral
% 2.39/2.78 thf(fact_3074_distrib__left__numeral,axiom,
% 2.39/2.78 ! [V2: num,B: code_natural,C: code_natural] :
% 2.39/2.78 ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ V2 ) @ ( plus_p4538020629002901425atural @ B @ C ) )
% 2.39/2.78 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ V2 ) @ B ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ V2 ) @ C ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % distrib_left_numeral
% 2.39/2.78 thf(fact_3075_right__diff__distrib__numeral,axiom,
% 2.39/2.78 ! [V2: num,B: int,C: int] :
% 2.39/2.78 ( ( times_times_int @ ( numeral_numeral_int @ V2 ) @ ( minus_minus_int @ B @ C ) )
% 2.39/2.78 = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ V2 ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V2 ) @ C ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % right_diff_distrib_numeral
% 2.39/2.78 thf(fact_3076_right__diff__distrib__numeral,axiom,
% 2.39/2.78 ! [V2: num,B: rat,C: rat] :
% 2.39/2.78 ( ( times_times_rat @ ( numeral_numeral_rat @ V2 ) @ ( minus_minus_rat @ B @ C ) )
% 2.39/2.78 = ( minus_minus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V2 ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V2 ) @ C ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % right_diff_distrib_numeral
% 2.39/2.78 thf(fact_3077_right__diff__distrib__numeral,axiom,
% 2.39/2.78 ! [V2: num,B: code_integer,C: code_integer] :
% 2.39/2.78 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V2 ) @ ( minus_8373710615458151222nteger @ B @ C ) )
% 2.39/2.78 = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V2 ) @ B ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V2 ) @ C ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % right_diff_distrib_numeral
% 2.39/2.78 thf(fact_3078_left__diff__distrib__numeral,axiom,
% 2.39/2.78 ! [A: int,B: int,V2: num] :
% 2.39/2.78 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( numeral_numeral_int @ V2 ) )
% 2.39/2.78 = ( minus_minus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V2 ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V2 ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % left_diff_distrib_numeral
% 2.39/2.78 thf(fact_3079_left__diff__distrib__numeral,axiom,
% 2.39/2.78 ! [A: rat,B: rat,V2: num] :
% 2.39/2.78 ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ ( numeral_numeral_rat @ V2 ) )
% 2.39/2.78 = ( minus_minus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V2 ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V2 ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % left_diff_distrib_numeral
% 2.39/2.78 thf(fact_3080_left__diff__distrib__numeral,axiom,
% 2.39/2.78 ! [A: code_integer,B: code_integer,V2: num] :
% 2.39/2.78 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ ( numera6620942414471956472nteger @ V2 ) )
% 2.39/2.78 = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ ( numera6620942414471956472nteger @ V2 ) ) @ ( times_3573771949741848930nteger @ B @ ( numera6620942414471956472nteger @ V2 ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % left_diff_distrib_numeral
% 2.39/2.78 thf(fact_3081_diff__0,axiom,
% 2.39/2.78 ! [A: int] :
% 2.39/2.78 ( ( minus_minus_int @ zero_zero_int @ A )
% 2.39/2.78 = ( uminus_uminus_int @ A ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_0
% 2.39/2.78 thf(fact_3082_diff__0,axiom,
% 2.39/2.78 ! [A: rat] :
% 2.39/2.78 ( ( minus_minus_rat @ zero_zero_rat @ A )
% 2.39/2.78 = ( uminus_uminus_rat @ A ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_0
% 2.39/2.78 thf(fact_3083_diff__0,axiom,
% 2.39/2.78 ! [A: code_integer] :
% 2.39/2.78 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.78 = ( uminus1351360451143612070nteger @ A ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_0
% 2.39/2.78 thf(fact_3084_mult__neg__numeral__simps_I1_J,axiom,
% 2.39/2.78 ! [M2: num,N: num] :
% 2.39/2.78 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 2.39/2.78 = ( numeral_numeral_int @ ( times_times_num @ M2 @ N ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % mult_neg_numeral_simps(1)
% 2.39/2.78 thf(fact_3085_mult__neg__numeral__simps_I1_J,axiom,
% 2.39/2.78 ! [M2: num,N: num] :
% 2.39/2.78 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 2.39/2.78 = ( numeral_numeral_rat @ ( times_times_num @ M2 @ N ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % mult_neg_numeral_simps(1)
% 2.39/2.78 thf(fact_3086_mult__neg__numeral__simps_I1_J,axiom,
% 2.39/2.78 ! [M2: num,N: num] :
% 2.39/2.78 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 2.39/2.78 = ( numera6620942414471956472nteger @ ( times_times_num @ M2 @ N ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % mult_neg_numeral_simps(1)
% 2.39/2.78 thf(fact_3087_mult__neg__numeral__simps_I2_J,axiom,
% 2.39/2.78 ! [M2: num,N: num] :
% 2.39/2.78 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) )
% 2.39/2.78 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % mult_neg_numeral_simps(2)
% 2.39/2.78 thf(fact_3088_mult__neg__numeral__simps_I2_J,axiom,
% 2.39/2.78 ! [M2: num,N: num] :
% 2.39/2.78 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( numeral_numeral_rat @ N ) )
% 2.39/2.78 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % mult_neg_numeral_simps(2)
% 2.39/2.78 thf(fact_3089_mult__neg__numeral__simps_I2_J,axiom,
% 2.39/2.78 ! [M2: num,N: num] :
% 2.39/2.78 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( numera6620942414471956472nteger @ N ) )
% 2.39/2.78 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % mult_neg_numeral_simps(2)
% 2.39/2.78 thf(fact_3090_mult__neg__numeral__simps_I3_J,axiom,
% 2.39/2.78 ! [M2: num,N: num] :
% 2.39/2.78 ( ( times_times_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 2.39/2.78 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % mult_neg_numeral_simps(3)
% 2.39/2.78 thf(fact_3091_mult__neg__numeral__simps_I3_J,axiom,
% 2.39/2.78 ! [M2: num,N: num] :
% 2.39/2.78 ( ( times_times_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 2.39/2.78 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % mult_neg_numeral_simps(3)
% 2.39/2.78 thf(fact_3092_mult__neg__numeral__simps_I3_J,axiom,
% 2.39/2.78 ! [M2: num,N: num] :
% 2.39/2.78 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 2.39/2.78 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % mult_neg_numeral_simps(3)
% 2.39/2.78 thf(fact_3093_diff__minus__eq__add,axiom,
% 2.39/2.78 ! [A: int,B: int] :
% 2.39/2.78 ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
% 2.39/2.78 = ( plus_plus_int @ A @ B ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_minus_eq_add
% 2.39/2.78 thf(fact_3094_diff__minus__eq__add,axiom,
% 2.39/2.78 ! [A: rat,B: rat] :
% 2.39/2.78 ( ( minus_minus_rat @ A @ ( uminus_uminus_rat @ B ) )
% 2.39/2.78 = ( plus_plus_rat @ A @ B ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_minus_eq_add
% 2.39/2.78 thf(fact_3095_diff__minus__eq__add,axiom,
% 2.39/2.78 ! [A: code_integer,B: code_integer] :
% 2.39/2.78 ( ( minus_8373710615458151222nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 2.39/2.78 = ( plus_p5714425477246183910nteger @ A @ B ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_minus_eq_add
% 2.39/2.78 thf(fact_3096_uminus__add__conv__diff,axiom,
% 2.39/2.78 ! [A: int,B: int] :
% 2.39/2.78 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
% 2.39/2.78 = ( minus_minus_int @ B @ A ) ) ).
% 2.39/2.78
% 2.39/2.78 % uminus_add_conv_diff
% 2.39/2.78 thf(fact_3097_uminus__add__conv__diff,axiom,
% 2.39/2.78 ! [A: rat,B: rat] :
% 2.39/2.78 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B )
% 2.39/2.78 = ( minus_minus_rat @ B @ A ) ) ).
% 2.39/2.78
% 2.39/2.78 % uminus_add_conv_diff
% 2.39/2.78 thf(fact_3098_uminus__add__conv__diff,axiom,
% 2.39/2.78 ! [A: code_integer,B: code_integer] :
% 2.39/2.78 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 2.39/2.78 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 2.39/2.78
% 2.39/2.78 % uminus_add_conv_diff
% 2.39/2.78 thf(fact_3099_divide__le__eq__numeral1_I1_J,axiom,
% 2.39/2.78 ! [B: rat,W: num,A: rat] :
% 2.39/2.78 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 2.39/2.78 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % divide_le_eq_numeral1(1)
% 2.39/2.78 thf(fact_3100_le__divide__eq__numeral1_I1_J,axiom,
% 2.39/2.78 ! [A: rat,B: rat,W: num] :
% 2.39/2.78 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 2.39/2.78 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 2.39/2.78
% 2.39/2.78 % le_divide_eq_numeral1(1)
% 2.39/2.78 thf(fact_3101_divide__eq__eq__numeral1_I1_J,axiom,
% 2.39/2.78 ! [B: rat,W: num,A: rat] :
% 2.39/2.78 ( ( ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) )
% 2.39/2.78 = A )
% 2.39/2.78 = ( ( ( ( numeral_numeral_rat @ W )
% 2.39/2.78 != zero_zero_rat )
% 2.39/2.78 => ( B
% 2.39/2.78 = ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) )
% 2.39/2.78 & ( ( ( numeral_numeral_rat @ W )
% 2.39/2.78 = zero_zero_rat )
% 2.39/2.78 => ( A = zero_zero_rat ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % divide_eq_eq_numeral1(1)
% 2.39/2.78 thf(fact_3102_eq__divide__eq__numeral1_I1_J,axiom,
% 2.39/2.78 ! [A: rat,B: rat,W: num] :
% 2.39/2.78 ( ( A
% 2.39/2.78 = ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 2.39/2.78 = ( ( ( ( numeral_numeral_rat @ W )
% 2.39/2.78 != zero_zero_rat )
% 2.39/2.78 => ( ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) )
% 2.39/2.78 = B ) )
% 2.39/2.78 & ( ( ( numeral_numeral_rat @ W )
% 2.39/2.78 = zero_zero_rat )
% 2.39/2.78 => ( A = zero_zero_rat ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % eq_divide_eq_numeral1(1)
% 2.39/2.78 thf(fact_3103_diff__numeral__special_I12_J,axiom,
% 2.39/2.78 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 2.39/2.78 = zero_zero_int ) ).
% 2.39/2.78
% 2.39/2.78 % diff_numeral_special(12)
% 2.39/2.78 thf(fact_3104_diff__numeral__special_I12_J,axiom,
% 2.39/2.78 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 2.39/2.78 = zero_zero_rat ) ).
% 2.39/2.78
% 2.39/2.78 % diff_numeral_special(12)
% 2.39/2.78 thf(fact_3105_diff__numeral__special_I12_J,axiom,
% 2.39/2.78 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 2.39/2.78 = zero_z3403309356797280102nteger ) ).
% 2.39/2.78
% 2.39/2.78 % diff_numeral_special(12)
% 2.39/2.78 thf(fact_3106_divide__less__eq__numeral1_I1_J,axiom,
% 2.39/2.78 ! [B: rat,W: num,A: rat] :
% 2.39/2.78 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 2.39/2.78 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % divide_less_eq_numeral1(1)
% 2.39/2.78 thf(fact_3107_less__divide__eq__numeral1_I1_J,axiom,
% 2.39/2.78 ! [A: rat,B: rat,W: num] :
% 2.39/2.78 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 2.39/2.78 = ( ord_less_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 2.39/2.78
% 2.39/2.78 % less_divide_eq_numeral1(1)
% 2.39/2.78 thf(fact_3108_divide__le__eq__numeral1_I2_J,axiom,
% 2.39/2.78 ! [B: rat,W: num,A: rat] :
% 2.39/2.78 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 2.39/2.78 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 2.39/2.78
% 2.39/2.78 % divide_le_eq_numeral1(2)
% 2.39/2.78 thf(fact_3109_le__divide__eq__numeral1_I2_J,axiom,
% 2.39/2.78 ! [A: rat,B: rat,W: num] :
% 2.39/2.78 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 2.39/2.78 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % le_divide_eq_numeral1(2)
% 2.39/2.78 thf(fact_3110_divide__eq__eq__numeral1_I2_J,axiom,
% 2.39/2.78 ! [B: rat,W: num,A: rat] :
% 2.39/2.78 ( ( ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 2.39/2.78 = A )
% 2.39/2.78 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 2.39/2.78 != zero_zero_rat )
% 2.39/2.78 => ( B
% 2.39/2.78 = ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) )
% 2.39/2.78 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 2.39/2.78 = zero_zero_rat )
% 2.39/2.78 => ( A = zero_zero_rat ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % divide_eq_eq_numeral1(2)
% 2.39/2.78 thf(fact_3111_eq__divide__eq__numeral1_I2_J,axiom,
% 2.39/2.78 ! [A: rat,B: rat,W: num] :
% 2.39/2.78 ( ( A
% 2.39/2.78 = ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 2.39/2.78 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 2.39/2.78 != zero_zero_rat )
% 2.39/2.78 => ( ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 2.39/2.78 = B ) )
% 2.39/2.78 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 2.39/2.78 = zero_zero_rat )
% 2.39/2.78 => ( A = zero_zero_rat ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % eq_divide_eq_numeral1(2)
% 2.39/2.78 thf(fact_3112_divide__less__eq__numeral1_I2_J,axiom,
% 2.39/2.78 ! [B: rat,W: num,A: rat] :
% 2.39/2.78 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 2.39/2.78 = ( ord_less_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 2.39/2.78
% 2.39/2.78 % divide_less_eq_numeral1(2)
% 2.39/2.78 thf(fact_3113_less__divide__eq__numeral1_I2_J,axiom,
% 2.39/2.78 ! [A: rat,B: rat,W: num] :
% 2.39/2.78 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 2.39/2.78 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % less_divide_eq_numeral1(2)
% 2.39/2.78 thf(fact_3114_diff__eq__diff__eq,axiom,
% 2.39/2.78 ! [A: int,B: int,C: int,D2: int] :
% 2.39/2.78 ( ( ( minus_minus_int @ A @ B )
% 2.39/2.78 = ( minus_minus_int @ C @ D2 ) )
% 2.39/2.78 => ( ( A = B )
% 2.39/2.78 = ( C = D2 ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_eq_diff_eq
% 2.39/2.78 thf(fact_3115_diff__eq__diff__eq,axiom,
% 2.39/2.78 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 2.39/2.78 ( ( ( minus_8373710615458151222nteger @ A @ B )
% 2.39/2.78 = ( minus_8373710615458151222nteger @ C @ D2 ) )
% 2.39/2.78 => ( ( A = B )
% 2.39/2.78 = ( C = D2 ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_eq_diff_eq
% 2.39/2.78 thf(fact_3116_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 2.39/2.78 ! [A: nat,C: nat,B: nat] :
% 2.39/2.78 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 2.39/2.78 = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 2.39/2.78
% 2.39/2.78 % cancel_ab_semigroup_add_class.diff_right_commute
% 2.39/2.78 thf(fact_3117_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 2.39/2.78 ! [A: int,C: int,B: int] :
% 2.39/2.78 ( ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B )
% 2.39/2.78 = ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 2.39/2.78
% 2.39/2.78 % cancel_ab_semigroup_add_class.diff_right_commute
% 2.39/2.78 thf(fact_3118_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 2.39/2.78 ! [A: code_integer,C: code_integer,B: code_integer] :
% 2.39/2.78 ( ( minus_8373710615458151222nteger @ ( minus_8373710615458151222nteger @ A @ C ) @ B )
% 2.39/2.78 = ( minus_8373710615458151222nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 2.39/2.78
% 2.39/2.78 % cancel_ab_semigroup_add_class.diff_right_commute
% 2.39/2.78 thf(fact_3119_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 2.39/2.78 ! [A: code_natural,C: code_natural,B: code_natural] :
% 2.39/2.78 ( ( minus_7197305767214868737atural @ ( minus_7197305767214868737atural @ A @ C ) @ B )
% 2.39/2.78 = ( minus_7197305767214868737atural @ ( minus_7197305767214868737atural @ A @ B ) @ C ) ) ).
% 2.39/2.78
% 2.39/2.78 % cancel_ab_semigroup_add_class.diff_right_commute
% 2.39/2.78 thf(fact_3120_diff__mono,axiom,
% 2.39/2.78 ! [A: code_integer,B: code_integer,D2: code_integer,C: code_integer] :
% 2.39/2.78 ( ( ord_le3102999989581377725nteger @ A @ B )
% 2.39/2.78 => ( ( ord_le3102999989581377725nteger @ D2 @ C )
% 2.39/2.78 => ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ C ) @ ( minus_8373710615458151222nteger @ B @ D2 ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_mono
% 2.39/2.78 thf(fact_3121_diff__mono,axiom,
% 2.39/2.78 ! [A: rat,B: rat,D2: rat,C: rat] :
% 2.39/2.78 ( ( ord_less_eq_rat @ A @ B )
% 2.39/2.78 => ( ( ord_less_eq_rat @ D2 @ C )
% 2.39/2.78 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D2 ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_mono
% 2.39/2.78 thf(fact_3122_diff__mono,axiom,
% 2.39/2.78 ! [A: int,B: int,D2: int,C: int] :
% 2.39/2.78 ( ( ord_less_eq_int @ A @ B )
% 2.39/2.78 => ( ( ord_less_eq_int @ D2 @ C )
% 2.39/2.78 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D2 ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_mono
% 2.39/2.78 thf(fact_3123_diff__left__mono,axiom,
% 2.39/2.78 ! [B: code_integer,A: code_integer,C: code_integer] :
% 2.39/2.78 ( ( ord_le3102999989581377725nteger @ B @ A )
% 2.39/2.78 => ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ C @ A ) @ ( minus_8373710615458151222nteger @ C @ B ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_left_mono
% 2.39/2.78 thf(fact_3124_diff__left__mono,axiom,
% 2.39/2.78 ! [B: rat,A: rat,C: rat] :
% 2.39/2.78 ( ( ord_less_eq_rat @ B @ A )
% 2.39/2.78 => ( ord_less_eq_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_left_mono
% 2.39/2.78 thf(fact_3125_diff__left__mono,axiom,
% 2.39/2.78 ! [B: int,A: int,C: int] :
% 2.39/2.78 ( ( ord_less_eq_int @ B @ A )
% 2.39/2.78 => ( ord_less_eq_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_left_mono
% 2.39/2.78 thf(fact_3126_diff__right__mono,axiom,
% 2.39/2.78 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.78 ( ( ord_le3102999989581377725nteger @ A @ B )
% 2.39/2.78 => ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ C ) @ ( minus_8373710615458151222nteger @ B @ C ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_right_mono
% 2.39/2.78 thf(fact_3127_diff__right__mono,axiom,
% 2.39/2.78 ! [A: rat,B: rat,C: rat] :
% 2.39/2.78 ( ( ord_less_eq_rat @ A @ B )
% 2.39/2.78 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_right_mono
% 2.39/2.78 thf(fact_3128_diff__right__mono,axiom,
% 2.39/2.78 ! [A: int,B: int,C: int] :
% 2.39/2.78 ( ( ord_less_eq_int @ A @ B )
% 2.39/2.78 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_right_mono
% 2.39/2.78 thf(fact_3129_diff__eq__diff__less__eq,axiom,
% 2.39/2.78 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 2.39/2.78 ( ( ( minus_8373710615458151222nteger @ A @ B )
% 2.39/2.78 = ( minus_8373710615458151222nteger @ C @ D2 ) )
% 2.39/2.78 => ( ( ord_le3102999989581377725nteger @ A @ B )
% 2.39/2.78 = ( ord_le3102999989581377725nteger @ C @ D2 ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_eq_diff_less_eq
% 2.39/2.78 thf(fact_3130_diff__eq__diff__less__eq,axiom,
% 2.39/2.78 ! [A: rat,B: rat,C: rat,D2: rat] :
% 2.39/2.78 ( ( ( minus_minus_rat @ A @ B )
% 2.39/2.78 = ( minus_minus_rat @ C @ D2 ) )
% 2.39/2.78 => ( ( ord_less_eq_rat @ A @ B )
% 2.39/2.78 = ( ord_less_eq_rat @ C @ D2 ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_eq_diff_less_eq
% 2.39/2.78 thf(fact_3131_diff__eq__diff__less__eq,axiom,
% 2.39/2.78 ! [A: int,B: int,C: int,D2: int] :
% 2.39/2.78 ( ( ( minus_minus_int @ A @ B )
% 2.39/2.78 = ( minus_minus_int @ C @ D2 ) )
% 2.39/2.78 => ( ( ord_less_eq_int @ A @ B )
% 2.39/2.78 = ( ord_less_eq_int @ C @ D2 ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_eq_diff_less_eq
% 2.39/2.78 thf(fact_3132_eq__iff__diff__eq__0,axiom,
% 2.39/2.78 ( ( ^ [Y4: rat,Z4: rat] : ( Y4 = Z4 ) )
% 2.39/2.78 = ( ^ [A2: rat,B2: rat] :
% 2.39/2.78 ( ( minus_minus_rat @ A2 @ B2 )
% 2.39/2.78 = zero_zero_rat ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % eq_iff_diff_eq_0
% 2.39/2.78 thf(fact_3133_eq__iff__diff__eq__0,axiom,
% 2.39/2.78 ( ( ^ [Y4: int,Z4: int] : ( Y4 = Z4 ) )
% 2.39/2.78 = ( ^ [A2: int,B2: int] :
% 2.39/2.78 ( ( minus_minus_int @ A2 @ B2 )
% 2.39/2.78 = zero_zero_int ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % eq_iff_diff_eq_0
% 2.39/2.78 thf(fact_3134_eq__iff__diff__eq__0,axiom,
% 2.39/2.78 ( ( ^ [Y4: code_integer,Z4: code_integer] : ( Y4 = Z4 ) )
% 2.39/2.78 = ( ^ [A2: code_integer,B2: code_integer] :
% 2.39/2.78 ( ( minus_8373710615458151222nteger @ A2 @ B2 )
% 2.39/2.78 = zero_z3403309356797280102nteger ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % eq_iff_diff_eq_0
% 2.39/2.78 thf(fact_3135_diff__strict__mono,axiom,
% 2.39/2.78 ! [A: code_integer,B: code_integer,D2: code_integer,C: code_integer] :
% 2.39/2.78 ( ( ord_le6747313008572928689nteger @ A @ B )
% 2.39/2.78 => ( ( ord_le6747313008572928689nteger @ D2 @ C )
% 2.39/2.78 => ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ C ) @ ( minus_8373710615458151222nteger @ B @ D2 ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_strict_mono
% 2.39/2.78 thf(fact_3136_diff__strict__mono,axiom,
% 2.39/2.78 ! [A: rat,B: rat,D2: rat,C: rat] :
% 2.39/2.78 ( ( ord_less_rat @ A @ B )
% 2.39/2.78 => ( ( ord_less_rat @ D2 @ C )
% 2.39/2.78 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D2 ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_strict_mono
% 2.39/2.78 thf(fact_3137_diff__strict__mono,axiom,
% 2.39/2.78 ! [A: int,B: int,D2: int,C: int] :
% 2.39/2.78 ( ( ord_less_int @ A @ B )
% 2.39/2.78 => ( ( ord_less_int @ D2 @ C )
% 2.39/2.78 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D2 ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_strict_mono
% 2.39/2.78 thf(fact_3138_diff__eq__diff__less,axiom,
% 2.39/2.78 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 2.39/2.78 ( ( ( minus_8373710615458151222nteger @ A @ B )
% 2.39/2.78 = ( minus_8373710615458151222nteger @ C @ D2 ) )
% 2.39/2.78 => ( ( ord_le6747313008572928689nteger @ A @ B )
% 2.39/2.78 = ( ord_le6747313008572928689nteger @ C @ D2 ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_eq_diff_less
% 2.39/2.78 thf(fact_3139_diff__eq__diff__less,axiom,
% 2.39/2.78 ! [A: rat,B: rat,C: rat,D2: rat] :
% 2.39/2.78 ( ( ( minus_minus_rat @ A @ B )
% 2.39/2.78 = ( minus_minus_rat @ C @ D2 ) )
% 2.39/2.78 => ( ( ord_less_rat @ A @ B )
% 2.39/2.78 = ( ord_less_rat @ C @ D2 ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_eq_diff_less
% 2.39/2.78 thf(fact_3140_diff__eq__diff__less,axiom,
% 2.39/2.78 ! [A: int,B: int,C: int,D2: int] :
% 2.39/2.78 ( ( ( minus_minus_int @ A @ B )
% 2.39/2.78 = ( minus_minus_int @ C @ D2 ) )
% 2.39/2.78 => ( ( ord_less_int @ A @ B )
% 2.39/2.78 = ( ord_less_int @ C @ D2 ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_eq_diff_less
% 2.39/2.78 thf(fact_3141_diff__strict__left__mono,axiom,
% 2.39/2.78 ! [B: code_integer,A: code_integer,C: code_integer] :
% 2.39/2.78 ( ( ord_le6747313008572928689nteger @ B @ A )
% 2.39/2.78 => ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ C @ A ) @ ( minus_8373710615458151222nteger @ C @ B ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_strict_left_mono
% 2.39/2.78 thf(fact_3142_diff__strict__left__mono,axiom,
% 2.39/2.78 ! [B: rat,A: rat,C: rat] :
% 2.39/2.78 ( ( ord_less_rat @ B @ A )
% 2.39/2.78 => ( ord_less_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_strict_left_mono
% 2.39/2.78 thf(fact_3143_diff__strict__left__mono,axiom,
% 2.39/2.78 ! [B: int,A: int,C: int] :
% 2.39/2.78 ( ( ord_less_int @ B @ A )
% 2.39/2.78 => ( ord_less_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_strict_left_mono
% 2.39/2.78 thf(fact_3144_diff__strict__right__mono,axiom,
% 2.39/2.78 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.78 ( ( ord_le6747313008572928689nteger @ A @ B )
% 2.39/2.78 => ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ C ) @ ( minus_8373710615458151222nteger @ B @ C ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_strict_right_mono
% 2.39/2.78 thf(fact_3145_diff__strict__right__mono,axiom,
% 2.39/2.78 ! [A: rat,B: rat,C: rat] :
% 2.39/2.78 ( ( ord_less_rat @ A @ B )
% 2.39/2.78 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_strict_right_mono
% 2.39/2.78 thf(fact_3146_diff__strict__right__mono,axiom,
% 2.39/2.78 ! [A: int,B: int,C: int] :
% 2.39/2.78 ( ( ord_less_int @ A @ B )
% 2.39/2.78 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_strict_right_mono
% 2.39/2.78 thf(fact_3147_group__cancel_Osub1,axiom,
% 2.39/2.78 ! [A3: rat,K: rat,A: rat,B: rat] :
% 2.39/2.78 ( ( A3
% 2.39/2.78 = ( plus_plus_rat @ K @ A ) )
% 2.39/2.78 => ( ( minus_minus_rat @ A3 @ B )
% 2.39/2.78 = ( plus_plus_rat @ K @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % group_cancel.sub1
% 2.39/2.78 thf(fact_3148_group__cancel_Osub1,axiom,
% 2.39/2.78 ! [A3: int,K: int,A: int,B: int] :
% 2.39/2.78 ( ( A3
% 2.39/2.78 = ( plus_plus_int @ K @ A ) )
% 2.39/2.78 => ( ( minus_minus_int @ A3 @ B )
% 2.39/2.78 = ( plus_plus_int @ K @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % group_cancel.sub1
% 2.39/2.78 thf(fact_3149_group__cancel_Osub1,axiom,
% 2.39/2.78 ! [A3: code_integer,K: code_integer,A: code_integer,B: code_integer] :
% 2.39/2.78 ( ( A3
% 2.39/2.78 = ( plus_p5714425477246183910nteger @ K @ A ) )
% 2.39/2.78 => ( ( minus_8373710615458151222nteger @ A3 @ B )
% 2.39/2.78 = ( plus_p5714425477246183910nteger @ K @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % group_cancel.sub1
% 2.39/2.78 thf(fact_3150_diff__eq__eq,axiom,
% 2.39/2.78 ! [A: rat,B: rat,C: rat] :
% 2.39/2.78 ( ( ( minus_minus_rat @ A @ B )
% 2.39/2.78 = C )
% 2.39/2.78 = ( A
% 2.39/2.78 = ( plus_plus_rat @ C @ B ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_eq_eq
% 2.39/2.78 thf(fact_3151_diff__eq__eq,axiom,
% 2.39/2.78 ! [A: int,B: int,C: int] :
% 2.39/2.78 ( ( ( minus_minus_int @ A @ B )
% 2.39/2.78 = C )
% 2.39/2.78 = ( A
% 2.39/2.78 = ( plus_plus_int @ C @ B ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_eq_eq
% 2.39/2.78 thf(fact_3152_diff__eq__eq,axiom,
% 2.39/2.78 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.78 ( ( ( minus_8373710615458151222nteger @ A @ B )
% 2.39/2.78 = C )
% 2.39/2.78 = ( A
% 2.39/2.78 = ( plus_p5714425477246183910nteger @ C @ B ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_eq_eq
% 2.39/2.78 thf(fact_3153_eq__diff__eq,axiom,
% 2.39/2.78 ! [A: rat,C: rat,B: rat] :
% 2.39/2.78 ( ( A
% 2.39/2.78 = ( minus_minus_rat @ C @ B ) )
% 2.39/2.78 = ( ( plus_plus_rat @ A @ B )
% 2.39/2.78 = C ) ) ).
% 2.39/2.78
% 2.39/2.78 % eq_diff_eq
% 2.39/2.78 thf(fact_3154_eq__diff__eq,axiom,
% 2.39/2.78 ! [A: int,C: int,B: int] :
% 2.39/2.78 ( ( A
% 2.39/2.78 = ( minus_minus_int @ C @ B ) )
% 2.39/2.78 = ( ( plus_plus_int @ A @ B )
% 2.39/2.78 = C ) ) ).
% 2.39/2.78
% 2.39/2.78 % eq_diff_eq
% 2.39/2.78 thf(fact_3155_eq__diff__eq,axiom,
% 2.39/2.78 ! [A: code_integer,C: code_integer,B: code_integer] :
% 2.39/2.78 ( ( A
% 2.39/2.78 = ( minus_8373710615458151222nteger @ C @ B ) )
% 2.39/2.78 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 2.39/2.78 = C ) ) ).
% 2.39/2.78
% 2.39/2.78 % eq_diff_eq
% 2.39/2.78 thf(fact_3156_add__diff__eq,axiom,
% 2.39/2.78 ! [A: rat,B: rat,C: rat] :
% 2.39/2.78 ( ( plus_plus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 2.39/2.78 = ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 2.39/2.78
% 2.39/2.78 % add_diff_eq
% 2.39/2.78 thf(fact_3157_add__diff__eq,axiom,
% 2.39/2.78 ! [A: int,B: int,C: int] :
% 2.39/2.78 ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C ) )
% 2.39/2.78 = ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 2.39/2.78
% 2.39/2.78 % add_diff_eq
% 2.39/2.78 thf(fact_3158_add__diff__eq,axiom,
% 2.39/2.78 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.78 ( ( plus_p5714425477246183910nteger @ A @ ( minus_8373710615458151222nteger @ B @ C ) )
% 2.39/2.78 = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 2.39/2.78
% 2.39/2.78 % add_diff_eq
% 2.39/2.78 thf(fact_3159_diff__diff__eq2,axiom,
% 2.39/2.78 ! [A: rat,B: rat,C: rat] :
% 2.39/2.78 ( ( minus_minus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 2.39/2.78 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_diff_eq2
% 2.39/2.78 thf(fact_3160_diff__diff__eq2,axiom,
% 2.39/2.78 ! [A: int,B: int,C: int] :
% 2.39/2.78 ( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C ) )
% 2.39/2.78 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_diff_eq2
% 2.39/2.78 thf(fact_3161_diff__diff__eq2,axiom,
% 2.39/2.78 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.78 ( ( minus_8373710615458151222nteger @ A @ ( minus_8373710615458151222nteger @ B @ C ) )
% 2.39/2.78 = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ B ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_diff_eq2
% 2.39/2.78 thf(fact_3162_diff__add__eq,axiom,
% 2.39/2.78 ! [A: rat,B: rat,C: rat] :
% 2.39/2.78 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 2.39/2.78 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_add_eq
% 2.39/2.78 thf(fact_3163_diff__add__eq,axiom,
% 2.39/2.78 ! [A: int,B: int,C: int] :
% 2.39/2.78 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C )
% 2.39/2.78 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_add_eq
% 2.39/2.78 thf(fact_3164_diff__add__eq,axiom,
% 2.39/2.78 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.78 ( ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 2.39/2.78 = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ B ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_add_eq
% 2.39/2.78 thf(fact_3165_diff__add__eq__diff__diff__swap,axiom,
% 2.39/2.78 ! [A: rat,B: rat,C: rat] :
% 2.39/2.78 ( ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 2.39/2.78 = ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_add_eq_diff_diff_swap
% 2.39/2.78 thf(fact_3166_diff__add__eq__diff__diff__swap,axiom,
% 2.39/2.78 ! [A: int,B: int,C: int] :
% 2.39/2.78 ( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) )
% 2.39/2.78 = ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_add_eq_diff_diff_swap
% 2.39/2.78 thf(fact_3167_diff__add__eq__diff__diff__swap,axiom,
% 2.39/2.78 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.78 ( ( minus_8373710615458151222nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 2.39/2.78 = ( minus_8373710615458151222nteger @ ( minus_8373710615458151222nteger @ A @ C ) @ B ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_add_eq_diff_diff_swap
% 2.39/2.78 thf(fact_3168_add__implies__diff,axiom,
% 2.39/2.78 ! [C: rat,B: rat,A: rat] :
% 2.39/2.78 ( ( ( plus_plus_rat @ C @ B )
% 2.39/2.78 = A )
% 2.39/2.78 => ( C
% 2.39/2.78 = ( minus_minus_rat @ A @ B ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % add_implies_diff
% 2.39/2.78 thf(fact_3169_add__implies__diff,axiom,
% 2.39/2.78 ! [C: nat,B: nat,A: nat] :
% 2.39/2.78 ( ( ( plus_plus_nat @ C @ B )
% 2.39/2.78 = A )
% 2.39/2.78 => ( C
% 2.39/2.78 = ( minus_minus_nat @ A @ B ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % add_implies_diff
% 2.39/2.78 thf(fact_3170_add__implies__diff,axiom,
% 2.39/2.78 ! [C: int,B: int,A: int] :
% 2.39/2.78 ( ( ( plus_plus_int @ C @ B )
% 2.39/2.78 = A )
% 2.39/2.78 => ( C
% 2.39/2.78 = ( minus_minus_int @ A @ B ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % add_implies_diff
% 2.39/2.78 thf(fact_3171_add__implies__diff,axiom,
% 2.39/2.78 ! [C: code_integer,B: code_integer,A: code_integer] :
% 2.39/2.78 ( ( ( plus_p5714425477246183910nteger @ C @ B )
% 2.39/2.78 = A )
% 2.39/2.78 => ( C
% 2.39/2.78 = ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % add_implies_diff
% 2.39/2.78 thf(fact_3172_add__implies__diff,axiom,
% 2.39/2.78 ! [C: code_natural,B: code_natural,A: code_natural] :
% 2.39/2.78 ( ( ( plus_p4538020629002901425atural @ C @ B )
% 2.39/2.78 = A )
% 2.39/2.78 => ( C
% 2.39/2.78 = ( minus_7197305767214868737atural @ A @ B ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % add_implies_diff
% 2.39/2.78 thf(fact_3173_diff__diff__eq,axiom,
% 2.39/2.78 ! [A: rat,B: rat,C: rat] :
% 2.39/2.78 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 2.39/2.78 = ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_diff_eq
% 2.39/2.78 thf(fact_3174_diff__diff__eq,axiom,
% 2.39/2.78 ! [A: nat,B: nat,C: nat] :
% 2.39/2.78 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
% 2.39/2.78 = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_diff_eq
% 2.39/2.78 thf(fact_3175_diff__diff__eq,axiom,
% 2.39/2.78 ! [A: int,B: int,C: int] :
% 2.39/2.78 ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
% 2.39/2.78 = ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_diff_eq
% 2.39/2.78 thf(fact_3176_diff__diff__eq,axiom,
% 2.39/2.78 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.78 ( ( minus_8373710615458151222nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 2.39/2.78 = ( minus_8373710615458151222nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_diff_eq
% 2.39/2.78 thf(fact_3177_diff__diff__eq,axiom,
% 2.39/2.78 ! [A: code_natural,B: code_natural,C: code_natural] :
% 2.39/2.78 ( ( minus_7197305767214868737atural @ ( minus_7197305767214868737atural @ A @ B ) @ C )
% 2.39/2.78 = ( minus_7197305767214868737atural @ A @ ( plus_p4538020629002901425atural @ B @ C ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_diff_eq
% 2.39/2.78 thf(fact_3178_right__diff__distrib_H,axiom,
% 2.39/2.78 ! [A: nat,B: nat,C: nat] :
% 2.39/2.78 ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
% 2.39/2.78 = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % right_diff_distrib'
% 2.39/2.78 thf(fact_3179_right__diff__distrib_H,axiom,
% 2.39/2.78 ! [A: int,B: int,C: int] :
% 2.39/2.78 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 2.39/2.78 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % right_diff_distrib'
% 2.39/2.78 thf(fact_3180_right__diff__distrib_H,axiom,
% 2.39/2.78 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.78 ( ( times_3573771949741848930nteger @ A @ ( minus_8373710615458151222nteger @ B @ C ) )
% 2.39/2.78 = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % right_diff_distrib'
% 2.39/2.78 thf(fact_3181_right__diff__distrib_H,axiom,
% 2.39/2.78 ! [A: code_natural,B: code_natural,C: code_natural] :
% 2.39/2.78 ( ( times_2397367101498566445atural @ A @ ( minus_7197305767214868737atural @ B @ C ) )
% 2.39/2.78 = ( minus_7197305767214868737atural @ ( times_2397367101498566445atural @ A @ B ) @ ( times_2397367101498566445atural @ A @ C ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % right_diff_distrib'
% 2.39/2.78 thf(fact_3182_left__diff__distrib_H,axiom,
% 2.39/2.78 ! [B: nat,C: nat,A: nat] :
% 2.39/2.78 ( ( times_times_nat @ ( minus_minus_nat @ B @ C ) @ A )
% 2.39/2.78 = ( minus_minus_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % left_diff_distrib'
% 2.39/2.78 thf(fact_3183_left__diff__distrib_H,axiom,
% 2.39/2.78 ! [B: int,C: int,A: int] :
% 2.39/2.78 ( ( times_times_int @ ( minus_minus_int @ B @ C ) @ A )
% 2.39/2.78 = ( minus_minus_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % left_diff_distrib'
% 2.39/2.78 thf(fact_3184_left__diff__distrib_H,axiom,
% 2.39/2.78 ! [B: code_integer,C: code_integer,A: code_integer] :
% 2.39/2.78 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ B @ C ) @ A )
% 2.39/2.78 = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ B @ A ) @ ( times_3573771949741848930nteger @ C @ A ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % left_diff_distrib'
% 2.39/2.78 thf(fact_3185_left__diff__distrib_H,axiom,
% 2.39/2.78 ! [B: code_natural,C: code_natural,A: code_natural] :
% 2.39/2.78 ( ( times_2397367101498566445atural @ ( minus_7197305767214868737atural @ B @ C ) @ A )
% 2.39/2.78 = ( minus_7197305767214868737atural @ ( times_2397367101498566445atural @ B @ A ) @ ( times_2397367101498566445atural @ C @ A ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % left_diff_distrib'
% 2.39/2.78 thf(fact_3186_right__diff__distrib,axiom,
% 2.39/2.78 ! [A: int,B: int,C: int] :
% 2.39/2.78 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 2.39/2.78 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % right_diff_distrib
% 2.39/2.78 thf(fact_3187_right__diff__distrib,axiom,
% 2.39/2.78 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.78 ( ( times_3573771949741848930nteger @ A @ ( minus_8373710615458151222nteger @ B @ C ) )
% 2.39/2.78 = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % right_diff_distrib
% 2.39/2.78 thf(fact_3188_left__diff__distrib,axiom,
% 2.39/2.78 ! [A: int,B: int,C: int] :
% 2.39/2.78 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 2.39/2.78 = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % left_diff_distrib
% 2.39/2.78 thf(fact_3189_left__diff__distrib,axiom,
% 2.39/2.78 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.78 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 2.39/2.78 = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % left_diff_distrib
% 2.39/2.78 thf(fact_3190_minus__diff__commute,axiom,
% 2.39/2.78 ! [B: int,A: int] :
% 2.39/2.78 ( ( minus_minus_int @ ( uminus_uminus_int @ B ) @ A )
% 2.39/2.78 = ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 2.39/2.78
% 2.39/2.78 % minus_diff_commute
% 2.39/2.78 thf(fact_3191_minus__diff__commute,axiom,
% 2.39/2.78 ! [B: rat,A: rat] :
% 2.39/2.78 ( ( minus_minus_rat @ ( uminus_uminus_rat @ B ) @ A )
% 2.39/2.78 = ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 2.39/2.78
% 2.39/2.78 % minus_diff_commute
% 2.39/2.78 thf(fact_3192_minus__diff__commute,axiom,
% 2.39/2.78 ! [B: code_integer,A: code_integer] :
% 2.39/2.78 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ B ) @ A )
% 2.39/2.78 = ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 2.39/2.78
% 2.39/2.78 % minus_diff_commute
% 2.39/2.78 thf(fact_3193_left__diff__distrib__NO__MATCH,axiom,
% 2.39/2.78 ! [X: nat,Y: nat,C: int,A: int,B: int] :
% 2.39/2.78 ( ( nO_MATCH_nat_int @ ( divide_divide_nat @ X @ Y ) @ C )
% 2.39/2.78 => ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 2.39/2.78 = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % left_diff_distrib_NO_MATCH
% 2.39/2.78 thf(fact_3194_left__diff__distrib__NO__MATCH,axiom,
% 2.39/2.78 ! [X: nat,Y: nat,C: code_integer,A: code_integer,B: code_integer] :
% 2.39/2.78 ( ( nO_MAT8694959213317031834nteger @ ( divide_divide_nat @ X @ Y ) @ C )
% 2.39/2.78 => ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 2.39/2.78 = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % left_diff_distrib_NO_MATCH
% 2.39/2.78 thf(fact_3195_left__diff__distrib__NO__MATCH,axiom,
% 2.39/2.78 ! [X: int,Y: int,C: int,A: int,B: int] :
% 2.39/2.78 ( ( nO_MATCH_int_int @ ( divide_divide_int @ X @ Y ) @ C )
% 2.39/2.78 => ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 2.39/2.78 = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % left_diff_distrib_NO_MATCH
% 2.39/2.78 thf(fact_3196_left__diff__distrib__NO__MATCH,axiom,
% 2.39/2.78 ! [X: int,Y: int,C: code_integer,A: code_integer,B: code_integer] :
% 2.39/2.78 ( ( nO_MAT9066612773553876470nteger @ ( divide_divide_int @ X @ Y ) @ C )
% 2.39/2.78 => ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 2.39/2.78 = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % left_diff_distrib_NO_MATCH
% 2.39/2.78 thf(fact_3197_left__diff__distrib__NO__MATCH,axiom,
% 2.39/2.78 ! [X: rat,Y: rat,C: int,A: int,B: int] :
% 2.39/2.78 ( ( nO_MATCH_rat_int @ ( divide_divide_rat @ X @ Y ) @ C )
% 2.39/2.78 => ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 2.39/2.78 = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % left_diff_distrib_NO_MATCH
% 2.39/2.78 thf(fact_3198_left__diff__distrib__NO__MATCH,axiom,
% 2.39/2.78 ! [X: rat,Y: rat,C: code_integer,A: code_integer,B: code_integer] :
% 2.39/2.78 ( ( nO_MAT243659986023775650nteger @ ( divide_divide_rat @ X @ Y ) @ C )
% 2.39/2.78 => ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 2.39/2.78 = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % left_diff_distrib_NO_MATCH
% 2.39/2.78 thf(fact_3199_left__diff__distrib__NO__MATCH,axiom,
% 2.39/2.78 ! [X: code_natural,Y: code_natural,C: int,A: int,B: int] :
% 2.39/2.78 ( ( nO_MAT4469370267861770177al_int @ ( divide5121882707175180666atural @ X @ Y ) @ C )
% 2.39/2.78 => ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 2.39/2.78 = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % left_diff_distrib_NO_MATCH
% 2.39/2.78 thf(fact_3200_left__diff__distrib__NO__MATCH,axiom,
% 2.39/2.78 ! [X: code_natural,Y: code_natural,C: code_integer,A: code_integer,B: code_integer] :
% 2.39/2.78 ( ( nO_MAT2693162092599435762nteger @ ( divide5121882707175180666atural @ X @ Y ) @ C )
% 2.39/2.78 => ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 2.39/2.78 = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % left_diff_distrib_NO_MATCH
% 2.39/2.78 thf(fact_3201_right__diff__distrib__NO__MATCH,axiom,
% 2.39/2.78 ! [X: nat,Y: nat,A: int,B: int,C: int] :
% 2.39/2.78 ( ( nO_MATCH_nat_int @ ( divide_divide_nat @ X @ Y ) @ A )
% 2.39/2.78 => ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 2.39/2.78 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % right_diff_distrib_NO_MATCH
% 2.39/2.78 thf(fact_3202_right__diff__distrib__NO__MATCH,axiom,
% 2.39/2.78 ! [X: nat,Y: nat,A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.78 ( ( nO_MAT8694959213317031834nteger @ ( divide_divide_nat @ X @ Y ) @ A )
% 2.39/2.78 => ( ( times_3573771949741848930nteger @ A @ ( minus_8373710615458151222nteger @ B @ C ) )
% 2.39/2.78 = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % right_diff_distrib_NO_MATCH
% 2.39/2.78 thf(fact_3203_right__diff__distrib__NO__MATCH,axiom,
% 2.39/2.78 ! [X: int,Y: int,A: int,B: int,C: int] :
% 2.39/2.78 ( ( nO_MATCH_int_int @ ( divide_divide_int @ X @ Y ) @ A )
% 2.39/2.78 => ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 2.39/2.78 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % right_diff_distrib_NO_MATCH
% 2.39/2.78 thf(fact_3204_right__diff__distrib__NO__MATCH,axiom,
% 2.39/2.78 ! [X: int,Y: int,A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.78 ( ( nO_MAT9066612773553876470nteger @ ( divide_divide_int @ X @ Y ) @ A )
% 2.39/2.78 => ( ( times_3573771949741848930nteger @ A @ ( minus_8373710615458151222nteger @ B @ C ) )
% 2.39/2.78 = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % right_diff_distrib_NO_MATCH
% 2.39/2.78 thf(fact_3205_right__diff__distrib__NO__MATCH,axiom,
% 2.39/2.78 ! [X: rat,Y: rat,A: int,B: int,C: int] :
% 2.39/2.78 ( ( nO_MATCH_rat_int @ ( divide_divide_rat @ X @ Y ) @ A )
% 2.39/2.78 => ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 2.39/2.78 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % right_diff_distrib_NO_MATCH
% 2.39/2.78 thf(fact_3206_right__diff__distrib__NO__MATCH,axiom,
% 2.39/2.78 ! [X: rat,Y: rat,A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.78 ( ( nO_MAT243659986023775650nteger @ ( divide_divide_rat @ X @ Y ) @ A )
% 2.39/2.78 => ( ( times_3573771949741848930nteger @ A @ ( minus_8373710615458151222nteger @ B @ C ) )
% 2.39/2.78 = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % right_diff_distrib_NO_MATCH
% 2.39/2.78 thf(fact_3207_right__diff__distrib__NO__MATCH,axiom,
% 2.39/2.78 ! [X: code_natural,Y: code_natural,A: int,B: int,C: int] :
% 2.39/2.78 ( ( nO_MAT4469370267861770177al_int @ ( divide5121882707175180666atural @ X @ Y ) @ A )
% 2.39/2.78 => ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 2.39/2.78 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % right_diff_distrib_NO_MATCH
% 2.39/2.78 thf(fact_3208_right__diff__distrib__NO__MATCH,axiom,
% 2.39/2.78 ! [X: code_natural,Y: code_natural,A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.78 ( ( nO_MAT2693162092599435762nteger @ ( divide5121882707175180666atural @ X @ Y ) @ A )
% 2.39/2.78 => ( ( times_3573771949741848930nteger @ A @ ( minus_8373710615458151222nteger @ B @ C ) )
% 2.39/2.78 = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % right_diff_distrib_NO_MATCH
% 2.39/2.78 thf(fact_3209_le__iff__diff__le__0,axiom,
% 2.39/2.78 ( ord_le3102999989581377725nteger
% 2.39/2.78 = ( ^ [A2: code_integer,B2: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A2 @ B2 ) @ zero_z3403309356797280102nteger ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % le_iff_diff_le_0
% 2.39/2.78 thf(fact_3210_le__iff__diff__le__0,axiom,
% 2.39/2.78 ( ord_less_eq_rat
% 2.39/2.78 = ( ^ [A2: rat,B2: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A2 @ B2 ) @ zero_zero_rat ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % le_iff_diff_le_0
% 2.39/2.78 thf(fact_3211_le__iff__diff__le__0,axiom,
% 2.39/2.78 ( ord_less_eq_int
% 2.39/2.78 = ( ^ [A2: int,B2: int] : ( ord_less_eq_int @ ( minus_minus_int @ A2 @ B2 ) @ zero_zero_int ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % le_iff_diff_le_0
% 2.39/2.78 thf(fact_3212_less__iff__diff__less__0,axiom,
% 2.39/2.78 ( ord_le6747313008572928689nteger
% 2.39/2.78 = ( ^ [A2: code_integer,B2: code_integer] : ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A2 @ B2 ) @ zero_z3403309356797280102nteger ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % less_iff_diff_less_0
% 2.39/2.78 thf(fact_3213_less__iff__diff__less__0,axiom,
% 2.39/2.78 ( ord_less_rat
% 2.39/2.78 = ( ^ [A2: rat,B2: rat] : ( ord_less_rat @ ( minus_minus_rat @ A2 @ B2 ) @ zero_zero_rat ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % less_iff_diff_less_0
% 2.39/2.78 thf(fact_3214_less__iff__diff__less__0,axiom,
% 2.39/2.78 ( ord_less_int
% 2.39/2.78 = ( ^ [A2: int,B2: int] : ( ord_less_int @ ( minus_minus_int @ A2 @ B2 ) @ zero_zero_int ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % less_iff_diff_less_0
% 2.39/2.78 thf(fact_3215_diff__le__eq,axiom,
% 2.39/2.78 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.78 ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 2.39/2.78 = ( ord_le3102999989581377725nteger @ A @ ( plus_p5714425477246183910nteger @ C @ B ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_le_eq
% 2.39/2.78 thf(fact_3216_diff__le__eq,axiom,
% 2.39/2.78 ! [A: rat,B: rat,C: rat] :
% 2.39/2.78 ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 2.39/2.78 = ( ord_less_eq_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_le_eq
% 2.39/2.78 thf(fact_3217_diff__le__eq,axiom,
% 2.39/2.78 ! [A: int,B: int,C: int] :
% 2.39/2.78 ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C )
% 2.39/2.78 = ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_le_eq
% 2.39/2.78 thf(fact_3218_le__diff__eq,axiom,
% 2.39/2.78 ! [A: code_integer,C: code_integer,B: code_integer] :
% 2.39/2.78 ( ( ord_le3102999989581377725nteger @ A @ ( minus_8373710615458151222nteger @ C @ B ) )
% 2.39/2.78 = ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 2.39/2.78
% 2.39/2.78 % le_diff_eq
% 2.39/2.78 thf(fact_3219_le__diff__eq,axiom,
% 2.39/2.78 ! [A: rat,C: rat,B: rat] :
% 2.39/2.78 ( ( ord_less_eq_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 2.39/2.78 = ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 2.39/2.78
% 2.39/2.78 % le_diff_eq
% 2.39/2.78 thf(fact_3220_le__diff__eq,axiom,
% 2.39/2.78 ! [A: int,C: int,B: int] :
% 2.39/2.78 ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B ) )
% 2.39/2.78 = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 2.39/2.78
% 2.39/2.78 % le_diff_eq
% 2.39/2.78 thf(fact_3221_ordered__cancel__comm__monoid__diff__class_Odiff__add,axiom,
% 2.39/2.78 ! [A: nat,B: nat] :
% 2.39/2.78 ( ( ord_less_eq_nat @ A @ B )
% 2.39/2.78 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 2.39/2.78 = B ) ) ).
% 2.39/2.78
% 2.39/2.78 % ordered_cancel_comm_monoid_diff_class.diff_add
% 2.39/2.78 thf(fact_3222_le__add__diff,axiom,
% 2.39/2.78 ! [A: nat,B: nat,C: nat] :
% 2.39/2.78 ( ( ord_less_eq_nat @ A @ B )
% 2.39/2.78 => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % le_add_diff
% 2.39/2.78 thf(fact_3223_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 2.39/2.78 ! [A: nat,B: nat,C: nat] :
% 2.39/2.78 ( ( ord_less_eq_nat @ A @ B )
% 2.39/2.78 => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 2.39/2.78 = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % ordered_cancel_comm_monoid_diff_class.le_diff_conv2
% 2.39/2.78 thf(fact_3224_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 2.39/2.78 ! [A: nat,B: nat,C: nat] :
% 2.39/2.78 ( ( ord_less_eq_nat @ A @ B )
% 2.39/2.78 => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 2.39/2.78 = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc
% 2.39/2.78 thf(fact_3225_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 2.39/2.78 ! [A: nat,B: nat,C: nat] :
% 2.39/2.78 ( ( ord_less_eq_nat @ A @ B )
% 2.39/2.78 => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
% 2.39/2.78 = ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc
% 2.39/2.78 thf(fact_3226_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 2.39/2.78 ! [A: nat,B: nat,C: nat] :
% 2.39/2.78 ( ( ord_less_eq_nat @ A @ B )
% 2.39/2.78 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
% 2.39/2.78 = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
% 2.39/2.78 thf(fact_3227_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 2.39/2.78 ! [A: nat,B: nat,C: nat] :
% 2.39/2.78 ( ( ord_less_eq_nat @ A @ B )
% 2.39/2.78 => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
% 2.39/2.78 = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
% 2.39/2.78 thf(fact_3228_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 2.39/2.78 ! [A: nat,B: nat,C: nat] :
% 2.39/2.78 ( ( ord_less_eq_nat @ A @ B )
% 2.39/2.78 => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 2.39/2.78 = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % ordered_cancel_comm_monoid_diff_class.diff_diff_right
% 2.39/2.78 thf(fact_3229_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 2.39/2.78 ! [A: nat,B: nat] :
% 2.39/2.78 ( ( ord_less_eq_nat @ A @ B )
% 2.39/2.78 => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 2.39/2.78 = B ) ) ).
% 2.39/2.78
% 2.39/2.78 % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
% 2.39/2.78 thf(fact_3230_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 2.39/2.78 ! [A: nat,B: nat,C: nat] :
% 2.39/2.78 ( ( ord_less_eq_nat @ A @ B )
% 2.39/2.78 => ( ( ord_less_eq_nat @ A @ B )
% 2.39/2.78 => ( ( ( minus_minus_nat @ B @ A )
% 2.39/2.78 = C )
% 2.39/2.78 = ( B
% 2.39/2.78 = ( plus_plus_nat @ C @ A ) ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
% 2.39/2.78 thf(fact_3231_less__diff__eq,axiom,
% 2.39/2.78 ! [A: code_integer,C: code_integer,B: code_integer] :
% 2.39/2.78 ( ( ord_le6747313008572928689nteger @ A @ ( minus_8373710615458151222nteger @ C @ B ) )
% 2.39/2.78 = ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 2.39/2.78
% 2.39/2.78 % less_diff_eq
% 2.39/2.78 thf(fact_3232_less__diff__eq,axiom,
% 2.39/2.78 ! [A: rat,C: rat,B: rat] :
% 2.39/2.78 ( ( ord_less_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 2.39/2.78 = ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 2.39/2.78
% 2.39/2.78 % less_diff_eq
% 2.39/2.78 thf(fact_3233_less__diff__eq,axiom,
% 2.39/2.78 ! [A: int,C: int,B: int] :
% 2.39/2.78 ( ( ord_less_int @ A @ ( minus_minus_int @ C @ B ) )
% 2.39/2.78 = ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 2.39/2.78
% 2.39/2.78 % less_diff_eq
% 2.39/2.78 thf(fact_3234_diff__less__eq,axiom,
% 2.39/2.78 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.78 ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 2.39/2.78 = ( ord_le6747313008572928689nteger @ A @ ( plus_p5714425477246183910nteger @ C @ B ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_less_eq
% 2.39/2.78 thf(fact_3235_diff__less__eq,axiom,
% 2.39/2.78 ! [A: rat,B: rat,C: rat] :
% 2.39/2.78 ( ( ord_less_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 2.39/2.78 = ( ord_less_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_less_eq
% 2.39/2.78 thf(fact_3236_diff__less__eq,axiom,
% 2.39/2.78 ! [A: int,B: int,C: int] :
% 2.39/2.78 ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C )
% 2.39/2.78 = ( ord_less_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_less_eq
% 2.39/2.78 thf(fact_3237_eq__add__iff1,axiom,
% 2.39/2.78 ! [A: rat,E2: rat,C: rat,B: rat,D2: rat] :
% 2.39/2.78 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C )
% 2.39/2.78 = ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D2 ) )
% 2.39/2.78 = ( ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C )
% 2.39/2.78 = D2 ) ) ).
% 2.39/2.78
% 2.39/2.78 % eq_add_iff1
% 2.39/2.78 thf(fact_3238_eq__add__iff1,axiom,
% 2.39/2.78 ! [A: int,E2: int,C: int,B: int,D2: int] :
% 2.39/2.78 ( ( ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C )
% 2.39/2.78 = ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D2 ) )
% 2.39/2.78 = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C )
% 2.39/2.78 = D2 ) ) ).
% 2.39/2.78
% 2.39/2.78 % eq_add_iff1
% 2.39/2.78 thf(fact_3239_eq__add__iff1,axiom,
% 2.39/2.78 ! [A: code_integer,E2: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 2.39/2.78 ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E2 ) @ C )
% 2.39/2.78 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E2 ) @ D2 ) )
% 2.39/2.78 = ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ E2 ) @ C )
% 2.39/2.78 = D2 ) ) ).
% 2.39/2.78
% 2.39/2.78 % eq_add_iff1
% 2.39/2.78 thf(fact_3240_eq__add__iff2,axiom,
% 2.39/2.78 ! [A: rat,E2: rat,C: rat,B: rat,D2: rat] :
% 2.39/2.78 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C )
% 2.39/2.78 = ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D2 ) )
% 2.39/2.78 = ( C
% 2.39/2.78 = ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D2 ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % eq_add_iff2
% 2.39/2.78 thf(fact_3241_eq__add__iff2,axiom,
% 2.39/2.78 ! [A: int,E2: int,C: int,B: int,D2: int] :
% 2.39/2.78 ( ( ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C )
% 2.39/2.78 = ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D2 ) )
% 2.39/2.78 = ( C
% 2.39/2.78 = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D2 ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % eq_add_iff2
% 2.39/2.78 thf(fact_3242_eq__add__iff2,axiom,
% 2.39/2.78 ! [A: code_integer,E2: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 2.39/2.78 ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E2 ) @ C )
% 2.39/2.78 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E2 ) @ D2 ) )
% 2.39/2.78 = ( C
% 2.39/2.78 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ E2 ) @ D2 ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % eq_add_iff2
% 2.39/2.78 thf(fact_3243_square__diff__square__factored,axiom,
% 2.39/2.78 ! [X: rat,Y: rat] :
% 2.39/2.78 ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 2.39/2.78 = ( times_times_rat @ ( plus_plus_rat @ X @ Y ) @ ( minus_minus_rat @ X @ Y ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % square_diff_square_factored
% 2.39/2.78 thf(fact_3244_square__diff__square__factored,axiom,
% 2.39/2.78 ! [X: int,Y: int] :
% 2.39/2.78 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 2.39/2.78 = ( times_times_int @ ( plus_plus_int @ X @ Y ) @ ( minus_minus_int @ X @ Y ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % square_diff_square_factored
% 2.39/2.78 thf(fact_3245_square__diff__square__factored,axiom,
% 2.39/2.78 ! [X: code_integer,Y: code_integer] :
% 2.39/2.78 ( ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) )
% 2.39/2.78 = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ X @ Y ) @ ( minus_8373710615458151222nteger @ X @ Y ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % square_diff_square_factored
% 2.39/2.78 thf(fact_3246_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 2.39/2.78 ( minus_minus_int
% 2.39/2.78 = ( ^ [A2: int,B2: int] : ( plus_plus_int @ A2 @ ( uminus_uminus_int @ B2 ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % ab_group_add_class.ab_diff_conv_add_uminus
% 2.39/2.78 thf(fact_3247_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 2.39/2.78 ( minus_minus_rat
% 2.39/2.78 = ( ^ [A2: rat,B2: rat] : ( plus_plus_rat @ A2 @ ( uminus_uminus_rat @ B2 ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % ab_group_add_class.ab_diff_conv_add_uminus
% 2.39/2.78 thf(fact_3248_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 2.39/2.78 ( minus_8373710615458151222nteger
% 2.39/2.78 = ( ^ [A2: code_integer,B2: code_integer] : ( plus_p5714425477246183910nteger @ A2 @ ( uminus1351360451143612070nteger @ B2 ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % ab_group_add_class.ab_diff_conv_add_uminus
% 2.39/2.78 thf(fact_3249_diff__conv__add__uminus,axiom,
% 2.39/2.78 ( minus_minus_int
% 2.39/2.78 = ( ^ [A2: int,B2: int] : ( plus_plus_int @ A2 @ ( uminus_uminus_int @ B2 ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_conv_add_uminus
% 2.39/2.78 thf(fact_3250_diff__conv__add__uminus,axiom,
% 2.39/2.78 ( minus_minus_rat
% 2.39/2.78 = ( ^ [A2: rat,B2: rat] : ( plus_plus_rat @ A2 @ ( uminus_uminus_rat @ B2 ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_conv_add_uminus
% 2.39/2.78 thf(fact_3251_diff__conv__add__uminus,axiom,
% 2.39/2.78 ( minus_8373710615458151222nteger
% 2.39/2.78 = ( ^ [A2: code_integer,B2: code_integer] : ( plus_p5714425477246183910nteger @ A2 @ ( uminus1351360451143612070nteger @ B2 ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_conv_add_uminus
% 2.39/2.78 thf(fact_3252_group__cancel_Osub2,axiom,
% 2.39/2.78 ! [B3: int,K: int,B: int,A: int] :
% 2.39/2.78 ( ( B3
% 2.39/2.78 = ( plus_plus_int @ K @ B ) )
% 2.39/2.78 => ( ( minus_minus_int @ A @ B3 )
% 2.39/2.78 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % group_cancel.sub2
% 2.39/2.78 thf(fact_3253_group__cancel_Osub2,axiom,
% 2.39/2.78 ! [B3: rat,K: rat,B: rat,A: rat] :
% 2.39/2.78 ( ( B3
% 2.39/2.78 = ( plus_plus_rat @ K @ B ) )
% 2.39/2.78 => ( ( minus_minus_rat @ A @ B3 )
% 2.39/2.78 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % group_cancel.sub2
% 2.39/2.78 thf(fact_3254_group__cancel_Osub2,axiom,
% 2.39/2.78 ! [B3: code_integer,K: code_integer,B: code_integer,A: code_integer] :
% 2.39/2.78 ( ( B3
% 2.39/2.78 = ( plus_p5714425477246183910nteger @ K @ B ) )
% 2.39/2.78 => ( ( minus_8373710615458151222nteger @ A @ B3 )
% 2.39/2.78 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % group_cancel.sub2
% 2.39/2.78 thf(fact_3255_diff__eq,axiom,
% 2.39/2.78 ( minus_1356011639430497352at_nat
% 2.39/2.78 = ( ^ [X2: set_Pr1261947904930325089at_nat,Y2: set_Pr1261947904930325089at_nat] : ( inf_in2572325071724192079at_nat @ X2 @ ( uminus6524753893492686040at_nat @ Y2 ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_eq
% 2.39/2.78 thf(fact_3256_diff__eq,axiom,
% 2.39/2.78 ( minus_minus_set_nat
% 2.39/2.78 = ( ^ [X2: set_nat,Y2: set_nat] : ( inf_inf_set_nat @ X2 @ ( uminus5710092332889474511et_nat @ Y2 ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_eq
% 2.39/2.78 thf(fact_3257_diff__eq,axiom,
% 2.39/2.78 ( minus_711738161318947805_int_o
% 2.39/2.78 = ( ^ [X2: product_prod_int_int > $o,Y2: product_prod_int_int > $o] : ( inf_in3604695632404883862_int_o @ X2 @ ( uminus7117520113953359693_int_o @ Y2 ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_eq
% 2.39/2.78 thf(fact_3258_diff__eq,axiom,
% 2.39/2.78 ( minus_minus_assn
% 2.39/2.78 = ( ^ [X2: assn,Y2: assn] : ( inf_inf_assn @ X2 @ ( uminus_uminus_assn @ Y2 ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_eq
% 2.39/2.78 thf(fact_3259_one__le__numeral,axiom,
% 2.39/2.78 ! [N: num] : ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N ) ) ).
% 2.39/2.78
% 2.39/2.78 % one_le_numeral
% 2.39/2.78 thf(fact_3260_one__le__numeral,axiom,
% 2.39/2.78 ! [N: num] : ( ord_le1926595141338095240atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ N ) ) ).
% 2.39/2.78
% 2.39/2.78 % one_le_numeral
% 2.39/2.78 thf(fact_3261_one__le__numeral,axiom,
% 2.39/2.78 ! [N: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) ) ).
% 2.39/2.78
% 2.39/2.78 % one_le_numeral
% 2.39/2.78 thf(fact_3262_one__le__numeral,axiom,
% 2.39/2.78 ! [N: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) ) ).
% 2.39/2.78
% 2.39/2.78 % one_le_numeral
% 2.39/2.78 thf(fact_3263_one__le__numeral,axiom,
% 2.39/2.78 ! [N: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N ) ) ).
% 2.39/2.78
% 2.39/2.78 % one_le_numeral
% 2.39/2.78 thf(fact_3264_not__numeral__less__one,axiom,
% 2.39/2.78 ! [N: num] :
% 2.39/2.78 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat ) ).
% 2.39/2.78
% 2.39/2.78 % not_numeral_less_one
% 2.39/2.78 thf(fact_3265_not__numeral__less__one,axiom,
% 2.39/2.78 ! [N: num] :
% 2.39/2.78 ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ).
% 2.39/2.78
% 2.39/2.78 % not_numeral_less_one
% 2.39/2.78 thf(fact_3266_not__numeral__less__one,axiom,
% 2.39/2.78 ! [N: num] :
% 2.39/2.78 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat ) ).
% 2.39/2.78
% 2.39/2.78 % not_numeral_less_one
% 2.39/2.78 thf(fact_3267_not__numeral__less__one,axiom,
% 2.39/2.78 ! [N: num] :
% 2.39/2.78 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ N ) @ one_one_Code_integer ) ).
% 2.39/2.78
% 2.39/2.78 % not_numeral_less_one
% 2.39/2.78 thf(fact_3268_not__numeral__less__one,axiom,
% 2.39/2.78 ! [N: num] :
% 2.39/2.78 ~ ( ord_le5570908160329646204atural @ ( numera5444537566228673987atural @ N ) @ one_one_Code_natural ) ).
% 2.39/2.78
% 2.39/2.78 % not_numeral_less_one
% 2.39/2.78 thf(fact_3269_one__plus__numeral__commute,axiom,
% 2.39/2.78 ! [X: num] :
% 2.39/2.78 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 2.39/2.78 = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 2.39/2.78
% 2.39/2.78 % one_plus_numeral_commute
% 2.39/2.78 thf(fact_3270_one__plus__numeral__commute,axiom,
% 2.39/2.78 ! [X: num] :
% 2.39/2.78 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 2.39/2.78 = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 2.39/2.78
% 2.39/2.78 % one_plus_numeral_commute
% 2.39/2.78 thf(fact_3271_one__plus__numeral__commute,axiom,
% 2.39/2.78 ! [X: num] :
% 2.39/2.78 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ X ) )
% 2.39/2.78 = ( plus_plus_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat ) ) ).
% 2.39/2.78
% 2.39/2.78 % one_plus_numeral_commute
% 2.39/2.78 thf(fact_3272_one__plus__numeral__commute,axiom,
% 2.39/2.78 ! [X: num] :
% 2.39/2.78 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ X ) )
% 2.39/2.78 = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ X ) @ one_one_Code_integer ) ) ).
% 2.39/2.78
% 2.39/2.78 % one_plus_numeral_commute
% 2.39/2.78 thf(fact_3273_one__plus__numeral__commute,axiom,
% 2.39/2.78 ! [X: num] :
% 2.39/2.78 ( ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ X ) )
% 2.39/2.78 = ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ X ) @ one_one_Code_natural ) ) ).
% 2.39/2.78
% 2.39/2.78 % one_plus_numeral_commute
% 2.39/2.78 thf(fact_3274_one__neq__neg__numeral,axiom,
% 2.39/2.78 ! [N: num] :
% 2.39/2.78 ( one_one_int
% 2.39/2.78 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % one_neq_neg_numeral
% 2.39/2.78 thf(fact_3275_one__neq__neg__numeral,axiom,
% 2.39/2.78 ! [N: num] :
% 2.39/2.78 ( one_one_rat
% 2.39/2.78 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % one_neq_neg_numeral
% 2.39/2.78 thf(fact_3276_one__neq__neg__numeral,axiom,
% 2.39/2.78 ! [N: num] :
% 2.39/2.78 ( one_one_Code_integer
% 2.39/2.78 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % one_neq_neg_numeral
% 2.39/2.78 thf(fact_3277_numeral__neq__neg__one,axiom,
% 2.39/2.78 ! [N: num] :
% 2.39/2.78 ( ( numeral_numeral_int @ N )
% 2.39/2.78 != ( uminus_uminus_int @ one_one_int ) ) ).
% 2.39/2.78
% 2.39/2.78 % numeral_neq_neg_one
% 2.39/2.78 thf(fact_3278_numeral__neq__neg__one,axiom,
% 2.39/2.78 ! [N: num] :
% 2.39/2.78 ( ( numeral_numeral_rat @ N )
% 2.39/2.78 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 2.39/2.78
% 2.39/2.78 % numeral_neq_neg_one
% 2.39/2.78 thf(fact_3279_numeral__neq__neg__one,axiom,
% 2.39/2.78 ! [N: num] :
% 2.39/2.78 ( ( numera6620942414471956472nteger @ N )
% 2.39/2.78 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 2.39/2.78
% 2.39/2.78 % numeral_neq_neg_one
% 2.39/2.78 thf(fact_3280_le__add__iff1,axiom,
% 2.39/2.78 ! [A: code_integer,E2: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 2.39/2.78 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E2 ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E2 ) @ D2 ) )
% 2.39/2.78 = ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ E2 ) @ C ) @ D2 ) ) ).
% 2.39/2.78
% 2.39/2.78 % le_add_iff1
% 2.39/2.78 thf(fact_3281_le__add__iff1,axiom,
% 2.39/2.78 ! [A: rat,E2: rat,C: rat,B: rat,D2: rat] :
% 2.39/2.78 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D2 ) )
% 2.39/2.78 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C ) @ D2 ) ) ).
% 2.39/2.78
% 2.39/2.78 % le_add_iff1
% 2.39/2.78 thf(fact_3282_le__add__iff1,axiom,
% 2.39/2.78 ! [A: int,E2: int,C: int,B: int,D2: int] :
% 2.39/2.78 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D2 ) )
% 2.39/2.78 = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C ) @ D2 ) ) ).
% 2.39/2.78
% 2.39/2.78 % le_add_iff1
% 2.39/2.78 thf(fact_3283_le__add__iff2,axiom,
% 2.39/2.78 ! [A: code_integer,E2: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 2.39/2.78 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E2 ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E2 ) @ D2 ) )
% 2.39/2.78 = ( ord_le3102999989581377725nteger @ C @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ E2 ) @ D2 ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % le_add_iff2
% 2.39/2.78 thf(fact_3284_le__add__iff2,axiom,
% 2.39/2.78 ! [A: rat,E2: rat,C: rat,B: rat,D2: rat] :
% 2.39/2.78 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D2 ) )
% 2.39/2.78 = ( ord_less_eq_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D2 ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % le_add_iff2
% 2.39/2.78 thf(fact_3285_le__add__iff2,axiom,
% 2.39/2.78 ! [A: int,E2: int,C: int,B: int,D2: int] :
% 2.39/2.78 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D2 ) )
% 2.39/2.78 = ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D2 ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % le_add_iff2
% 2.39/2.78 thf(fact_3286_less__add__iff1,axiom,
% 2.39/2.78 ! [A: code_integer,E2: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 2.39/2.78 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E2 ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E2 ) @ D2 ) )
% 2.39/2.78 = ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ E2 ) @ C ) @ D2 ) ) ).
% 2.39/2.78
% 2.39/2.78 % less_add_iff1
% 2.39/2.78 thf(fact_3287_less__add__iff1,axiom,
% 2.39/2.78 ! [A: rat,E2: rat,C: rat,B: rat,D2: rat] :
% 2.39/2.78 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D2 ) )
% 2.39/2.78 = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C ) @ D2 ) ) ).
% 2.39/2.78
% 2.39/2.78 % less_add_iff1
% 2.39/2.78 thf(fact_3288_less__add__iff1,axiom,
% 2.39/2.78 ! [A: int,E2: int,C: int,B: int,D2: int] :
% 2.39/2.78 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D2 ) )
% 2.39/2.78 = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C ) @ D2 ) ) ).
% 2.39/2.78
% 2.39/2.78 % less_add_iff1
% 2.39/2.78 thf(fact_3289_less__add__iff2,axiom,
% 2.39/2.78 ! [A: code_integer,E2: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 2.39/2.78 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E2 ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E2 ) @ D2 ) )
% 2.39/2.78 = ( ord_le6747313008572928689nteger @ C @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ E2 ) @ D2 ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % less_add_iff2
% 2.39/2.78 thf(fact_3290_less__add__iff2,axiom,
% 2.39/2.78 ! [A: rat,E2: rat,C: rat,B: rat,D2: rat] :
% 2.39/2.78 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D2 ) )
% 2.39/2.78 = ( ord_less_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D2 ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % less_add_iff2
% 2.39/2.78 thf(fact_3291_less__add__iff2,axiom,
% 2.39/2.78 ! [A: int,E2: int,C: int,B: int,D2: int] :
% 2.39/2.78 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D2 ) )
% 2.39/2.78 = ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D2 ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % less_add_iff2
% 2.39/2.78 thf(fact_3292_square__diff__one__factored,axiom,
% 2.39/2.78 ! [X: rat] :
% 2.39/2.78 ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ one_one_rat )
% 2.39/2.78 = ( times_times_rat @ ( plus_plus_rat @ X @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % square_diff_one_factored
% 2.39/2.78 thf(fact_3293_square__diff__one__factored,axiom,
% 2.39/2.78 ! [X: int] :
% 2.39/2.78 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ one_one_int )
% 2.39/2.78 = ( times_times_int @ ( plus_plus_int @ X @ one_one_int ) @ ( minus_minus_int @ X @ one_one_int ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % square_diff_one_factored
% 2.39/2.78 thf(fact_3294_square__diff__one__factored,axiom,
% 2.39/2.78 ! [X: code_integer] :
% 2.39/2.78 ( ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ X @ X ) @ one_one_Code_integer )
% 2.39/2.78 = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ X @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ X @ one_one_Code_integer ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % square_diff_one_factored
% 2.39/2.78 thf(fact_3295_divide__diff__eq__iff,axiom,
% 2.39/2.78 ! [Z: rat,X: rat,Y: rat] :
% 2.39/2.78 ( ( Z != zero_zero_rat )
% 2.39/2.78 => ( ( minus_minus_rat @ ( divide_divide_rat @ X @ Z ) @ Y )
% 2.39/2.78 = ( divide_divide_rat @ ( minus_minus_rat @ X @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % divide_diff_eq_iff
% 2.39/2.78 thf(fact_3296_diff__divide__eq__iff,axiom,
% 2.39/2.78 ! [Z: rat,X: rat,Y: rat] :
% 2.39/2.78 ( ( Z != zero_zero_rat )
% 2.39/2.78 => ( ( minus_minus_rat @ X @ ( divide_divide_rat @ Y @ Z ) )
% 2.39/2.78 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_divide_eq_iff
% 2.39/2.78 thf(fact_3297_diff__frac__eq,axiom,
% 2.39/2.78 ! [Y: rat,Z: rat,X: rat,W: rat] :
% 2.39/2.78 ( ( Y != zero_zero_rat )
% 2.39/2.78 => ( ( Z != zero_zero_rat )
% 2.39/2.78 => ( ( minus_minus_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 2.39/2.78 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % diff_frac_eq
% 2.39/2.78 thf(fact_3298_add__divide__eq__if__simps_I4_J,axiom,
% 2.39/2.78 ! [Z: rat,A: rat,B: rat] :
% 2.39/2.78 ( ( ( Z = zero_zero_rat )
% 2.39/2.78 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 2.39/2.78 = A ) )
% 2.39/2.78 & ( ( Z != zero_zero_rat )
% 2.39/2.78 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 2.39/2.78 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % add_divide_eq_if_simps(4)
% 2.39/2.78 thf(fact_3299_not__one__le__neg__numeral,axiom,
% 2.39/2.78 ! [M2: num] :
% 2.39/2.78 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % not_one_le_neg_numeral
% 2.39/2.78 thf(fact_3300_not__one__le__neg__numeral,axiom,
% 2.39/2.78 ! [M2: num] :
% 2.39/2.78 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % not_one_le_neg_numeral
% 2.39/2.78 thf(fact_3301_not__one__le__neg__numeral,axiom,
% 2.39/2.78 ! [M2: num] :
% 2.39/2.78 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % not_one_le_neg_numeral
% 2.39/2.78 thf(fact_3302_not__numeral__le__neg__one,axiom,
% 2.39/2.78 ! [M2: num] :
% 2.39/2.78 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 2.39/2.78
% 2.39/2.78 % not_numeral_le_neg_one
% 2.39/2.78 thf(fact_3303_not__numeral__le__neg__one,axiom,
% 2.39/2.78 ! [M2: num] :
% 2.39/2.78 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 2.39/2.78
% 2.39/2.78 % not_numeral_le_neg_one
% 2.39/2.78 thf(fact_3304_not__numeral__le__neg__one,axiom,
% 2.39/2.78 ! [M2: num] :
% 2.39/2.78 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 2.39/2.78
% 2.39/2.78 % not_numeral_le_neg_one
% 2.39/2.78 thf(fact_3305_neg__numeral__le__neg__one,axiom,
% 2.39/2.78 ! [M2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 2.39/2.78
% 2.39/2.78 % neg_numeral_le_neg_one
% 2.39/2.78 thf(fact_3306_neg__numeral__le__neg__one,axiom,
% 2.39/2.78 ! [M2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 2.39/2.78
% 2.39/2.78 % neg_numeral_le_neg_one
% 2.39/2.78 thf(fact_3307_neg__numeral__le__neg__one,axiom,
% 2.39/2.78 ! [M2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 2.39/2.78
% 2.39/2.78 % neg_numeral_le_neg_one
% 2.39/2.78 thf(fact_3308_neg__one__le__numeral,axiom,
% 2.39/2.78 ! [M2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M2 ) ) ).
% 2.39/2.78
% 2.39/2.78 % neg_one_le_numeral
% 2.39/2.78 thf(fact_3309_neg__one__le__numeral,axiom,
% 2.39/2.78 ! [M2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M2 ) ) ).
% 2.39/2.78
% 2.39/2.78 % neg_one_le_numeral
% 2.39/2.78 thf(fact_3310_neg__one__le__numeral,axiom,
% 2.39/2.78 ! [M2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M2 ) ) ).
% 2.39/2.78
% 2.39/2.78 % neg_one_le_numeral
% 2.39/2.78 thf(fact_3311_neg__numeral__le__one,axiom,
% 2.39/2.78 ! [M2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ one_one_Code_integer ) ).
% 2.39/2.78
% 2.39/2.78 % neg_numeral_le_one
% 2.39/2.78 thf(fact_3312_neg__numeral__le__one,axiom,
% 2.39/2.78 ! [M2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ one_one_rat ) ).
% 2.39/2.78
% 2.39/2.78 % neg_numeral_le_one
% 2.39/2.78 thf(fact_3313_neg__numeral__le__one,axiom,
% 2.39/2.78 ! [M2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int ) ).
% 2.39/2.78
% 2.39/2.78 % neg_numeral_le_one
% 2.39/2.78 thf(fact_3314_divide__eq__eq__numeral_I1_J,axiom,
% 2.39/2.78 ! [B: rat,C: rat,W: num] :
% 2.39/2.78 ( ( ( divide_divide_rat @ B @ C )
% 2.39/2.78 = ( numeral_numeral_rat @ W ) )
% 2.39/2.78 = ( ( ( C != zero_zero_rat )
% 2.39/2.78 => ( B
% 2.39/2.78 = ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 2.39/2.78 & ( ( C = zero_zero_rat )
% 2.39/2.78 => ( ( numeral_numeral_rat @ W )
% 2.39/2.78 = zero_zero_rat ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % divide_eq_eq_numeral(1)
% 2.39/2.78 thf(fact_3315_eq__divide__eq__numeral_I1_J,axiom,
% 2.39/2.78 ! [W: num,B: rat,C: rat] :
% 2.39/2.78 ( ( ( numeral_numeral_rat @ W )
% 2.39/2.78 = ( divide_divide_rat @ B @ C ) )
% 2.39/2.78 = ( ( ( C != zero_zero_rat )
% 2.39/2.78 => ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C )
% 2.39/2.78 = B ) )
% 2.39/2.78 & ( ( C = zero_zero_rat )
% 2.39/2.78 => ( ( numeral_numeral_rat @ W )
% 2.39/2.78 = zero_zero_rat ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % eq_divide_eq_numeral(1)
% 2.39/2.78 thf(fact_3316_not__neg__one__less__neg__numeral,axiom,
% 2.39/2.78 ! [M2: num] :
% 2.39/2.78 ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % not_neg_one_less_neg_numeral
% 2.39/2.78 thf(fact_3317_not__neg__one__less__neg__numeral,axiom,
% 2.39/2.78 ! [M2: num] :
% 2.39/2.78 ~ ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % not_neg_one_less_neg_numeral
% 2.39/2.78 thf(fact_3318_not__neg__one__less__neg__numeral,axiom,
% 2.39/2.78 ! [M2: num] :
% 2.39/2.78 ~ ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % not_neg_one_less_neg_numeral
% 2.39/2.78 thf(fact_3319_not__one__less__neg__numeral,axiom,
% 2.39/2.78 ! [M2: num] :
% 2.39/2.78 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % not_one_less_neg_numeral
% 2.39/2.78 thf(fact_3320_not__one__less__neg__numeral,axiom,
% 2.39/2.78 ! [M2: num] :
% 2.39/2.78 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % not_one_less_neg_numeral
% 2.39/2.78 thf(fact_3321_not__one__less__neg__numeral,axiom,
% 2.39/2.78 ! [M2: num] :
% 2.39/2.78 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % not_one_less_neg_numeral
% 2.39/2.78 thf(fact_3322_not__numeral__less__neg__one,axiom,
% 2.39/2.78 ! [M2: num] :
% 2.39/2.78 ~ ( ord_less_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 2.39/2.78
% 2.39/2.78 % not_numeral_less_neg_one
% 2.39/2.78 thf(fact_3323_not__numeral__less__neg__one,axiom,
% 2.39/2.78 ! [M2: num] :
% 2.39/2.78 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 2.39/2.78
% 2.39/2.78 % not_numeral_less_neg_one
% 2.39/2.78 thf(fact_3324_not__numeral__less__neg__one,axiom,
% 2.39/2.78 ! [M2: num] :
% 2.39/2.78 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 2.39/2.78
% 2.39/2.78 % not_numeral_less_neg_one
% 2.39/2.78 thf(fact_3325_neg__one__less__numeral,axiom,
% 2.39/2.78 ! [M2: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M2 ) ) ).
% 2.39/2.78
% 2.39/2.78 % neg_one_less_numeral
% 2.39/2.78 thf(fact_3326_neg__one__less__numeral,axiom,
% 2.39/2.78 ! [M2: num] : ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M2 ) ) ).
% 2.39/2.78
% 2.39/2.78 % neg_one_less_numeral
% 2.39/2.78 thf(fact_3327_neg__one__less__numeral,axiom,
% 2.39/2.78 ! [M2: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M2 ) ) ).
% 2.39/2.78
% 2.39/2.78 % neg_one_less_numeral
% 2.39/2.78 thf(fact_3328_neg__numeral__less__one,axiom,
% 2.39/2.78 ! [M2: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int ) ).
% 2.39/2.78
% 2.39/2.78 % neg_numeral_less_one
% 2.39/2.78 thf(fact_3329_neg__numeral__less__one,axiom,
% 2.39/2.78 ! [M2: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ one_one_rat ) ).
% 2.39/2.78
% 2.39/2.78 % neg_numeral_less_one
% 2.39/2.78 thf(fact_3330_neg__numeral__less__one,axiom,
% 2.39/2.78 ! [M2: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ one_one_Code_integer ) ).
% 2.39/2.78
% 2.39/2.78 % neg_numeral_less_one
% 2.39/2.78 thf(fact_3331_dbl__dec__def,axiom,
% 2.39/2.78 ( neg_nu3179335615603231917ec_rat
% 2.39/2.78 = ( ^ [X2: rat] : ( minus_minus_rat @ ( plus_plus_rat @ X2 @ X2 ) @ one_one_rat ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % dbl_dec_def
% 2.39/2.78 thf(fact_3332_dbl__dec__def,axiom,
% 2.39/2.78 ( neg_nu3811975205180677377ec_int
% 2.39/2.78 = ( ^ [X2: int] : ( minus_minus_int @ ( plus_plus_int @ X2 @ X2 ) @ one_one_int ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % dbl_dec_def
% 2.39/2.78 thf(fact_3333_dbl__dec__def,axiom,
% 2.39/2.78 ( neg_nu7757733837767384882nteger
% 2.39/2.78 = ( ^ [X2: code_integer] : ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ X2 @ X2 ) @ one_one_Code_integer ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % dbl_dec_def
% 2.39/2.78 thf(fact_3334_frac__le__eq,axiom,
% 2.39/2.78 ! [Y: rat,Z: rat,X: rat,W: rat] :
% 2.39/2.78 ( ( Y != zero_zero_rat )
% 2.39/2.78 => ( ( Z != zero_zero_rat )
% 2.39/2.78 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 2.39/2.78 = ( ord_less_eq_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % frac_le_eq
% 2.39/2.78 thf(fact_3335_frac__less__eq,axiom,
% 2.39/2.78 ! [Y: rat,Z: rat,X: rat,W: rat] :
% 2.39/2.78 ( ( Y != zero_zero_rat )
% 2.39/2.78 => ( ( Z != zero_zero_rat )
% 2.39/2.78 => ( ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 2.39/2.78 = ( ord_less_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % frac_less_eq
% 2.39/2.78 thf(fact_3336_minus__divide__diff__eq__iff,axiom,
% 2.39/2.78 ! [Z: rat,X: rat,Y: rat] :
% 2.39/2.78 ( ( Z != zero_zero_rat )
% 2.39/2.78 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z ) ) @ Y )
% 2.39/2.78 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % minus_divide_diff_eq_iff
% 2.39/2.78 thf(fact_3337_add__divide__eq__if__simps_I5_J,axiom,
% 2.39/2.78 ! [Z: rat,A: rat,B: rat] :
% 2.39/2.78 ( ( ( Z = zero_zero_rat )
% 2.39/2.78 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 2.39/2.78 = ( uminus_uminus_rat @ B ) ) )
% 2.39/2.78 & ( ( Z != zero_zero_rat )
% 2.39/2.78 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 2.39/2.78 = ( divide_divide_rat @ ( minus_minus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % add_divide_eq_if_simps(5)
% 2.39/2.78 thf(fact_3338_add__divide__eq__if__simps_I6_J,axiom,
% 2.39/2.78 ! [Z: rat,A: rat,B: rat] :
% 2.39/2.78 ( ( ( Z = zero_zero_rat )
% 2.39/2.78 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 2.39/2.78 = ( uminus_uminus_rat @ B ) ) )
% 2.39/2.78 & ( ( Z != zero_zero_rat )
% 2.39/2.78 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 2.39/2.78 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % add_divide_eq_if_simps(6)
% 2.39/2.78 thf(fact_3339_count__list_Osimps_I1_J,axiom,
% 2.39/2.78 ! [Y: produc6575502325842934193n_assn] :
% 2.39/2.78 ( ( count_2530312006313534765n_assn @ nil_Pr5671120429643327159n_assn @ Y )
% 2.39/2.78 = zero_zero_nat ) ).
% 2.39/2.78
% 2.39/2.78 % count_list.simps(1)
% 2.39/2.78 thf(fact_3340_count__list_Osimps_I1_J,axiom,
% 2.39/2.78 ! [Y: int] :
% 2.39/2.78 ( ( count_list_int @ nil_int @ Y )
% 2.39/2.78 = zero_zero_nat ) ).
% 2.39/2.78
% 2.39/2.78 % count_list.simps(1)
% 2.39/2.78 thf(fact_3341_count__list_Osimps_I1_J,axiom,
% 2.39/2.78 ! [Y: nat] :
% 2.39/2.78 ( ( count_list_nat @ nil_nat @ Y )
% 2.39/2.78 = zero_zero_nat ) ).
% 2.39/2.78
% 2.39/2.78 % count_list.simps(1)
% 2.39/2.78 thf(fact_3342_divide__less__eq__numeral_I1_J,axiom,
% 2.39/2.78 ! [B: rat,C: rat,W: num] :
% 2.39/2.78 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 2.39/2.78 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.78 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 2.39/2.78 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.78 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.78 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 2.39/2.78 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.78 => ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % divide_less_eq_numeral(1)
% 2.39/2.78 thf(fact_3343_less__divide__eq__numeral_I1_J,axiom,
% 2.39/2.78 ! [W: num,B: rat,C: rat] :
% 2.39/2.78 ( ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 2.39/2.78 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.78 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 2.39/2.78 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.78 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.78 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 2.39/2.78 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.78 => ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % less_divide_eq_numeral(1)
% 2.39/2.78 thf(fact_3344_divide__eq__eq__numeral_I2_J,axiom,
% 2.39/2.78 ! [B: rat,C: rat,W: num] :
% 2.39/2.78 ( ( ( divide_divide_rat @ B @ C )
% 2.39/2.78 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 2.39/2.78 = ( ( ( C != zero_zero_rat )
% 2.39/2.78 => ( B
% 2.39/2.78 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 2.39/2.78 & ( ( C = zero_zero_rat )
% 2.39/2.78 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 2.39/2.78 = zero_zero_rat ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % divide_eq_eq_numeral(2)
% 2.39/2.78 thf(fact_3345_eq__divide__eq__numeral_I2_J,axiom,
% 2.39/2.78 ! [W: num,B: rat,C: rat] :
% 2.39/2.78 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 2.39/2.78 = ( divide_divide_rat @ B @ C ) )
% 2.39/2.78 = ( ( ( C != zero_zero_rat )
% 2.39/2.78 => ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C )
% 2.39/2.78 = B ) )
% 2.39/2.78 & ( ( C = zero_zero_rat )
% 2.39/2.78 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 2.39/2.78 = zero_zero_rat ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % eq_divide_eq_numeral(2)
% 2.39/2.78 thf(fact_3346_mult__eq__if,axiom,
% 2.39/2.78 ( times_times_nat
% 2.39/2.78 = ( ^ [M3: nat,N3: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N3 @ ( times_times_nat @ ( minus_minus_nat @ M3 @ one_one_nat ) @ N3 ) ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % mult_eq_if
% 2.39/2.78 thf(fact_3347_scaling__mono,axiom,
% 2.39/2.78 ! [U: rat,V2: rat,R2: rat,S3: rat] :
% 2.39/2.78 ( ( ord_less_eq_rat @ U @ V2 )
% 2.39/2.78 => ( ( ord_less_eq_rat @ zero_zero_rat @ R2 )
% 2.39/2.78 => ( ( ord_less_eq_rat @ R2 @ S3 )
% 2.39/2.78 => ( ord_less_eq_rat @ ( plus_plus_rat @ U @ ( divide_divide_rat @ ( times_times_rat @ R2 @ ( minus_minus_rat @ V2 @ U ) ) @ S3 ) ) @ V2 ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % scaling_mono
% 2.39/2.78 thf(fact_3348_divide__le__eq__numeral_I1_J,axiom,
% 2.39/2.78 ! [B: rat,C: rat,W: num] :
% 2.39/2.78 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 2.39/2.78 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.78 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 2.39/2.78 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.78 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.78 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 2.39/2.78 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.78 => ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % divide_le_eq_numeral(1)
% 2.39/2.78 thf(fact_3349_le__divide__eq__numeral_I1_J,axiom,
% 2.39/2.78 ! [W: num,B: rat,C: rat] :
% 2.39/2.78 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 2.39/2.78 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.78 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 2.39/2.78 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.78 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.78 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 2.39/2.78 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.78 => ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % le_divide_eq_numeral(1)
% 2.39/2.78 thf(fact_3350_less__divide__eq__numeral_I2_J,axiom,
% 2.39/2.78 ! [W: num,B: rat,C: rat] :
% 2.39/2.78 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 2.39/2.78 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.78 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 2.39/2.78 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.78 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.78 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 2.39/2.78 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.78 => ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % less_divide_eq_numeral(2)
% 2.39/2.78 thf(fact_3351_divide__less__eq__numeral_I2_J,axiom,
% 2.39/2.78 ! [B: rat,C: rat,W: num] :
% 2.39/2.78 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 2.39/2.78 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.78 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 2.39/2.78 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 2.39/2.78 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.78 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 2.39/2.78 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 2.39/2.78 => ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % divide_less_eq_numeral(2)
% 2.39/2.78 thf(fact_3352_power__diff__power__eq,axiom,
% 2.39/2.78 ! [A: code_integer,N: nat,M2: nat] :
% 2.39/2.78 ( ( A != zero_z3403309356797280102nteger )
% 2.39/2.78 => ( ( ( ord_less_eq_nat @ N @ M2 )
% 2.39/2.78 => ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M2 ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 2.39/2.78 = ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ M2 @ N ) ) ) )
% 2.39/2.78 & ( ~ ( ord_less_eq_nat @ N @ M2 )
% 2.39/2.78 => ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M2 ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 2.39/2.78 = ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % power_diff_power_eq
% 2.39/2.78 thf(fact_3353_power__diff__power__eq,axiom,
% 2.39/2.78 ! [A: nat,N: nat,M2: nat] :
% 2.39/2.78 ( ( A != zero_zero_nat )
% 2.39/2.78 => ( ( ( ord_less_eq_nat @ N @ M2 )
% 2.39/2.78 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N ) )
% 2.39/2.78 = ( power_power_nat @ A @ ( minus_minus_nat @ M2 @ N ) ) ) )
% 2.39/2.78 & ( ~ ( ord_less_eq_nat @ N @ M2 )
% 2.39/2.78 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N ) )
% 2.39/2.78 = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % power_diff_power_eq
% 2.39/2.78 thf(fact_3354_power__diff__power__eq,axiom,
% 2.39/2.78 ! [A: int,N: nat,M2: nat] :
% 2.39/2.78 ( ( A != zero_zero_int )
% 2.39/2.78 => ( ( ( ord_less_eq_nat @ N @ M2 )
% 2.39/2.78 => ( ( divide_divide_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N ) )
% 2.39/2.78 = ( power_power_int @ A @ ( minus_minus_nat @ M2 @ N ) ) ) )
% 2.39/2.78 & ( ~ ( ord_less_eq_nat @ N @ M2 )
% 2.39/2.78 => ( ( divide_divide_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N ) )
% 2.39/2.78 = ( divide_divide_int @ one_one_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % power_diff_power_eq
% 2.39/2.78 thf(fact_3355_power__diff__power__eq,axiom,
% 2.39/2.78 ! [A: code_natural,N: nat,M2: nat] :
% 2.39/2.78 ( ( A != zero_z2226904508553997617atural )
% 2.39/2.78 => ( ( ( ord_less_eq_nat @ N @ M2 )
% 2.39/2.78 => ( ( divide5121882707175180666atural @ ( power_7079662738309270450atural @ A @ M2 ) @ ( power_7079662738309270450atural @ A @ N ) )
% 2.39/2.78 = ( power_7079662738309270450atural @ A @ ( minus_minus_nat @ M2 @ N ) ) ) )
% 2.39/2.78 & ( ~ ( ord_less_eq_nat @ N @ M2 )
% 2.39/2.78 => ( ( divide5121882707175180666atural @ ( power_7079662738309270450atural @ A @ M2 ) @ ( power_7079662738309270450atural @ A @ N ) )
% 2.39/2.78 = ( divide5121882707175180666atural @ one_one_Code_natural @ ( power_7079662738309270450atural @ A @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % power_diff_power_eq
% 2.39/2.78 thf(fact_3356_power__eq__if,axiom,
% 2.39/2.78 ( power_power_rat
% 2.39/2.78 = ( ^ [P6: rat,M3: nat] : ( if_rat @ ( M3 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ P6 @ ( power_power_rat @ P6 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % power_eq_if
% 2.39/2.78 thf(fact_3357_power__eq__if,axiom,
% 2.39/2.78 ( power_power_assn
% 2.39/2.78 = ( ^ [P6: assn,M3: nat] : ( if_assn @ ( M3 = zero_zero_nat ) @ one_one_assn @ ( times_times_assn @ P6 @ ( power_power_assn @ P6 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % power_eq_if
% 2.39/2.78 thf(fact_3358_power__eq__if,axiom,
% 2.39/2.78 ( power_power_nat
% 2.39/2.78 = ( ^ [P6: nat,M3: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P6 @ ( power_power_nat @ P6 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % power_eq_if
% 2.39/2.78 thf(fact_3359_power__eq__if,axiom,
% 2.39/2.78 ( power_power_int
% 2.39/2.78 = ( ^ [P6: int,M3: nat] : ( if_int @ ( M3 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P6 @ ( power_power_int @ P6 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % power_eq_if
% 2.39/2.78 thf(fact_3360_power__eq__if,axiom,
% 2.39/2.78 ( power_8256067586552552935nteger
% 2.39/2.78 = ( ^ [P6: code_integer,M3: nat] : ( if_Code_integer @ ( M3 = zero_zero_nat ) @ one_one_Code_integer @ ( times_3573771949741848930nteger @ P6 @ ( power_8256067586552552935nteger @ P6 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % power_eq_if
% 2.39/2.78 thf(fact_3361_power__eq__if,axiom,
% 2.39/2.78 ( power_7079662738309270450atural
% 2.39/2.78 = ( ^ [P6: code_natural,M3: nat] : ( if_Code_natural @ ( M3 = zero_zero_nat ) @ one_one_Code_natural @ ( times_2397367101498566445atural @ P6 @ ( power_7079662738309270450atural @ P6 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % power_eq_if
% 2.39/2.78 thf(fact_3362_semiring__norm_I170_J,axiom,
% 2.39/2.78 ! [V2: num,W: num,Y: int] :
% 2.39/2.78 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V2 ) ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Y ) )
% 2.39/2.78 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V2 @ W ) ) ) @ Y ) ) ).
% 2.39/2.78
% 2.39/2.78 % semiring_norm(170)
% 2.39/2.78 thf(fact_3363_semiring__norm_I170_J,axiom,
% 2.39/2.78 ! [V2: num,W: num,Y: rat] :
% 2.39/2.78 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V2 ) ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Y ) )
% 2.39/2.78 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V2 @ W ) ) ) @ Y ) ) ).
% 2.39/2.78
% 2.39/2.78 % semiring_norm(170)
% 2.39/2.78 thf(fact_3364_semiring__norm_I170_J,axiom,
% 2.39/2.78 ! [V2: num,W: num,Y: code_integer] :
% 2.39/2.78 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V2 ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ Y ) )
% 2.39/2.78 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V2 @ W ) ) ) @ Y ) ) ).
% 2.39/2.78
% 2.39/2.78 % semiring_norm(170)
% 2.39/2.78 thf(fact_3365_semiring__norm_I171_J,axiom,
% 2.39/2.78 ! [V2: num,W: num,Y: int] :
% 2.39/2.78 ( ( times_times_int @ ( numeral_numeral_int @ V2 ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 2.39/2.78 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V2 @ W ) ) ) @ Y ) ) ).
% 2.39/2.78
% 2.39/2.78 % semiring_norm(171)
% 2.39/2.78 thf(fact_3366_semiring__norm_I171_J,axiom,
% 2.39/2.78 ! [V2: num,W: num,Y: rat] :
% 2.39/2.78 ( ( times_times_rat @ ( numeral_numeral_rat @ V2 ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 2.39/2.78 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V2 @ W ) ) ) @ Y ) ) ).
% 2.39/2.78
% 2.39/2.78 % semiring_norm(171)
% 2.39/2.78 thf(fact_3367_semiring__norm_I171_J,axiom,
% 2.39/2.78 ! [V2: num,W: num,Y: code_integer] :
% 2.39/2.78 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V2 ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 2.39/2.78 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V2 @ W ) ) ) @ Y ) ) ).
% 2.39/2.78
% 2.39/2.78 % semiring_norm(171)
% 2.39/2.78 thf(fact_3368_semiring__norm_I172_J,axiom,
% 2.39/2.78 ! [V2: num,W: num,Y: int] :
% 2.39/2.78 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V2 ) ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 2.39/2.78 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V2 @ W ) ) @ Y ) ) ).
% 2.39/2.78
% 2.39/2.78 % semiring_norm(172)
% 2.39/2.78 thf(fact_3369_semiring__norm_I172_J,axiom,
% 2.39/2.78 ! [V2: num,W: num,Y: rat] :
% 2.39/2.78 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V2 ) ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 2.39/2.78 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V2 @ W ) ) @ Y ) ) ).
% 2.39/2.78
% 2.39/2.78 % semiring_norm(172)
% 2.39/2.78 thf(fact_3370_semiring__norm_I172_J,axiom,
% 2.39/2.78 ! [V2: num,W: num,Y: code_integer] :
% 2.39/2.78 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V2 ) ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 2.39/2.78 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V2 @ W ) ) @ Y ) ) ).
% 2.39/2.78
% 2.39/2.78 % semiring_norm(172)
% 2.39/2.78 thf(fact_3371_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 2.39/2.78 ! [K: nat,N: nat] :
% 2.39/2.78 ( ( ord_less_eq_nat @ K @ N )
% 2.39/2.78 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N @ K ) )
% 2.39/2.78 = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % neg_one_power_add_eq_neg_one_power_diff
% 2.39/2.78 thf(fact_3372_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 2.39/2.78 ! [K: nat,N: nat] :
% 2.39/2.78 ( ( ord_less_eq_nat @ K @ N )
% 2.39/2.78 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N @ K ) )
% 2.39/2.78 = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % neg_one_power_add_eq_neg_one_power_diff
% 2.39/2.78 thf(fact_3373_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 2.39/2.78 ! [K: nat,N: nat] :
% 2.39/2.78 ( ( ord_less_eq_nat @ K @ N )
% 2.39/2.78 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( plus_plus_nat @ N @ K ) )
% 2.39/2.78 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % neg_one_power_add_eq_neg_one_power_diff
% 2.39/2.78 thf(fact_3374_numeral__times__minus__swap,axiom,
% 2.39/2.78 ! [W: num,X: int] :
% 2.39/2.78 ( ( times_times_int @ ( numeral_numeral_int @ W ) @ ( uminus_uminus_int @ X ) )
% 2.39/2.78 = ( times_times_int @ X @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % numeral_times_minus_swap
% 2.39/2.78 thf(fact_3375_numeral__times__minus__swap,axiom,
% 2.39/2.78 ! [W: num,X: rat] :
% 2.39/2.78 ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ ( uminus_uminus_rat @ X ) )
% 2.39/2.78 = ( times_times_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % numeral_times_minus_swap
% 2.39/2.78 thf(fact_3376_numeral__times__minus__swap,axiom,
% 2.39/2.78 ! [W: num,X: code_integer] :
% 2.39/2.78 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ ( uminus1351360451143612070nteger @ X ) )
% 2.39/2.78 = ( times_3573771949741848930nteger @ X @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % numeral_times_minus_swap
% 2.39/2.78 thf(fact_3377_slice__Cons,axiom,
% 2.39/2.78 ! [Begin: nat,End: nat,X: int,Xs: list_int] :
% 2.39/2.78 ( ( ( ( Begin = zero_zero_nat )
% 2.39/2.78 & ( ord_less_nat @ zero_zero_nat @ End ) )
% 2.39/2.78 => ( ( slice_int @ Begin @ End @ ( cons_int @ X @ Xs ) )
% 2.39/2.78 = ( cons_int @ X @ ( slice_int @ Begin @ ( minus_minus_nat @ End @ one_one_nat ) @ Xs ) ) ) )
% 2.39/2.78 & ( ~ ( ( Begin = zero_zero_nat )
% 2.39/2.78 & ( ord_less_nat @ zero_zero_nat @ End ) )
% 2.39/2.78 => ( ( slice_int @ Begin @ End @ ( cons_int @ X @ Xs ) )
% 2.39/2.78 = ( slice_int @ ( minus_minus_nat @ Begin @ one_one_nat ) @ ( minus_minus_nat @ End @ one_one_nat ) @ Xs ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % slice_Cons
% 2.39/2.78 thf(fact_3378_slice__Cons,axiom,
% 2.39/2.78 ! [Begin: nat,End: nat,X: nat,Xs: list_nat] :
% 2.39/2.78 ( ( ( ( Begin = zero_zero_nat )
% 2.39/2.78 & ( ord_less_nat @ zero_zero_nat @ End ) )
% 2.39/2.78 => ( ( slice_nat @ Begin @ End @ ( cons_nat @ X @ Xs ) )
% 2.39/2.78 = ( cons_nat @ X @ ( slice_nat @ Begin @ ( minus_minus_nat @ End @ one_one_nat ) @ Xs ) ) ) )
% 2.39/2.78 & ( ~ ( ( Begin = zero_zero_nat )
% 2.39/2.78 & ( ord_less_nat @ zero_zero_nat @ End ) )
% 2.39/2.78 => ( ( slice_nat @ Begin @ End @ ( cons_nat @ X @ Xs ) )
% 2.39/2.78 = ( slice_nat @ ( minus_minus_nat @ Begin @ one_one_nat ) @ ( minus_minus_nat @ End @ one_one_nat ) @ Xs ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % slice_Cons
% 2.39/2.78 thf(fact_3379_inf__period_I1_J,axiom,
% 2.39/2.78 ! [P2: int > $o,D: int,Q2: int > $o] :
% 2.39/2.78 ( ! [X3: int,K2: int] :
% 2.39/2.78 ( ( P2 @ X3 )
% 2.39/2.78 = ( P2 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D ) ) ) )
% 2.39/2.78 => ( ! [X3: int,K2: int] :
% 2.39/2.78 ( ( Q2 @ X3 )
% 2.39/2.78 = ( Q2 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D ) ) ) )
% 2.39/2.78 => ! [X4: int,K3: int] :
% 2.39/2.78 ( ( ( P2 @ X4 )
% 2.39/2.78 & ( Q2 @ X4 ) )
% 2.39/2.78 = ( ( P2 @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D ) ) )
% 2.39/2.78 & ( Q2 @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D ) ) ) ) ) ) ) ).
% 2.39/2.78
% 2.39/2.78 % inf_period(1)
% 2.39/2.78 thf(fact_3380_inf__period_I1_J,axiom,
% 2.39/2.78 ! [P2: code_integer > $o,D: code_integer,Q2: code_integer > $o] :
% 2.39/2.78 ( ! [X3: code_integer,K2: code_integer] :
% 2.39/2.78 ( ( P2 @ X3 )
% 2.39/2.78 = ( P2 @ ( minus_8373710615458151222nteger @ X3 @ ( times_3573771949741848930nteger @ K2 @ D ) ) ) )
% 2.39/2.78 => ( ! [X3: code_integer,K2: code_integer] :
% 2.39/2.78 ( ( Q2 @ X3 )
% 2.39/2.78 = ( Q2 @ ( minus_8373710615458151222nteger @ X3 @ ( times_3573771949741848930nteger @ K2 @ D ) ) ) )
% 2.39/2.78 => ! [X4: code_integer,K3: code_integer] :
% 2.39/2.78 ( ( ( P2 @ X4 )
% 2.39/2.78 & ( Q2 @ X4 ) )
% 2.39/2.78 = ( ( P2 @ ( minus_8373710615458151222nteger @ X4 @ ( times_3573771949741848930nteger @ K3 @ D ) ) )
% 2.39/2.79 & ( Q2 @ ( minus_8373710615458151222nteger @ X4 @ ( times_3573771949741848930nteger @ K3 @ D ) ) ) ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % inf_period(1)
% 2.39/2.79 thf(fact_3381_inf__period_I2_J,axiom,
% 2.39/2.79 ! [P2: int > $o,D: int,Q2: int > $o] :
% 2.39/2.79 ( ! [X3: int,K2: int] :
% 2.39/2.79 ( ( P2 @ X3 )
% 2.39/2.79 = ( P2 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D ) ) ) )
% 2.39/2.79 => ( ! [X3: int,K2: int] :
% 2.39/2.79 ( ( Q2 @ X3 )
% 2.39/2.79 = ( Q2 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D ) ) ) )
% 2.39/2.79 => ! [X4: int,K3: int] :
% 2.39/2.79 ( ( ( P2 @ X4 )
% 2.39/2.79 | ( Q2 @ X4 ) )
% 2.39/2.79 = ( ( P2 @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D ) ) )
% 2.39/2.79 | ( Q2 @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D ) ) ) ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % inf_period(2)
% 2.39/2.79 thf(fact_3382_inf__period_I2_J,axiom,
% 2.39/2.79 ! [P2: code_integer > $o,D: code_integer,Q2: code_integer > $o] :
% 2.39/2.79 ( ! [X3: code_integer,K2: code_integer] :
% 2.39/2.79 ( ( P2 @ X3 )
% 2.39/2.79 = ( P2 @ ( minus_8373710615458151222nteger @ X3 @ ( times_3573771949741848930nteger @ K2 @ D ) ) ) )
% 2.39/2.79 => ( ! [X3: code_integer,K2: code_integer] :
% 2.39/2.79 ( ( Q2 @ X3 )
% 2.39/2.79 = ( Q2 @ ( minus_8373710615458151222nteger @ X3 @ ( times_3573771949741848930nteger @ K2 @ D ) ) ) )
% 2.39/2.79 => ! [X4: code_integer,K3: code_integer] :
% 2.39/2.79 ( ( ( P2 @ X4 )
% 2.39/2.79 | ( Q2 @ X4 ) )
% 2.39/2.79 = ( ( P2 @ ( minus_8373710615458151222nteger @ X4 @ ( times_3573771949741848930nteger @ K3 @ D ) ) )
% 2.39/2.79 | ( Q2 @ ( minus_8373710615458151222nteger @ X4 @ ( times_3573771949741848930nteger @ K3 @ D ) ) ) ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % inf_period(2)
% 2.39/2.79 thf(fact_3383_diff__numeral__special_I5_J,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 2.39/2.79 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % diff_numeral_special(5)
% 2.39/2.79 thf(fact_3384_diff__numeral__special_I5_J,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ N ) )
% 2.39/2.79 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % diff_numeral_special(5)
% 2.39/2.79 thf(fact_3385_diff__numeral__special_I5_J,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ N ) )
% 2.39/2.79 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % diff_numeral_special(5)
% 2.39/2.79 thf(fact_3386_Diff__disjoint,axiom,
% 2.39/2.79 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.79 ( ( inf_in2572325071724192079at_nat @ A3 @ ( minus_1356011639430497352at_nat @ B3 @ A3 ) )
% 2.39/2.79 = bot_bo2099793752762293965at_nat ) ).
% 2.39/2.79
% 2.39/2.79 % Diff_disjoint
% 2.39/2.79 thf(fact_3387_Diff__disjoint,axiom,
% 2.39/2.79 ! [A3: set_nat,B3: set_nat] :
% 2.39/2.79 ( ( inf_inf_set_nat @ A3 @ ( minus_minus_set_nat @ B3 @ A3 ) )
% 2.39/2.79 = bot_bot_set_nat ) ).
% 2.39/2.79
% 2.39/2.79 % Diff_disjoint
% 2.39/2.79 thf(fact_3388_Diff__disjoint,axiom,
% 2.39/2.79 ! [A3: set_int,B3: set_int] :
% 2.39/2.79 ( ( inf_inf_set_int @ A3 @ ( minus_minus_set_int @ B3 @ A3 ) )
% 2.39/2.79 = bot_bot_set_int ) ).
% 2.39/2.79
% 2.39/2.79 % Diff_disjoint
% 2.39/2.79 thf(fact_3389_inter__compl__diff__conv,axiom,
% 2.39/2.79 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.79 ( ( inf_in2572325071724192079at_nat @ A3 @ ( uminus6524753893492686040at_nat @ B3 ) )
% 2.39/2.79 = ( minus_1356011639430497352at_nat @ A3 @ B3 ) ) ).
% 2.39/2.79
% 2.39/2.79 % inter_compl_diff_conv
% 2.39/2.79 thf(fact_3390_inter__compl__diff__conv,axiom,
% 2.39/2.79 ! [A3: set_nat,B3: set_nat] :
% 2.39/2.79 ( ( inf_inf_set_nat @ A3 @ ( uminus5710092332889474511et_nat @ B3 ) )
% 2.39/2.79 = ( minus_minus_set_nat @ A3 @ B3 ) ) ).
% 2.39/2.79
% 2.39/2.79 % inter_compl_diff_conv
% 2.39/2.79 thf(fact_3391_Diff__Compl,axiom,
% 2.39/2.79 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.79 ( ( minus_1356011639430497352at_nat @ A3 @ ( uminus6524753893492686040at_nat @ B3 ) )
% 2.39/2.79 = ( inf_in2572325071724192079at_nat @ A3 @ B3 ) ) ).
% 2.39/2.79
% 2.39/2.79 % Diff_Compl
% 2.39/2.79 thf(fact_3392_Diff__Compl,axiom,
% 2.39/2.79 ! [A3: set_nat,B3: set_nat] :
% 2.39/2.79 ( ( minus_minus_set_nat @ A3 @ ( uminus5710092332889474511et_nat @ B3 ) )
% 2.39/2.79 = ( inf_inf_set_nat @ A3 @ B3 ) ) ).
% 2.39/2.79
% 2.39/2.79 % Diff_Compl
% 2.39/2.79 thf(fact_3393_slice__Nil,axiom,
% 2.39/2.79 ! [Begin: nat,End: nat] :
% 2.39/2.79 ( ( slice_7964966981652229398n_assn @ Begin @ End @ nil_Pr5671120429643327159n_assn )
% 2.39/2.79 = nil_Pr5671120429643327159n_assn ) ).
% 2.39/2.79
% 2.39/2.79 % slice_Nil
% 2.39/2.79 thf(fact_3394_slice__Nil,axiom,
% 2.39/2.79 ! [Begin: nat,End: nat] :
% 2.39/2.79 ( ( slice_int @ Begin @ End @ nil_int )
% 2.39/2.79 = nil_int ) ).
% 2.39/2.79
% 2.39/2.79 % slice_Nil
% 2.39/2.79 thf(fact_3395_slice__Nil,axiom,
% 2.39/2.79 ! [Begin: nat,End: nat] :
% 2.39/2.79 ( ( slice_nat @ Begin @ End @ nil_nat )
% 2.39/2.79 = nil_nat ) ).
% 2.39/2.79
% 2.39/2.79 % slice_Nil
% 2.39/2.79 thf(fact_3396_slice__eq__bounds__empty,axiom,
% 2.39/2.79 ! [I2: nat,Xs: list_P8527749157015355191n_assn] :
% 2.39/2.79 ( ( slice_7964966981652229398n_assn @ I2 @ I2 @ Xs )
% 2.39/2.79 = nil_Pr5671120429643327159n_assn ) ).
% 2.39/2.79
% 2.39/2.79 % slice_eq_bounds_empty
% 2.39/2.79 thf(fact_3397_slice__eq__bounds__empty,axiom,
% 2.39/2.79 ! [I2: nat,Xs: list_int] :
% 2.39/2.79 ( ( slice_int @ I2 @ I2 @ Xs )
% 2.39/2.79 = nil_int ) ).
% 2.39/2.79
% 2.39/2.79 % slice_eq_bounds_empty
% 2.39/2.79 thf(fact_3398_slice__eq__bounds__empty,axiom,
% 2.39/2.79 ! [I2: nat,Xs: list_nat] :
% 2.39/2.79 ( ( slice_nat @ I2 @ I2 @ Xs )
% 2.39/2.79 = nil_nat ) ).
% 2.39/2.79
% 2.39/2.79 % slice_eq_bounds_empty
% 2.39/2.79 thf(fact_3399_add__neg__numeral__special_I6_J,axiom,
% 2.39/2.79 ! [M2: num] :
% 2.39/2.79 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 2.39/2.79 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ M2 ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % add_neg_numeral_special(6)
% 2.39/2.79 thf(fact_3400_add__neg__numeral__special_I6_J,axiom,
% 2.39/2.79 ! [M2: num] :
% 2.39/2.79 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 2.39/2.79 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ M2 ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % add_neg_numeral_special(6)
% 2.39/2.79 thf(fact_3401_add__neg__numeral__special_I6_J,axiom,
% 2.39/2.79 ! [M2: num] :
% 2.39/2.79 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 2.39/2.79 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ M2 ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % add_neg_numeral_special(6)
% 2.39/2.79 thf(fact_3402_add__neg__numeral__special_I5_J,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 2.39/2.79 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % add_neg_numeral_special(5)
% 2.39/2.79 thf(fact_3403_add__neg__numeral__special_I5_J,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 2.39/2.79 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % add_neg_numeral_special(5)
% 2.39/2.79 thf(fact_3404_add__neg__numeral__special_I5_J,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 2.39/2.79 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % add_neg_numeral_special(5)
% 2.39/2.79 thf(fact_3405_diff__numeral__special_I6_J,axiom,
% 2.39/2.79 ! [M2: num] :
% 2.39/2.79 ( ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ one_one_int ) )
% 2.39/2.79 = ( numeral_numeral_int @ ( inc @ M2 ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % diff_numeral_special(6)
% 2.39/2.79 thf(fact_3406_diff__numeral__special_I6_J,axiom,
% 2.39/2.79 ! [M2: num] :
% 2.39/2.79 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 2.39/2.79 = ( numeral_numeral_rat @ ( inc @ M2 ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % diff_numeral_special(6)
% 2.39/2.79 thf(fact_3407_diff__numeral__special_I6_J,axiom,
% 2.39/2.79 ! [M2: num] :
% 2.39/2.79 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 2.39/2.79 = ( numera6620942414471956472nteger @ ( inc @ M2 ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % diff_numeral_special(6)
% 2.39/2.79 thf(fact_3408_Int__Diff,axiom,
% 2.39/2.79 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 2.39/2.79 ( ( minus_1356011639430497352at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) @ C2 )
% 2.39/2.79 = ( inf_in2572325071724192079at_nat @ A3 @ ( minus_1356011639430497352at_nat @ B3 @ C2 ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % Int_Diff
% 2.39/2.79 thf(fact_3409_Int__Diff,axiom,
% 2.39/2.79 ! [A3: set_nat,B3: set_nat,C2: set_nat] :
% 2.39/2.79 ( ( minus_minus_set_nat @ ( inf_inf_set_nat @ A3 @ B3 ) @ C2 )
% 2.39/2.79 = ( inf_inf_set_nat @ A3 @ ( minus_minus_set_nat @ B3 @ C2 ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % Int_Diff
% 2.39/2.79 thf(fact_3410_Diff__Int2,axiom,
% 2.39/2.79 ! [A3: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.79 ( ( minus_1356011639430497352at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ C2 ) @ ( inf_in2572325071724192079at_nat @ B3 @ C2 ) )
% 2.39/2.79 = ( minus_1356011639430497352at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ C2 ) @ B3 ) ) ).
% 2.39/2.79
% 2.39/2.79 % Diff_Int2
% 2.39/2.79 thf(fact_3411_Diff__Int2,axiom,
% 2.39/2.79 ! [A3: set_nat,C2: set_nat,B3: set_nat] :
% 2.39/2.79 ( ( minus_minus_set_nat @ ( inf_inf_set_nat @ A3 @ C2 ) @ ( inf_inf_set_nat @ B3 @ C2 ) )
% 2.39/2.79 = ( minus_minus_set_nat @ ( inf_inf_set_nat @ A3 @ C2 ) @ B3 ) ) ).
% 2.39/2.79
% 2.39/2.79 % Diff_Int2
% 2.39/2.79 thf(fact_3412_Diff__Diff__Int,axiom,
% 2.39/2.79 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.79 ( ( minus_1356011639430497352at_nat @ A3 @ ( minus_1356011639430497352at_nat @ A3 @ B3 ) )
% 2.39/2.79 = ( inf_in2572325071724192079at_nat @ A3 @ B3 ) ) ).
% 2.39/2.79
% 2.39/2.79 % Diff_Diff_Int
% 2.39/2.79 thf(fact_3413_Diff__Diff__Int,axiom,
% 2.39/2.79 ! [A3: set_nat,B3: set_nat] :
% 2.39/2.79 ( ( minus_minus_set_nat @ A3 @ ( minus_minus_set_nat @ A3 @ B3 ) )
% 2.39/2.79 = ( inf_inf_set_nat @ A3 @ B3 ) ) ).
% 2.39/2.79
% 2.39/2.79 % Diff_Diff_Int
% 2.39/2.79 thf(fact_3414_Diff__Int__distrib,axiom,
% 2.39/2.79 ! [C2: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.79 ( ( inf_in2572325071724192079at_nat @ C2 @ ( minus_1356011639430497352at_nat @ A3 @ B3 ) )
% 2.39/2.79 = ( minus_1356011639430497352at_nat @ ( inf_in2572325071724192079at_nat @ C2 @ A3 ) @ ( inf_in2572325071724192079at_nat @ C2 @ B3 ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % Diff_Int_distrib
% 2.39/2.79 thf(fact_3415_Diff__Int__distrib,axiom,
% 2.39/2.79 ! [C2: set_nat,A3: set_nat,B3: set_nat] :
% 2.39/2.79 ( ( inf_inf_set_nat @ C2 @ ( minus_minus_set_nat @ A3 @ B3 ) )
% 2.39/2.79 = ( minus_minus_set_nat @ ( inf_inf_set_nat @ C2 @ A3 ) @ ( inf_inf_set_nat @ C2 @ B3 ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % Diff_Int_distrib
% 2.39/2.79 thf(fact_3416_Diff__Int__distrib2,axiom,
% 2.39/2.79 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 2.39/2.79 ( ( inf_in2572325071724192079at_nat @ ( minus_1356011639430497352at_nat @ A3 @ B3 ) @ C2 )
% 2.39/2.79 = ( minus_1356011639430497352at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ C2 ) @ ( inf_in2572325071724192079at_nat @ B3 @ C2 ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % Diff_Int_distrib2
% 2.39/2.79 thf(fact_3417_Diff__Int__distrib2,axiom,
% 2.39/2.79 ! [A3: set_nat,B3: set_nat,C2: set_nat] :
% 2.39/2.79 ( ( inf_inf_set_nat @ ( minus_minus_set_nat @ A3 @ B3 ) @ C2 )
% 2.39/2.79 = ( minus_minus_set_nat @ ( inf_inf_set_nat @ A3 @ C2 ) @ ( inf_inf_set_nat @ B3 @ C2 ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % Diff_Int_distrib2
% 2.39/2.79 thf(fact_3418_disjoint__alt__simp3,axiom,
% 2.39/2.79 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.79 ( ( ord_le7866589430770878221at_nat @ ( minus_1356011639430497352at_nat @ A3 @ B3 ) @ A3 )
% 2.39/2.79 = ( ( inf_in2572325071724192079at_nat @ A3 @ B3 )
% 2.39/2.79 != bot_bo2099793752762293965at_nat ) ) ).
% 2.39/2.79
% 2.39/2.79 % disjoint_alt_simp3
% 2.39/2.79 thf(fact_3419_disjoint__alt__simp3,axiom,
% 2.39/2.79 ! [A3: set_nat,B3: set_nat] :
% 2.39/2.79 ( ( ord_less_set_nat @ ( minus_minus_set_nat @ A3 @ B3 ) @ A3 )
% 2.39/2.79 = ( ( inf_inf_set_nat @ A3 @ B3 )
% 2.39/2.79 != bot_bot_set_nat ) ) ).
% 2.39/2.79
% 2.39/2.79 % disjoint_alt_simp3
% 2.39/2.79 thf(fact_3420_disjoint__alt__simp3,axiom,
% 2.39/2.79 ! [A3: set_int,B3: set_int] :
% 2.39/2.79 ( ( ord_less_set_int @ ( minus_minus_set_int @ A3 @ B3 ) @ A3 )
% 2.39/2.79 = ( ( inf_inf_set_int @ A3 @ B3 )
% 2.39/2.79 != bot_bot_set_int ) ) ).
% 2.39/2.79
% 2.39/2.79 % disjoint_alt_simp3
% 2.39/2.79 thf(fact_3421_disjoint__alt__simp1,axiom,
% 2.39/2.79 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.79 ( ( ( minus_1356011639430497352at_nat @ A3 @ B3 )
% 2.39/2.79 = A3 )
% 2.39/2.79 = ( ( inf_in2572325071724192079at_nat @ A3 @ B3 )
% 2.39/2.79 = bot_bo2099793752762293965at_nat ) ) ).
% 2.39/2.79
% 2.39/2.79 % disjoint_alt_simp1
% 2.39/2.79 thf(fact_3422_disjoint__alt__simp1,axiom,
% 2.39/2.79 ! [A3: set_nat,B3: set_nat] :
% 2.39/2.79 ( ( ( minus_minus_set_nat @ A3 @ B3 )
% 2.39/2.79 = A3 )
% 2.39/2.79 = ( ( inf_inf_set_nat @ A3 @ B3 )
% 2.39/2.79 = bot_bot_set_nat ) ) ).
% 2.39/2.79
% 2.39/2.79 % disjoint_alt_simp1
% 2.39/2.79 thf(fact_3423_disjoint__alt__simp1,axiom,
% 2.39/2.79 ! [A3: set_int,B3: set_int] :
% 2.39/2.79 ( ( ( minus_minus_set_int @ A3 @ B3 )
% 2.39/2.79 = A3 )
% 2.39/2.79 = ( ( inf_inf_set_int @ A3 @ B3 )
% 2.39/2.79 = bot_bot_set_int ) ) ).
% 2.39/2.79
% 2.39/2.79 % disjoint_alt_simp1
% 2.39/2.79 thf(fact_3424_disjoint__alt__simp2,axiom,
% 2.39/2.79 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.79 ( ( ( minus_1356011639430497352at_nat @ A3 @ B3 )
% 2.39/2.79 != A3 )
% 2.39/2.79 = ( ( inf_in2572325071724192079at_nat @ A3 @ B3 )
% 2.39/2.79 != bot_bo2099793752762293965at_nat ) ) ).
% 2.39/2.79
% 2.39/2.79 % disjoint_alt_simp2
% 2.39/2.79 thf(fact_3425_disjoint__alt__simp2,axiom,
% 2.39/2.79 ! [A3: set_nat,B3: set_nat] :
% 2.39/2.79 ( ( ( minus_minus_set_nat @ A3 @ B3 )
% 2.39/2.79 != A3 )
% 2.39/2.79 = ( ( inf_inf_set_nat @ A3 @ B3 )
% 2.39/2.79 != bot_bot_set_nat ) ) ).
% 2.39/2.79
% 2.39/2.79 % disjoint_alt_simp2
% 2.39/2.79 thf(fact_3426_disjoint__alt__simp2,axiom,
% 2.39/2.79 ! [A3: set_int,B3: set_int] :
% 2.39/2.79 ( ( ( minus_minus_set_int @ A3 @ B3 )
% 2.39/2.79 != A3 )
% 2.39/2.79 = ( ( inf_inf_set_int @ A3 @ B3 )
% 2.39/2.79 != bot_bot_set_int ) ) ).
% 2.39/2.79
% 2.39/2.79 % disjoint_alt_simp2
% 2.39/2.79 thf(fact_3427_Diff__triv,axiom,
% 2.39/2.79 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.79 ( ( ( inf_in2572325071724192079at_nat @ A3 @ B3 )
% 2.39/2.79 = bot_bo2099793752762293965at_nat )
% 2.39/2.79 => ( ( minus_1356011639430497352at_nat @ A3 @ B3 )
% 2.39/2.79 = A3 ) ) ).
% 2.39/2.79
% 2.39/2.79 % Diff_triv
% 2.39/2.79 thf(fact_3428_Diff__triv,axiom,
% 2.39/2.79 ! [A3: set_nat,B3: set_nat] :
% 2.39/2.79 ( ( ( inf_inf_set_nat @ A3 @ B3 )
% 2.39/2.79 = bot_bot_set_nat )
% 2.39/2.79 => ( ( minus_minus_set_nat @ A3 @ B3 )
% 2.39/2.79 = A3 ) ) ).
% 2.39/2.79
% 2.39/2.79 % Diff_triv
% 2.39/2.79 thf(fact_3429_Diff__triv,axiom,
% 2.39/2.79 ! [A3: set_int,B3: set_int] :
% 2.39/2.79 ( ( ( inf_inf_set_int @ A3 @ B3 )
% 2.39/2.79 = bot_bot_set_int )
% 2.39/2.79 => ( ( minus_minus_set_int @ A3 @ B3 )
% 2.39/2.79 = A3 ) ) ).
% 2.39/2.79
% 2.39/2.79 % Diff_triv
% 2.39/2.79 thf(fact_3430_Int__Diff__disjoint,axiom,
% 2.39/2.79 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.79 ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) @ ( minus_1356011639430497352at_nat @ A3 @ B3 ) )
% 2.39/2.79 = bot_bo2099793752762293965at_nat ) ).
% 2.39/2.79
% 2.39/2.79 % Int_Diff_disjoint
% 2.39/2.79 thf(fact_3431_Int__Diff__disjoint,axiom,
% 2.39/2.79 ! [A3: set_nat,B3: set_nat] :
% 2.39/2.79 ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ A3 @ B3 ) @ ( minus_minus_set_nat @ A3 @ B3 ) )
% 2.39/2.79 = bot_bot_set_nat ) ).
% 2.39/2.79
% 2.39/2.79 % Int_Diff_disjoint
% 2.39/2.79 thf(fact_3432_Int__Diff__disjoint,axiom,
% 2.39/2.79 ! [A3: set_int,B3: set_int] :
% 2.39/2.79 ( ( inf_inf_set_int @ ( inf_inf_set_int @ A3 @ B3 ) @ ( minus_minus_set_int @ A3 @ B3 ) )
% 2.39/2.79 = bot_bot_set_int ) ).
% 2.39/2.79
% 2.39/2.79 % Int_Diff_disjoint
% 2.39/2.79 thf(fact_3433_Diff__Un,axiom,
% 2.39/2.79 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 2.39/2.79 ( ( minus_1356011639430497352at_nat @ A3 @ ( sup_su6327502436637775413at_nat @ B3 @ C2 ) )
% 2.39/2.79 = ( inf_in2572325071724192079at_nat @ ( minus_1356011639430497352at_nat @ A3 @ B3 ) @ ( minus_1356011639430497352at_nat @ A3 @ C2 ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % Diff_Un
% 2.39/2.79 thf(fact_3434_Diff__Un,axiom,
% 2.39/2.79 ! [A3: set_nat,B3: set_nat,C2: set_nat] :
% 2.39/2.79 ( ( minus_minus_set_nat @ A3 @ ( sup_sup_set_nat @ B3 @ C2 ) )
% 2.39/2.79 = ( inf_inf_set_nat @ ( minus_minus_set_nat @ A3 @ B3 ) @ ( minus_minus_set_nat @ A3 @ C2 ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % Diff_Un
% 2.39/2.79 thf(fact_3435_Diff__Int,axiom,
% 2.39/2.79 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 2.39/2.79 ( ( minus_1356011639430497352at_nat @ A3 @ ( inf_in2572325071724192079at_nat @ B3 @ C2 ) )
% 2.39/2.79 = ( sup_su6327502436637775413at_nat @ ( minus_1356011639430497352at_nat @ A3 @ B3 ) @ ( minus_1356011639430497352at_nat @ A3 @ C2 ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % Diff_Int
% 2.39/2.79 thf(fact_3436_Diff__Int,axiom,
% 2.39/2.79 ! [A3: set_nat,B3: set_nat,C2: set_nat] :
% 2.39/2.79 ( ( minus_minus_set_nat @ A3 @ ( inf_inf_set_nat @ B3 @ C2 ) )
% 2.39/2.79 = ( sup_sup_set_nat @ ( minus_minus_set_nat @ A3 @ B3 ) @ ( minus_minus_set_nat @ A3 @ C2 ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % Diff_Int
% 2.39/2.79 thf(fact_3437_Int__Diff__Un,axiom,
% 2.39/2.79 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.79 ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) @ ( minus_1356011639430497352at_nat @ A3 @ B3 ) )
% 2.39/2.79 = A3 ) ).
% 2.39/2.79
% 2.39/2.79 % Int_Diff_Un
% 2.39/2.79 thf(fact_3438_Int__Diff__Un,axiom,
% 2.39/2.79 ! [A3: set_nat,B3: set_nat] :
% 2.39/2.79 ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ A3 @ B3 ) @ ( minus_minus_set_nat @ A3 @ B3 ) )
% 2.39/2.79 = A3 ) ).
% 2.39/2.79
% 2.39/2.79 % Int_Diff_Un
% 2.39/2.79 thf(fact_3439_Un__Diff__Int,axiom,
% 2.39/2.79 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.79 ( ( sup_su6327502436637775413at_nat @ ( minus_1356011639430497352at_nat @ A3 @ B3 ) @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) )
% 2.39/2.79 = A3 ) ).
% 2.39/2.79
% 2.39/2.79 % Un_Diff_Int
% 2.39/2.79 thf(fact_3440_Un__Diff__Int,axiom,
% 2.39/2.79 ! [A3: set_nat,B3: set_nat] :
% 2.39/2.79 ( ( sup_sup_set_nat @ ( minus_minus_set_nat @ A3 @ B3 ) @ ( inf_inf_set_nat @ A3 @ B3 ) )
% 2.39/2.79 = A3 ) ).
% 2.39/2.79
% 2.39/2.79 % Un_Diff_Int
% 2.39/2.79 thf(fact_3441_minus__assn__def,axiom,
% 2.39/2.79 ( minus_minus_assn
% 2.39/2.79 = ( ^ [A2: assn,B2: assn] : ( inf_inf_assn @ A2 @ ( uminus_uminus_assn @ B2 ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % minus_assn_def
% 2.39/2.79 thf(fact_3442_numeral__inc,axiom,
% 2.39/2.79 ! [X: num] :
% 2.39/2.79 ( ( numeral_numeral_nat @ ( inc @ X ) )
% 2.39/2.79 = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 2.39/2.79
% 2.39/2.79 % numeral_inc
% 2.39/2.79 thf(fact_3443_numeral__inc,axiom,
% 2.39/2.79 ! [X: num] :
% 2.39/2.79 ( ( numeral_numeral_int @ ( inc @ X ) )
% 2.39/2.79 = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 2.39/2.79
% 2.39/2.79 % numeral_inc
% 2.39/2.79 thf(fact_3444_numeral__inc,axiom,
% 2.39/2.79 ! [X: num] :
% 2.39/2.79 ( ( numeral_numeral_rat @ ( inc @ X ) )
% 2.39/2.79 = ( plus_plus_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat ) ) ).
% 2.39/2.79
% 2.39/2.79 % numeral_inc
% 2.39/2.79 thf(fact_3445_numeral__inc,axiom,
% 2.39/2.79 ! [X: num] :
% 2.39/2.79 ( ( numera6620942414471956472nteger @ ( inc @ X ) )
% 2.39/2.79 = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ X ) @ one_one_Code_integer ) ) ).
% 2.39/2.79
% 2.39/2.79 % numeral_inc
% 2.39/2.79 thf(fact_3446_numeral__inc,axiom,
% 2.39/2.79 ! [X: num] :
% 2.39/2.79 ( ( numera5444537566228673987atural @ ( inc @ X ) )
% 2.39/2.79 = ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ X ) @ one_one_Code_natural ) ) ).
% 2.39/2.79
% 2.39/2.79 % numeral_inc
% 2.39/2.79 thf(fact_3447_diff__numeral__special_I4_J,axiom,
% 2.39/2.79 ! [M2: num] :
% 2.39/2.79 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int )
% 2.39/2.79 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M2 @ one ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % diff_numeral_special(4)
% 2.39/2.79 thf(fact_3448_diff__numeral__special_I4_J,axiom,
% 2.39/2.79 ! [M2: num] :
% 2.39/2.79 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ one_one_rat )
% 2.39/2.79 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M2 @ one ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % diff_numeral_special(4)
% 2.39/2.79 thf(fact_3449_diff__numeral__special_I4_J,axiom,
% 2.39/2.79 ! [M2: num] :
% 2.39/2.79 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ one_one_Code_integer )
% 2.39/2.79 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M2 @ one ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % diff_numeral_special(4)
% 2.39/2.79 thf(fact_3450_diff__numeral__special_I3_J,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 2.39/2.79 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % diff_numeral_special(3)
% 2.39/2.79 thf(fact_3451_diff__numeral__special_I3_J,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 2.39/2.79 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % diff_numeral_special(3)
% 2.39/2.79 thf(fact_3452_diff__numeral__special_I3_J,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 2.39/2.79 = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % diff_numeral_special(3)
% 2.39/2.79 thf(fact_3453_nth__Cons__pos,axiom,
% 2.39/2.79 ! [N: nat,X: int,Xs: list_int] :
% 2.39/2.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.39/2.79 => ( ( nth_int @ ( cons_int @ X @ Xs ) @ N )
% 2.39/2.79 = ( nth_int @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % nth_Cons_pos
% 2.39/2.79 thf(fact_3454_nth__Cons__pos,axiom,
% 2.39/2.79 ! [N: nat,X: nat,Xs: list_nat] :
% 2.39/2.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.39/2.79 => ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ N )
% 2.39/2.79 = ( nth_nat @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % nth_Cons_pos
% 2.39/2.79 thf(fact_3455_one__plus__numeral,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 2.39/2.79 = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % one_plus_numeral
% 2.39/2.79 thf(fact_3456_one__plus__numeral,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 2.39/2.79 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % one_plus_numeral
% 2.39/2.79 thf(fact_3457_one__plus__numeral,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 2.39/2.79 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % one_plus_numeral
% 2.39/2.79 thf(fact_3458_one__plus__numeral,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 2.39/2.79 = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % one_plus_numeral
% 2.39/2.79 thf(fact_3459_one__plus__numeral,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ N ) )
% 2.39/2.79 = ( numera5444537566228673987atural @ ( plus_plus_num @ one @ N ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % one_plus_numeral
% 2.39/2.79 thf(fact_3460_numeral__plus__one,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 2.39/2.79 = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % numeral_plus_one
% 2.39/2.79 thf(fact_3461_numeral__plus__one,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( plus_plus_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 2.39/2.79 = ( numeral_numeral_int @ ( plus_plus_num @ N @ one ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % numeral_plus_one
% 2.39/2.79 thf(fact_3462_numeral__plus__one,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 2.39/2.79 = ( numeral_numeral_rat @ ( plus_plus_num @ N @ one ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % numeral_plus_one
% 2.39/2.79 thf(fact_3463_numeral__plus__one,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N ) @ one_one_Code_integer )
% 2.39/2.79 = ( numera6620942414471956472nteger @ ( plus_plus_num @ N @ one ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % numeral_plus_one
% 2.39/2.79 thf(fact_3464_numeral__plus__one,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ N ) @ one_one_Code_natural )
% 2.39/2.79 = ( numera5444537566228673987atural @ ( plus_plus_num @ N @ one ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % numeral_plus_one
% 2.39/2.79 thf(fact_3465_neg__numeral__less__neg__one__iff,axiom,
% 2.39/2.79 ! [M2: num] :
% 2.39/2.79 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 2.39/2.79 = ( M2 != one ) ) ).
% 2.39/2.79
% 2.39/2.79 % neg_numeral_less_neg_one_iff
% 2.39/2.79 thf(fact_3466_neg__numeral__less__neg__one__iff,axiom,
% 2.39/2.79 ! [M2: num] :
% 2.39/2.79 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 2.39/2.79 = ( M2 != one ) ) ).
% 2.39/2.79
% 2.39/2.79 % neg_numeral_less_neg_one_iff
% 2.39/2.79 thf(fact_3467_neg__numeral__less__neg__one__iff,axiom,
% 2.39/2.79 ! [M2: num] :
% 2.39/2.79 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 2.39/2.79 = ( M2 != one ) ) ).
% 2.39/2.79
% 2.39/2.79 % neg_numeral_less_neg_one_iff
% 2.39/2.79 thf(fact_3468_not__neg__one__le__neg__numeral__iff,axiom,
% 2.39/2.79 ! [M2: num] :
% 2.39/2.79 ( ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) ) )
% 2.39/2.79 = ( M2 != one ) ) ).
% 2.39/2.79
% 2.39/2.79 % not_neg_one_le_neg_numeral_iff
% 2.39/2.79 thf(fact_3469_not__neg__one__le__neg__numeral__iff,axiom,
% 2.39/2.79 ! [M2: num] :
% 2.39/2.79 ( ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) ) )
% 2.39/2.79 = ( M2 != one ) ) ).
% 2.39/2.79
% 2.39/2.79 % not_neg_one_le_neg_numeral_iff
% 2.39/2.79 thf(fact_3470_not__neg__one__le__neg__numeral__iff,axiom,
% 2.39/2.79 ! [M2: num] :
% 2.39/2.79 ( ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) ) )
% 2.39/2.79 = ( M2 != one ) ) ).
% 2.39/2.79
% 2.39/2.79 % not_neg_one_le_neg_numeral_iff
% 2.39/2.79 thf(fact_3471_Suc__diff__1,axiom,
% 2.39/2.79 ! [N: nat] :
% 2.39/2.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.39/2.79 => ( ( suc @ ( minus_minus_nat @ N @ one_one_nat ) )
% 2.39/2.79 = N ) ) ).
% 2.39/2.79
% 2.39/2.79 % Suc_diff_1
% 2.39/2.79 thf(fact_3472_numeral__eq__one__iff,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( ( numeral_numeral_nat @ N )
% 2.39/2.79 = one_one_nat )
% 2.39/2.79 = ( N = one ) ) ).
% 2.39/2.79
% 2.39/2.79 % numeral_eq_one_iff
% 2.39/2.79 thf(fact_3473_numeral__eq__one__iff,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( ( numeral_numeral_int @ N )
% 2.39/2.79 = one_one_int )
% 2.39/2.79 = ( N = one ) ) ).
% 2.39/2.79
% 2.39/2.79 % numeral_eq_one_iff
% 2.39/2.79 thf(fact_3474_numeral__eq__one__iff,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( ( numeral_numeral_rat @ N )
% 2.39/2.79 = one_one_rat )
% 2.39/2.79 = ( N = one ) ) ).
% 2.39/2.79
% 2.39/2.79 % numeral_eq_one_iff
% 2.39/2.79 thf(fact_3475_numeral__eq__one__iff,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( ( numera6620942414471956472nteger @ N )
% 2.39/2.79 = one_one_Code_integer )
% 2.39/2.79 = ( N = one ) ) ).
% 2.39/2.79
% 2.39/2.79 % numeral_eq_one_iff
% 2.39/2.79 thf(fact_3476_numeral__eq__one__iff,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( ( numera5444537566228673987atural @ N )
% 2.39/2.79 = one_one_Code_natural )
% 2.39/2.79 = ( N = one ) ) ).
% 2.39/2.79
% 2.39/2.79 % numeral_eq_one_iff
% 2.39/2.79 thf(fact_3477_one__eq__numeral__iff,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( one_one_nat
% 2.39/2.79 = ( numeral_numeral_nat @ N ) )
% 2.39/2.79 = ( one = N ) ) ).
% 2.39/2.79
% 2.39/2.79 % one_eq_numeral_iff
% 2.39/2.79 thf(fact_3478_one__eq__numeral__iff,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( one_one_int
% 2.39/2.79 = ( numeral_numeral_int @ N ) )
% 2.39/2.79 = ( one = N ) ) ).
% 2.39/2.79
% 2.39/2.79 % one_eq_numeral_iff
% 2.39/2.79 thf(fact_3479_one__eq__numeral__iff,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( one_one_rat
% 2.39/2.79 = ( numeral_numeral_rat @ N ) )
% 2.39/2.79 = ( one = N ) ) ).
% 2.39/2.79
% 2.39/2.79 % one_eq_numeral_iff
% 2.39/2.79 thf(fact_3480_one__eq__numeral__iff,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( one_one_Code_integer
% 2.39/2.79 = ( numera6620942414471956472nteger @ N ) )
% 2.39/2.79 = ( one = N ) ) ).
% 2.39/2.79
% 2.39/2.79 % one_eq_numeral_iff
% 2.39/2.79 thf(fact_3481_one__eq__numeral__iff,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( one_one_Code_natural
% 2.39/2.79 = ( numera5444537566228673987atural @ N ) )
% 2.39/2.79 = ( one = N ) ) ).
% 2.39/2.79
% 2.39/2.79 % one_eq_numeral_iff
% 2.39/2.79 thf(fact_3482_nth__Cons__0,axiom,
% 2.39/2.79 ! [X: int,Xs: list_int] :
% 2.39/2.79 ( ( nth_int @ ( cons_int @ X @ Xs ) @ zero_zero_nat )
% 2.39/2.79 = X ) ).
% 2.39/2.79
% 2.39/2.79 % nth_Cons_0
% 2.39/2.79 thf(fact_3483_nth__Cons__0,axiom,
% 2.39/2.79 ! [X: nat,Xs: list_nat] :
% 2.39/2.79 ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ zero_zero_nat )
% 2.39/2.79 = X ) ).
% 2.39/2.79
% 2.39/2.79 % nth_Cons_0
% 2.39/2.79 thf(fact_3484_nth__Cons__Suc,axiom,
% 2.39/2.79 ! [X: int,Xs: list_int,N: nat] :
% 2.39/2.79 ( ( nth_int @ ( cons_int @ X @ Xs ) @ ( suc @ N ) )
% 2.39/2.79 = ( nth_int @ Xs @ N ) ) ).
% 2.39/2.79
% 2.39/2.79 % nth_Cons_Suc
% 2.39/2.79 thf(fact_3485_nth__Cons__Suc,axiom,
% 2.39/2.79 ! [X: nat,Xs: list_nat,N: nat] :
% 2.39/2.79 ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ ( suc @ N ) )
% 2.39/2.79 = ( nth_nat @ Xs @ N ) ) ).
% 2.39/2.79
% 2.39/2.79 % nth_Cons_Suc
% 2.39/2.79 thf(fact_3486_diff__Suc__1,axiom,
% 2.39/2.79 ! [N: nat] :
% 2.39/2.79 ( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
% 2.39/2.79 = N ) ).
% 2.39/2.79
% 2.39/2.79 % diff_Suc_1
% 2.39/2.79 thf(fact_3487_enumerate__simps_I2_J,axiom,
% 2.39/2.79 ! [N: nat,X: int,Xs: list_int] :
% 2.39/2.79 ( ( enumerate_int @ N @ ( cons_int @ X @ Xs ) )
% 2.39/2.79 = ( cons_P2335045147070616083at_int @ ( product_Pair_nat_int @ N @ X ) @ ( enumerate_int @ ( suc @ N ) @ Xs ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % enumerate_simps(2)
% 2.39/2.79 thf(fact_3488_enumerate__simps_I2_J,axiom,
% 2.39/2.79 ! [N: nat,X: nat,Xs: list_nat] :
% 2.39/2.79 ( ( enumerate_nat @ N @ ( cons_nat @ X @ Xs ) )
% 2.39/2.79 = ( cons_P6512896166579812791at_nat @ ( product_Pair_nat_nat @ N @ X ) @ ( enumerate_nat @ ( suc @ N ) @ Xs ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % enumerate_simps(2)
% 2.39/2.79 thf(fact_3489_numeral__le__one__iff,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ N ) @ one_one_Code_integer )
% 2.39/2.79 = ( ord_less_eq_num @ N @ one ) ) ).
% 2.39/2.79
% 2.39/2.79 % numeral_le_one_iff
% 2.39/2.79 thf(fact_3490_numeral__le__one__iff,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( ord_le1926595141338095240atural @ ( numera5444537566228673987atural @ N ) @ one_one_Code_natural )
% 2.39/2.79 = ( ord_less_eq_num @ N @ one ) ) ).
% 2.39/2.79
% 2.39/2.79 % numeral_le_one_iff
% 2.39/2.79 thf(fact_3491_numeral__le__one__iff,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 2.39/2.79 = ( ord_less_eq_num @ N @ one ) ) ).
% 2.39/2.79
% 2.39/2.79 % numeral_le_one_iff
% 2.39/2.79 thf(fact_3492_numeral__le__one__iff,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 2.39/2.79 = ( ord_less_eq_num @ N @ one ) ) ).
% 2.39/2.79
% 2.39/2.79 % numeral_le_one_iff
% 2.39/2.79 thf(fact_3493_numeral__le__one__iff,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 2.39/2.79 = ( ord_less_eq_num @ N @ one ) ) ).
% 2.39/2.79
% 2.39/2.79 % numeral_le_one_iff
% 2.39/2.79 thf(fact_3494_one__less__numeral__iff,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 2.39/2.79 = ( ord_less_num @ one @ N ) ) ).
% 2.39/2.79
% 2.39/2.79 % one_less_numeral_iff
% 2.39/2.79 thf(fact_3495_one__less__numeral__iff,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 2.39/2.79 = ( ord_less_num @ one @ N ) ) ).
% 2.39/2.79
% 2.39/2.79 % one_less_numeral_iff
% 2.39/2.79 thf(fact_3496_one__less__numeral__iff,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( ord_less_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 2.39/2.79 = ( ord_less_num @ one @ N ) ) ).
% 2.39/2.79
% 2.39/2.79 % one_less_numeral_iff
% 2.39/2.79 thf(fact_3497_one__less__numeral__iff,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 2.39/2.79 = ( ord_less_num @ one @ N ) ) ).
% 2.39/2.79
% 2.39/2.79 % one_less_numeral_iff
% 2.39/2.79 thf(fact_3498_one__less__numeral__iff,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ N ) )
% 2.39/2.79 = ( ord_less_num @ one @ N ) ) ).
% 2.39/2.79
% 2.39/2.79 % one_less_numeral_iff
% 2.39/2.79 thf(fact_3499_numeral__eq__neg__one__iff,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ N ) )
% 2.39/2.79 = ( uminus_uminus_int @ one_one_int ) )
% 2.39/2.79 = ( N = one ) ) ).
% 2.39/2.79
% 2.39/2.79 % numeral_eq_neg_one_iff
% 2.39/2.79 thf(fact_3500_numeral__eq__neg__one__iff,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) )
% 2.39/2.79 = ( uminus_uminus_rat @ one_one_rat ) )
% 2.39/2.79 = ( N = one ) ) ).
% 2.39/2.79
% 2.39/2.79 % numeral_eq_neg_one_iff
% 2.39/2.79 thf(fact_3501_numeral__eq__neg__one__iff,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) )
% 2.39/2.79 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 2.39/2.79 = ( N = one ) ) ).
% 2.39/2.79
% 2.39/2.79 % numeral_eq_neg_one_iff
% 2.39/2.79 thf(fact_3502_neg__one__eq__numeral__iff,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( ( uminus_uminus_int @ one_one_int )
% 2.39/2.79 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 2.39/2.79 = ( N = one ) ) ).
% 2.39/2.79
% 2.39/2.79 % neg_one_eq_numeral_iff
% 2.39/2.79 thf(fact_3503_neg__one__eq__numeral__iff,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( ( uminus_uminus_rat @ one_one_rat )
% 2.39/2.79 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 2.39/2.79 = ( N = one ) ) ).
% 2.39/2.79
% 2.39/2.79 % neg_one_eq_numeral_iff
% 2.39/2.79 thf(fact_3504_neg__one__eq__numeral__iff,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( ( uminus1351360451143612070nteger @ one_one_Code_integer )
% 2.39/2.79 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 2.39/2.79 = ( N = one ) ) ).
% 2.39/2.79
% 2.39/2.79 % neg_one_eq_numeral_iff
% 2.39/2.79 thf(fact_3505_Suc__diff,axiom,
% 2.39/2.79 ! [M2: nat,N: nat] :
% 2.39/2.79 ( ( ord_less_eq_nat @ M2 @ N )
% 2.39/2.79 => ( ( ord_less_eq_nat @ one_one_nat @ M2 )
% 2.39/2.79 => ( ( suc @ ( minus_minus_nat @ N @ M2 ) )
% 2.39/2.79 = ( minus_minus_nat @ N @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % Suc_diff
% 2.39/2.79 thf(fact_3506_nth__Cons__numeral,axiom,
% 2.39/2.79 ! [X: int,Xs: list_int,V2: num] :
% 2.39/2.79 ( ( nth_int @ ( cons_int @ X @ Xs ) @ ( numeral_numeral_nat @ V2 ) )
% 2.39/2.79 = ( nth_int @ Xs @ ( minus_minus_nat @ ( numeral_numeral_nat @ V2 ) @ one_one_nat ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % nth_Cons_numeral
% 2.39/2.79 thf(fact_3507_nth__Cons__numeral,axiom,
% 2.39/2.79 ! [X: nat,Xs: list_nat,V2: num] :
% 2.39/2.79 ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ ( numeral_numeral_nat @ V2 ) )
% 2.39/2.79 = ( nth_nat @ Xs @ ( minus_minus_nat @ ( numeral_numeral_nat @ V2 ) @ one_one_nat ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % nth_Cons_numeral
% 2.39/2.79 thf(fact_3508_power__Suc,axiom,
% 2.39/2.79 ! [A: assn,N: nat] :
% 2.39/2.79 ( ( power_power_assn @ A @ ( suc @ N ) )
% 2.39/2.79 = ( times_times_assn @ A @ ( power_power_assn @ A @ N ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % power_Suc
% 2.39/2.79 thf(fact_3509_power__Suc,axiom,
% 2.39/2.79 ! [A: nat,N: nat] :
% 2.39/2.79 ( ( power_power_nat @ A @ ( suc @ N ) )
% 2.39/2.79 = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % power_Suc
% 2.39/2.79 thf(fact_3510_power__Suc,axiom,
% 2.39/2.79 ! [A: int,N: nat] :
% 2.39/2.79 ( ( power_power_int @ A @ ( suc @ N ) )
% 2.39/2.79 = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % power_Suc
% 2.39/2.79 thf(fact_3511_power__Suc,axiom,
% 2.39/2.79 ! [A: code_integer,N: nat] :
% 2.39/2.79 ( ( power_8256067586552552935nteger @ A @ ( suc @ N ) )
% 2.39/2.79 = ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % power_Suc
% 2.39/2.79 thf(fact_3512_power__Suc,axiom,
% 2.39/2.79 ! [A: code_natural,N: nat] :
% 2.39/2.79 ( ( power_7079662738309270450atural @ A @ ( suc @ N ) )
% 2.39/2.79 = ( times_2397367101498566445atural @ A @ ( power_7079662738309270450atural @ A @ N ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % power_Suc
% 2.39/2.79 thf(fact_3513_power__Suc2,axiom,
% 2.39/2.79 ! [A: assn,N: nat] :
% 2.39/2.79 ( ( power_power_assn @ A @ ( suc @ N ) )
% 2.39/2.79 = ( times_times_assn @ ( power_power_assn @ A @ N ) @ A ) ) ).
% 2.39/2.79
% 2.39/2.79 % power_Suc2
% 2.39/2.79 thf(fact_3514_power__Suc2,axiom,
% 2.39/2.79 ! [A: nat,N: nat] :
% 2.39/2.79 ( ( power_power_nat @ A @ ( suc @ N ) )
% 2.39/2.79 = ( times_times_nat @ ( power_power_nat @ A @ N ) @ A ) ) ).
% 2.39/2.79
% 2.39/2.79 % power_Suc2
% 2.39/2.79 thf(fact_3515_power__Suc2,axiom,
% 2.39/2.79 ! [A: int,N: nat] :
% 2.39/2.79 ( ( power_power_int @ A @ ( suc @ N ) )
% 2.39/2.79 = ( times_times_int @ ( power_power_int @ A @ N ) @ A ) ) ).
% 2.39/2.79
% 2.39/2.79 % power_Suc2
% 2.39/2.79 thf(fact_3516_power__Suc2,axiom,
% 2.39/2.79 ! [A: code_integer,N: nat] :
% 2.39/2.79 ( ( power_8256067586552552935nteger @ A @ ( suc @ N ) )
% 2.39/2.79 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ N ) @ A ) ) ).
% 2.39/2.79
% 2.39/2.79 % power_Suc2
% 2.39/2.79 thf(fact_3517_power__Suc2,axiom,
% 2.39/2.79 ! [A: code_natural,N: nat] :
% 2.39/2.79 ( ( power_7079662738309270450atural @ A @ ( suc @ N ) )
% 2.39/2.79 = ( times_2397367101498566445atural @ ( power_7079662738309270450atural @ A @ N ) @ A ) ) ).
% 2.39/2.79
% 2.39/2.79 % power_Suc2
% 2.39/2.79 thf(fact_3518_One__nat__def,axiom,
% 2.39/2.79 ( one_one_nat
% 2.39/2.79 = ( suc @ zero_zero_nat ) ) ).
% 2.39/2.79
% 2.39/2.79 % One_nat_def
% 2.39/2.79 thf(fact_3519_Suc__eq__plus1,axiom,
% 2.39/2.79 ( suc
% 2.39/2.79 = ( ^ [N3: nat] : ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % Suc_eq_plus1
% 2.39/2.79 thf(fact_3520_plus__1__eq__Suc,axiom,
% 2.39/2.79 ( ( plus_plus_nat @ one_one_nat )
% 2.39/2.79 = suc ) ).
% 2.39/2.79
% 2.39/2.79 % plus_1_eq_Suc
% 2.39/2.79 thf(fact_3521_Suc__eq__plus1__left,axiom,
% 2.39/2.79 ( suc
% 2.39/2.79 = ( plus_plus_nat @ one_one_nat ) ) ).
% 2.39/2.79
% 2.39/2.79 % Suc_eq_plus1_left
% 2.39/2.79 thf(fact_3522_diff__Suc__eq__diff__pred,axiom,
% 2.39/2.79 ! [M2: nat,N: nat] :
% 2.39/2.79 ( ( minus_minus_nat @ M2 @ ( suc @ N ) )
% 2.39/2.79 = ( minus_minus_nat @ ( minus_minus_nat @ M2 @ one_one_nat ) @ N ) ) ).
% 2.39/2.79
% 2.39/2.79 % diff_Suc_eq_diff_pred
% 2.39/2.79 thf(fact_3523_mult__numeral__1__right,axiom,
% 2.39/2.79 ! [A: nat] :
% 2.39/2.79 ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
% 2.39/2.79 = A ) ).
% 2.39/2.79
% 2.39/2.79 % mult_numeral_1_right
% 2.39/2.79 thf(fact_3524_mult__numeral__1__right,axiom,
% 2.39/2.79 ! [A: int] :
% 2.39/2.79 ( ( times_times_int @ A @ ( numeral_numeral_int @ one ) )
% 2.39/2.79 = A ) ).
% 2.39/2.79
% 2.39/2.79 % mult_numeral_1_right
% 2.39/2.79 thf(fact_3525_mult__numeral__1__right,axiom,
% 2.39/2.79 ! [A: rat] :
% 2.39/2.79 ( ( times_times_rat @ A @ ( numeral_numeral_rat @ one ) )
% 2.39/2.79 = A ) ).
% 2.39/2.79
% 2.39/2.79 % mult_numeral_1_right
% 2.39/2.79 thf(fact_3526_mult__numeral__1__right,axiom,
% 2.39/2.79 ! [A: code_integer] :
% 2.39/2.79 ( ( times_3573771949741848930nteger @ A @ ( numera6620942414471956472nteger @ one ) )
% 2.39/2.79 = A ) ).
% 2.39/2.79
% 2.39/2.79 % mult_numeral_1_right
% 2.39/2.79 thf(fact_3527_mult__numeral__1__right,axiom,
% 2.39/2.79 ! [A: code_natural] :
% 2.39/2.79 ( ( times_2397367101498566445atural @ A @ ( numera5444537566228673987atural @ one ) )
% 2.39/2.79 = A ) ).
% 2.39/2.79
% 2.39/2.79 % mult_numeral_1_right
% 2.39/2.79 thf(fact_3528_mult__numeral__1,axiom,
% 2.39/2.79 ! [A: nat] :
% 2.39/2.79 ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
% 2.39/2.79 = A ) ).
% 2.39/2.79
% 2.39/2.79 % mult_numeral_1
% 2.39/2.79 thf(fact_3529_mult__numeral__1,axiom,
% 2.39/2.79 ! [A: int] :
% 2.39/2.79 ( ( times_times_int @ ( numeral_numeral_int @ one ) @ A )
% 2.39/2.79 = A ) ).
% 2.39/2.79
% 2.39/2.79 % mult_numeral_1
% 2.39/2.79 thf(fact_3530_mult__numeral__1,axiom,
% 2.39/2.79 ! [A: rat] :
% 2.39/2.79 ( ( times_times_rat @ ( numeral_numeral_rat @ one ) @ A )
% 2.39/2.79 = A ) ).
% 2.39/2.79
% 2.39/2.79 % mult_numeral_1
% 2.39/2.79 thf(fact_3531_mult__numeral__1,axiom,
% 2.39/2.79 ! [A: code_integer] :
% 2.39/2.79 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ one ) @ A )
% 2.39/2.79 = A ) ).
% 2.39/2.79
% 2.39/2.79 % mult_numeral_1
% 2.39/2.79 thf(fact_3532_mult__numeral__1,axiom,
% 2.39/2.79 ! [A: code_natural] :
% 2.39/2.79 ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ one ) @ A )
% 2.39/2.79 = A ) ).
% 2.39/2.79
% 2.39/2.79 % mult_numeral_1
% 2.39/2.79 thf(fact_3533_numeral__One,axiom,
% 2.39/2.79 ( ( numeral_numeral_nat @ one )
% 2.39/2.79 = one_one_nat ) ).
% 2.39/2.79
% 2.39/2.79 % numeral_One
% 2.39/2.79 thf(fact_3534_numeral__One,axiom,
% 2.39/2.79 ( ( numeral_numeral_int @ one )
% 2.39/2.79 = one_one_int ) ).
% 2.39/2.79
% 2.39/2.79 % numeral_One
% 2.39/2.79 thf(fact_3535_numeral__One,axiom,
% 2.39/2.79 ( ( numeral_numeral_rat @ one )
% 2.39/2.79 = one_one_rat ) ).
% 2.39/2.79
% 2.39/2.79 % numeral_One
% 2.39/2.79 thf(fact_3536_numeral__One,axiom,
% 2.39/2.79 ( ( numera6620942414471956472nteger @ one )
% 2.39/2.79 = one_one_Code_integer ) ).
% 2.39/2.79
% 2.39/2.79 % numeral_One
% 2.39/2.79 thf(fact_3537_numeral__One,axiom,
% 2.39/2.79 ( ( numera5444537566228673987atural @ one )
% 2.39/2.79 = one_one_Code_natural ) ).
% 2.39/2.79
% 2.39/2.79 % numeral_One
% 2.39/2.79 thf(fact_3538_numerals_I1_J,axiom,
% 2.39/2.79 ( ( numeral_numeral_nat @ one )
% 2.39/2.79 = one_one_nat ) ).
% 2.39/2.79
% 2.39/2.79 % numerals(1)
% 2.39/2.79 thf(fact_3539_gen__length__code_I2_J,axiom,
% 2.39/2.79 ! [N: nat,X: int,Xs: list_int] :
% 2.39/2.79 ( ( gen_length_int @ N @ ( cons_int @ X @ Xs ) )
% 2.39/2.79 = ( gen_length_int @ ( suc @ N ) @ Xs ) ) ).
% 2.39/2.79
% 2.39/2.79 % gen_length_code(2)
% 2.39/2.79 thf(fact_3540_gen__length__code_I2_J,axiom,
% 2.39/2.79 ! [N: nat,X: nat,Xs: list_nat] :
% 2.39/2.79 ( ( gen_length_nat @ N @ ( cons_nat @ X @ Xs ) )
% 2.39/2.79 = ( gen_length_nat @ ( suc @ N ) @ Xs ) ) ).
% 2.39/2.79
% 2.39/2.79 % gen_length_code(2)
% 2.39/2.79 thf(fact_3541_power__gt1,axiom,
% 2.39/2.79 ! [A: code_integer,N: nat] :
% 2.39/2.79 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 2.39/2.79 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ ( suc @ N ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % power_gt1
% 2.39/2.79 thf(fact_3542_power__gt1,axiom,
% 2.39/2.79 ! [A: rat,N: nat] :
% 2.39/2.79 ( ( ord_less_rat @ one_one_rat @ A )
% 2.39/2.79 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ ( suc @ N ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % power_gt1
% 2.39/2.79 thf(fact_3543_power__gt1,axiom,
% 2.39/2.79 ! [A: nat,N: nat] :
% 2.39/2.79 ( ( ord_less_nat @ one_one_nat @ A )
% 2.39/2.79 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % power_gt1
% 2.39/2.79 thf(fact_3544_power__gt1,axiom,
% 2.39/2.79 ! [A: int,N: nat] :
% 2.39/2.79 ( ( ord_less_int @ one_one_int @ A )
% 2.39/2.79 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % power_gt1
% 2.39/2.79 thf(fact_3545_nat__induct__non__zero,axiom,
% 2.39/2.79 ! [N: nat,P2: nat > $o] :
% 2.39/2.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.39/2.79 => ( ( P2 @ one_one_nat )
% 2.39/2.79 => ( ! [N4: nat] :
% 2.39/2.79 ( ( ord_less_nat @ zero_zero_nat @ N4 )
% 2.39/2.79 => ( ( P2 @ N4 )
% 2.39/2.79 => ( P2 @ ( suc @ N4 ) ) ) )
% 2.39/2.79 => ( P2 @ N ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % nat_induct_non_zero
% 2.39/2.79 thf(fact_3546_mult__1s__ring__1_I1_J,axiom,
% 2.39/2.79 ! [B: int] :
% 2.39/2.79 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) @ B )
% 2.39/2.79 = ( uminus_uminus_int @ B ) ) ).
% 2.39/2.79
% 2.39/2.79 % mult_1s_ring_1(1)
% 2.39/2.79 thf(fact_3547_mult__1s__ring__1_I1_J,axiom,
% 2.39/2.79 ! [B: rat] :
% 2.39/2.79 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) @ B )
% 2.39/2.79 = ( uminus_uminus_rat @ B ) ) ).
% 2.39/2.79
% 2.39/2.79 % mult_1s_ring_1(1)
% 2.39/2.79 thf(fact_3548_mult__1s__ring__1_I1_J,axiom,
% 2.39/2.79 ! [B: code_integer] :
% 2.39/2.79 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) @ B )
% 2.39/2.79 = ( uminus1351360451143612070nteger @ B ) ) ).
% 2.39/2.79
% 2.39/2.79 % mult_1s_ring_1(1)
% 2.39/2.79 thf(fact_3549_mult__1s__ring__1_I2_J,axiom,
% 2.39/2.79 ! [B: int] :
% 2.39/2.79 ( ( times_times_int @ B @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) )
% 2.39/2.79 = ( uminus_uminus_int @ B ) ) ).
% 2.39/2.79
% 2.39/2.79 % mult_1s_ring_1(2)
% 2.39/2.79 thf(fact_3550_mult__1s__ring__1_I2_J,axiom,
% 2.39/2.79 ! [B: rat] :
% 2.39/2.79 ( ( times_times_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) )
% 2.39/2.79 = ( uminus_uminus_rat @ B ) ) ).
% 2.39/2.79
% 2.39/2.79 % mult_1s_ring_1(2)
% 2.39/2.79 thf(fact_3551_mult__1s__ring__1_I2_J,axiom,
% 2.39/2.79 ! [B: code_integer] :
% 2.39/2.79 ( ( times_3573771949741848930nteger @ B @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) )
% 2.39/2.79 = ( uminus1351360451143612070nteger @ B ) ) ).
% 2.39/2.79
% 2.39/2.79 % mult_1s_ring_1(2)
% 2.39/2.79 thf(fact_3552_uminus__numeral__One,axiom,
% 2.39/2.79 ( ( uminus_uminus_int @ ( numeral_numeral_int @ one ) )
% 2.39/2.79 = ( uminus_uminus_int @ one_one_int ) ) ).
% 2.39/2.79
% 2.39/2.79 % uminus_numeral_One
% 2.39/2.79 thf(fact_3553_uminus__numeral__One,axiom,
% 2.39/2.79 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) )
% 2.39/2.79 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 2.39/2.79
% 2.39/2.79 % uminus_numeral_One
% 2.39/2.79 thf(fact_3554_uminus__numeral__One,axiom,
% 2.39/2.79 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) )
% 2.39/2.79 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 2.39/2.79
% 2.39/2.79 % uminus_numeral_One
% 2.39/2.79 thf(fact_3555_nth__Cons_H,axiom,
% 2.39/2.79 ! [N: nat,X: int,Xs: list_int] :
% 2.39/2.79 ( ( ( N = zero_zero_nat )
% 2.39/2.79 => ( ( nth_int @ ( cons_int @ X @ Xs ) @ N )
% 2.39/2.79 = X ) )
% 2.39/2.79 & ( ( N != zero_zero_nat )
% 2.39/2.79 => ( ( nth_int @ ( cons_int @ X @ Xs ) @ N )
% 2.39/2.79 = ( nth_int @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % nth_Cons'
% 2.39/2.79 thf(fact_3556_nth__Cons_H,axiom,
% 2.39/2.79 ! [N: nat,X: nat,Xs: list_nat] :
% 2.39/2.79 ( ( ( N = zero_zero_nat )
% 2.39/2.79 => ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ N )
% 2.39/2.79 = X ) )
% 2.39/2.79 & ( ( N != zero_zero_nat )
% 2.39/2.79 => ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ N )
% 2.39/2.79 = ( nth_nat @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % nth_Cons'
% 2.39/2.79 thf(fact_3557_power__Suc__le__self,axiom,
% 2.39/2.79 ! [A: code_integer,N: nat] :
% 2.39/2.79 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.79 => ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 2.39/2.79 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % power_Suc_le_self
% 2.39/2.79 thf(fact_3558_power__Suc__le__self,axiom,
% 2.39/2.79 ! [A: code_natural,N: nat] :
% 2.39/2.79 ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A )
% 2.39/2.79 => ( ( ord_le1926595141338095240atural @ A @ one_one_Code_natural )
% 2.39/2.79 => ( ord_le1926595141338095240atural @ ( power_7079662738309270450atural @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % power_Suc_le_self
% 2.39/2.79 thf(fact_3559_power__Suc__le__self,axiom,
% 2.39/2.79 ! [A: rat,N: nat] :
% 2.39/2.79 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 2.39/2.79 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 2.39/2.79 => ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % power_Suc_le_self
% 2.39/2.79 thf(fact_3560_power__Suc__le__self,axiom,
% 2.39/2.79 ! [A: nat,N: nat] :
% 2.39/2.79 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 2.39/2.79 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 2.39/2.79 => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % power_Suc_le_self
% 2.39/2.79 thf(fact_3561_power__Suc__le__self,axiom,
% 2.39/2.79 ! [A: int,N: nat] :
% 2.39/2.79 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 2.39/2.79 => ( ( ord_less_eq_int @ A @ one_one_int )
% 2.39/2.79 => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % power_Suc_le_self
% 2.39/2.79 thf(fact_3562_power__Suc__less__one,axiom,
% 2.39/2.79 ! [A: code_natural,N: nat] :
% 2.39/2.79 ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A )
% 2.39/2.79 => ( ( ord_le5570908160329646204atural @ A @ one_one_Code_natural )
% 2.39/2.79 => ( ord_le5570908160329646204atural @ ( power_7079662738309270450atural @ A @ ( suc @ N ) ) @ one_one_Code_natural ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % power_Suc_less_one
% 2.39/2.79 thf(fact_3563_power__Suc__less__one,axiom,
% 2.39/2.79 ! [A: code_integer,N: nat] :
% 2.39/2.79 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.79 => ( ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer )
% 2.39/2.79 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ ( suc @ N ) ) @ one_one_Code_integer ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % power_Suc_less_one
% 2.39/2.79 thf(fact_3564_power__Suc__less__one,axiom,
% 2.39/2.79 ! [A: rat,N: nat] :
% 2.39/2.79 ( ( ord_less_rat @ zero_zero_rat @ A )
% 2.39/2.79 => ( ( ord_less_rat @ A @ one_one_rat )
% 2.39/2.79 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ one_one_rat ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % power_Suc_less_one
% 2.39/2.79 thf(fact_3565_power__Suc__less__one,axiom,
% 2.39/2.79 ! [A: nat,N: nat] :
% 2.39/2.79 ( ( ord_less_nat @ zero_zero_nat @ A )
% 2.39/2.79 => ( ( ord_less_nat @ A @ one_one_nat )
% 2.39/2.79 => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ one_one_nat ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % power_Suc_less_one
% 2.39/2.79 thf(fact_3566_power__Suc__less__one,axiom,
% 2.39/2.79 ! [A: int,N: nat] :
% 2.39/2.79 ( ( ord_less_int @ zero_zero_int @ A )
% 2.39/2.79 => ( ( ord_less_int @ A @ one_one_int )
% 2.39/2.79 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N ) ) @ one_one_int ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % power_Suc_less_one
% 2.39/2.79 thf(fact_3567_Suc__diff__eq__diff__pred,axiom,
% 2.39/2.79 ! [N: nat,M2: nat] :
% 2.39/2.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.39/2.79 => ( ( minus_minus_nat @ ( suc @ M2 ) @ N )
% 2.39/2.79 = ( minus_minus_nat @ M2 @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % Suc_diff_eq_diff_pred
% 2.39/2.79 thf(fact_3568_Suc__pred_H,axiom,
% 2.39/2.79 ! [N: nat] :
% 2.39/2.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.39/2.79 => ( N
% 2.39/2.79 = ( suc @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % Suc_pred'
% 2.39/2.79 thf(fact_3569_add__eq__if,axiom,
% 2.39/2.79 ( plus_plus_nat
% 2.39/2.79 = ( ^ [M3: nat,N3: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N3 @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M3 @ one_one_nat ) @ N3 ) ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % add_eq_if
% 2.39/2.79 thf(fact_3570_Suc__n__minus__m__eq,axiom,
% 2.39/2.79 ! [M2: nat,N: nat] :
% 2.39/2.79 ( ( ord_less_eq_nat @ M2 @ N )
% 2.39/2.79 => ( ( ord_less_nat @ one_one_nat @ M2 )
% 2.39/2.79 => ( ( suc @ ( minus_minus_nat @ N @ M2 ) )
% 2.39/2.79 = ( minus_minus_nat @ N @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % Suc_n_minus_m_eq
% 2.39/2.79 thf(fact_3571_nth__non__equal__first__eq,axiom,
% 2.39/2.79 ! [X: int,Y: int,Xs: list_int,N: nat] :
% 2.39/2.79 ( ( X != Y )
% 2.39/2.79 => ( ( ( nth_int @ ( cons_int @ X @ Xs ) @ N )
% 2.39/2.79 = Y )
% 2.39/2.79 = ( ( ( nth_int @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) )
% 2.39/2.79 = Y )
% 2.39/2.79 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % nth_non_equal_first_eq
% 2.39/2.79 thf(fact_3572_nth__non__equal__first__eq,axiom,
% 2.39/2.79 ! [X: nat,Y: nat,Xs: list_nat,N: nat] :
% 2.39/2.79 ( ( X != Y )
% 2.39/2.79 => ( ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ N )
% 2.39/2.79 = Y )
% 2.39/2.79 = ( ( ( nth_nat @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) )
% 2.39/2.79 = Y )
% 2.39/2.79 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % nth_non_equal_first_eq
% 2.39/2.79 thf(fact_3573_one__div__numeral,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 2.39/2.79 = ( produc8508995932063986495nteger @ ( unique3479559517661332726nteger @ one @ N ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % one_div_numeral
% 2.39/2.79 thf(fact_3574_one__div__numeral,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 2.39/2.79 = ( product_fst_nat_nat @ ( unique5055182867167087721od_nat @ one @ N ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % one_div_numeral
% 2.39/2.79 thf(fact_3575_one__div__numeral,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 2.39/2.79 = ( product_fst_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % one_div_numeral
% 2.39/2.79 thf(fact_3576_power__minus1__even,axiom,
% 2.39/2.79 ! [N: nat] :
% 2.39/2.79 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 2.39/2.79 = one_one_int ) ).
% 2.39/2.79
% 2.39/2.79 % power_minus1_even
% 2.39/2.79 thf(fact_3577_power__minus1__even,axiom,
% 2.39/2.79 ! [N: nat] :
% 2.39/2.79 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 2.39/2.79 = one_one_rat ) ).
% 2.39/2.79
% 2.39/2.79 % power_minus1_even
% 2.39/2.79 thf(fact_3578_power__minus1__even,axiom,
% 2.39/2.79 ! [N: nat] :
% 2.39/2.79 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 2.39/2.79 = one_one_Code_integer ) ).
% 2.39/2.79
% 2.39/2.79 % power_minus1_even
% 2.39/2.79 thf(fact_3579_power__minus1__odd,axiom,
% 2.39/2.79 ! [N: nat] :
% 2.39/2.79 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 2.39/2.79 = ( uminus_uminus_int @ one_one_int ) ) ).
% 2.39/2.79
% 2.39/2.79 % power_minus1_odd
% 2.39/2.79 thf(fact_3580_power__minus1__odd,axiom,
% 2.39/2.79 ! [N: nat] :
% 2.39/2.79 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 2.39/2.79 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 2.39/2.79
% 2.39/2.79 % power_minus1_odd
% 2.39/2.79 thf(fact_3581_power__minus1__odd,axiom,
% 2.39/2.79 ! [N: nat] :
% 2.39/2.79 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 2.39/2.79 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 2.39/2.79
% 2.39/2.79 % power_minus1_odd
% 2.39/2.79 thf(fact_3582_power2__diff,axiom,
% 2.39/2.79 ! [X: int,Y: int] :
% 2.39/2.79 ( ( power_power_int @ ( minus_minus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.79 = ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % power2_diff
% 2.39/2.79 thf(fact_3583_power2__diff,axiom,
% 2.39/2.79 ! [X: rat,Y: rat] :
% 2.39/2.79 ( ( power_power_rat @ ( minus_minus_rat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.79 = ( minus_minus_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % power2_diff
% 2.39/2.79 thf(fact_3584_power2__diff,axiom,
% 2.39/2.79 ! [X: code_integer,Y: code_integer] :
% 2.39/2.79 ( ( power_8256067586552552935nteger @ ( minus_8373710615458151222nteger @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.79 = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % power2_diff
% 2.39/2.79 thf(fact_3585_diff__numeral__special_I8_J,axiom,
% 2.39/2.79 ! [M2: num] :
% 2.39/2.79 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 2.39/2.79 = ( neg_numeral_sub_int @ one @ M2 ) ) ).
% 2.39/2.79
% 2.39/2.79 % diff_numeral_special(8)
% 2.39/2.79 thf(fact_3586_diff__numeral__special_I8_J,axiom,
% 2.39/2.79 ! [M2: num] :
% 2.39/2.79 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 2.39/2.79 = ( neg_numeral_sub_rat @ one @ M2 ) ) ).
% 2.39/2.79
% 2.39/2.79 % diff_numeral_special(8)
% 2.39/2.79 thf(fact_3587_diff__numeral__special_I8_J,axiom,
% 2.39/2.79 ! [M2: num] :
% 2.39/2.79 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 2.39/2.79 = ( neg_nu5755505904847501662nteger @ one @ M2 ) ) ).
% 2.39/2.79
% 2.39/2.79 % diff_numeral_special(8)
% 2.39/2.79 thf(fact_3588_diff__numeral__special_I7_J,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 2.39/2.79 = ( neg_numeral_sub_int @ N @ one ) ) ).
% 2.39/2.79
% 2.39/2.79 % diff_numeral_special(7)
% 2.39/2.79 thf(fact_3589_diff__numeral__special_I7_J,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 2.39/2.79 = ( neg_numeral_sub_rat @ N @ one ) ) ).
% 2.39/2.79
% 2.39/2.79 % diff_numeral_special(7)
% 2.39/2.79 thf(fact_3590_diff__numeral__special_I7_J,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 2.39/2.79 = ( neg_nu5755505904847501662nteger @ N @ one ) ) ).
% 2.39/2.79
% 2.39/2.79 % diff_numeral_special(7)
% 2.39/2.79 thf(fact_3591_minus__sub__one__diff__one,axiom,
% 2.39/2.79 ! [M2: num] :
% 2.39/2.79 ( ( minus_minus_int @ ( uminus_uminus_int @ ( neg_numeral_sub_int @ M2 @ one ) ) @ one_one_int )
% 2.39/2.79 = ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % minus_sub_one_diff_one
% 2.39/2.79 thf(fact_3592_minus__sub__one__diff__one,axiom,
% 2.39/2.79 ! [M2: num] :
% 2.39/2.79 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( neg_numeral_sub_rat @ M2 @ one ) ) @ one_one_rat )
% 2.39/2.79 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % minus_sub_one_diff_one
% 2.39/2.79 thf(fact_3593_minus__sub__one__diff__one,axiom,
% 2.39/2.79 ! [M2: num] :
% 2.39/2.79 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( neg_nu5755505904847501662nteger @ M2 @ one ) ) @ one_one_Code_integer )
% 2.39/2.79 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % minus_sub_one_diff_one
% 2.39/2.79 thf(fact_3594_add__neg__numeral__special_I1_J,axiom,
% 2.39/2.79 ! [M2: num] :
% 2.39/2.79 ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) )
% 2.39/2.79 = ( neg_numeral_sub_int @ one @ M2 ) ) ).
% 2.39/2.79
% 2.39/2.79 % add_neg_numeral_special(1)
% 2.39/2.79 thf(fact_3595_add__neg__numeral__special_I1_J,axiom,
% 2.39/2.79 ! [M2: num] :
% 2.39/2.79 ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) )
% 2.39/2.79 = ( neg_numeral_sub_rat @ one @ M2 ) ) ).
% 2.39/2.79
% 2.39/2.79 % add_neg_numeral_special(1)
% 2.39/2.79 thf(fact_3596_add__neg__numeral__special_I1_J,axiom,
% 2.39/2.79 ! [M2: num] :
% 2.39/2.79 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) )
% 2.39/2.79 = ( neg_nu5755505904847501662nteger @ one @ M2 ) ) ).
% 2.39/2.79
% 2.39/2.79 % add_neg_numeral_special(1)
% 2.39/2.79 thf(fact_3597_one__add__one,axiom,
% 2.39/2.79 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 2.39/2.79 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % one_add_one
% 2.39/2.79 thf(fact_3598_one__add__one,axiom,
% 2.39/2.79 ( ( plus_plus_int @ one_one_int @ one_one_int )
% 2.39/2.79 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % one_add_one
% 2.39/2.79 thf(fact_3599_one__add__one,axiom,
% 2.39/2.79 ( ( plus_plus_rat @ one_one_rat @ one_one_rat )
% 2.39/2.79 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % one_add_one
% 2.39/2.79 thf(fact_3600_one__add__one,axiom,
% 2.39/2.79 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ one_one_Code_integer )
% 2.39/2.79 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % one_add_one
% 2.39/2.79 thf(fact_3601_one__add__one,axiom,
% 2.39/2.79 ( ( plus_p4538020629002901425atural @ one_one_Code_natural @ one_one_Code_natural )
% 2.39/2.79 = ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % one_add_one
% 2.39/2.79 thf(fact_3602_Suc__1,axiom,
% 2.39/2.79 ( ( suc @ one_one_nat )
% 2.39/2.79 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % Suc_1
% 2.39/2.79 thf(fact_3603_diff__numeral__special_I2_J,axiom,
% 2.39/2.79 ! [M2: num] :
% 2.39/2.79 ( ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ one_one_int )
% 2.39/2.79 = ( neg_numeral_sub_int @ M2 @ one ) ) ).
% 2.39/2.79
% 2.39/2.79 % diff_numeral_special(2)
% 2.39/2.79 thf(fact_3604_diff__numeral__special_I2_J,axiom,
% 2.39/2.79 ! [M2: num] :
% 2.39/2.79 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M2 ) @ one_one_rat )
% 2.39/2.79 = ( neg_numeral_sub_rat @ M2 @ one ) ) ).
% 2.39/2.79
% 2.39/2.79 % diff_numeral_special(2)
% 2.39/2.79 thf(fact_3605_diff__numeral__special_I2_J,axiom,
% 2.39/2.79 ! [M2: num] :
% 2.39/2.79 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M2 ) @ one_one_Code_integer )
% 2.39/2.79 = ( neg_nu5755505904847501662nteger @ M2 @ one ) ) ).
% 2.39/2.79
% 2.39/2.79 % diff_numeral_special(2)
% 2.39/2.79 thf(fact_3606_diff__numeral__special_I1_J,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( minus_minus_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 2.39/2.79 = ( neg_numeral_sub_int @ one @ N ) ) ).
% 2.39/2.79
% 2.39/2.79 % diff_numeral_special(1)
% 2.39/2.79 thf(fact_3607_diff__numeral__special_I1_J,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( minus_minus_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 2.39/2.79 = ( neg_numeral_sub_rat @ one @ N ) ) ).
% 2.39/2.79
% 2.39/2.79 % diff_numeral_special(1)
% 2.39/2.79 thf(fact_3608_diff__numeral__special_I1_J,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 2.39/2.79 = ( neg_nu5755505904847501662nteger @ one @ N ) ) ).
% 2.39/2.79
% 2.39/2.79 % diff_numeral_special(1)
% 2.39/2.79 thf(fact_3609_one__div__two__eq__zero,axiom,
% 2.39/2.79 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 2.39/2.79 = zero_z3403309356797280102nteger ) ).
% 2.39/2.79
% 2.39/2.79 % one_div_two_eq_zero
% 2.39/2.79 thf(fact_3610_one__div__two__eq__zero,axiom,
% 2.39/2.79 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.79 = zero_zero_nat ) ).
% 2.39/2.79
% 2.39/2.79 % one_div_two_eq_zero
% 2.39/2.79 thf(fact_3611_one__div__two__eq__zero,axiom,
% 2.39/2.79 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 2.39/2.79 = zero_zero_int ) ).
% 2.39/2.79
% 2.39/2.79 % one_div_two_eq_zero
% 2.39/2.79 thf(fact_3612_one__div__two__eq__zero,axiom,
% 2.39/2.79 ( ( divide5121882707175180666atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 2.39/2.79 = zero_z2226904508553997617atural ) ).
% 2.39/2.79
% 2.39/2.79 % one_div_two_eq_zero
% 2.39/2.79 thf(fact_3613_bits__1__div__2,axiom,
% 2.39/2.79 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 2.39/2.79 = zero_z3403309356797280102nteger ) ).
% 2.39/2.79
% 2.39/2.79 % bits_1_div_2
% 2.39/2.79 thf(fact_3614_bits__1__div__2,axiom,
% 2.39/2.79 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.79 = zero_zero_nat ) ).
% 2.39/2.79
% 2.39/2.79 % bits_1_div_2
% 2.39/2.79 thf(fact_3615_bits__1__div__2,axiom,
% 2.39/2.79 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 2.39/2.79 = zero_zero_int ) ).
% 2.39/2.79
% 2.39/2.79 % bits_1_div_2
% 2.39/2.79 thf(fact_3616_bits__1__div__2,axiom,
% 2.39/2.79 ( ( divide5121882707175180666atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 2.39/2.79 = zero_z2226904508553997617atural ) ).
% 2.39/2.79
% 2.39/2.79 % bits_1_div_2
% 2.39/2.79 thf(fact_3617_add__neg__numeral__special_I9_J,axiom,
% 2.39/2.79 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 2.39/2.79 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % add_neg_numeral_special(9)
% 2.39/2.79 thf(fact_3618_add__neg__numeral__special_I9_J,axiom,
% 2.39/2.79 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 2.39/2.79 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % add_neg_numeral_special(9)
% 2.39/2.79 thf(fact_3619_add__neg__numeral__special_I9_J,axiom,
% 2.39/2.79 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 2.39/2.79 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % add_neg_numeral_special(9)
% 2.39/2.79 thf(fact_3620_diff__numeral__special_I10_J,axiom,
% 2.39/2.79 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 2.39/2.79 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % diff_numeral_special(10)
% 2.39/2.79 thf(fact_3621_diff__numeral__special_I10_J,axiom,
% 2.39/2.79 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 2.39/2.79 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % diff_numeral_special(10)
% 2.39/2.79 thf(fact_3622_diff__numeral__special_I10_J,axiom,
% 2.39/2.79 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 2.39/2.79 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % diff_numeral_special(10)
% 2.39/2.79 thf(fact_3623_diff__numeral__special_I11_J,axiom,
% 2.39/2.79 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 2.39/2.79 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % diff_numeral_special(11)
% 2.39/2.79 thf(fact_3624_diff__numeral__special_I11_J,axiom,
% 2.39/2.79 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 2.39/2.79 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % diff_numeral_special(11)
% 2.39/2.79 thf(fact_3625_diff__numeral__special_I11_J,axiom,
% 2.39/2.79 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 2.39/2.79 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % diff_numeral_special(11)
% 2.39/2.79 thf(fact_3626_minus__1__div__2__eq,axiom,
% 2.39/2.79 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 2.39/2.79 = ( uminus_uminus_int @ one_one_int ) ) ).
% 2.39/2.79
% 2.39/2.79 % minus_1_div_2_eq
% 2.39/2.79 thf(fact_3627_minus__1__div__2__eq,axiom,
% 2.39/2.79 ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 2.39/2.79 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 2.39/2.79
% 2.39/2.79 % minus_1_div_2_eq
% 2.39/2.79 thf(fact_3628_add__neg__numeral__special_I4_J,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 2.39/2.79 = ( neg_numeral_sub_int @ N @ one ) ) ).
% 2.39/2.79
% 2.39/2.79 % add_neg_numeral_special(4)
% 2.39/2.79 thf(fact_3629_add__neg__numeral__special_I4_J,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ N ) )
% 2.39/2.79 = ( neg_numeral_sub_rat @ N @ one ) ) ).
% 2.39/2.79
% 2.39/2.79 % add_neg_numeral_special(4)
% 2.39/2.79 thf(fact_3630_add__neg__numeral__special_I4_J,axiom,
% 2.39/2.79 ! [N: num] :
% 2.39/2.79 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ N ) )
% 2.39/2.79 = ( neg_nu5755505904847501662nteger @ N @ one ) ) ).
% 2.39/2.79
% 2.39/2.79 % add_neg_numeral_special(4)
% 2.39/2.79 thf(fact_3631_add__neg__numeral__special_I3_J,axiom,
% 2.39/2.79 ! [M2: num] :
% 2.39/2.79 ( ( plus_plus_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ one_one_int ) )
% 2.39/2.79 = ( neg_numeral_sub_int @ M2 @ one ) ) ).
% 2.39/2.79
% 2.39/2.79 % add_neg_numeral_special(3)
% 2.39/2.79 thf(fact_3632_add__neg__numeral__special_I3_J,axiom,
% 2.39/2.79 ! [M2: num] :
% 2.39/2.79 ( ( plus_plus_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 2.39/2.79 = ( neg_numeral_sub_rat @ M2 @ one ) ) ).
% 2.39/2.79
% 2.39/2.79 % add_neg_numeral_special(3)
% 2.39/2.79 thf(fact_3633_add__neg__numeral__special_I3_J,axiom,
% 2.39/2.79 ! [M2: num] :
% 2.39/2.79 ( ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 2.39/2.79 = ( neg_nu5755505904847501662nteger @ M2 @ one ) ) ).
% 2.39/2.79
% 2.39/2.79 % add_neg_numeral_special(3)
% 2.39/2.79 thf(fact_3634_add__neg__numeral__special_I2_J,axiom,
% 2.39/2.79 ! [M2: num] :
% 2.39/2.79 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int )
% 2.39/2.79 = ( neg_numeral_sub_int @ one @ M2 ) ) ).
% 2.39/2.79
% 2.39/2.79 % add_neg_numeral_special(2)
% 2.39/2.79 thf(fact_3635_add__neg__numeral__special_I2_J,axiom,
% 2.39/2.79 ! [M2: num] :
% 2.39/2.79 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ one_one_rat )
% 2.39/2.79 = ( neg_numeral_sub_rat @ one @ M2 ) ) ).
% 2.39/2.79
% 2.39/2.79 % add_neg_numeral_special(2)
% 2.39/2.79 thf(fact_3636_add__neg__numeral__special_I2_J,axiom,
% 2.39/2.79 ! [M2: num] :
% 2.39/2.79 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ one_one_Code_integer )
% 2.39/2.79 = ( neg_nu5755505904847501662nteger @ one @ M2 ) ) ).
% 2.39/2.79
% 2.39/2.79 % add_neg_numeral_special(2)
% 2.39/2.79 thf(fact_3637_pos__zdiv__mult__2,axiom,
% 2.39/2.79 ! [A: int,B: int] :
% 2.39/2.79 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 2.39/2.79 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 2.39/2.79 = ( divide_divide_int @ B @ A ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % pos_zdiv_mult_2
% 2.39/2.79 thf(fact_3638_neg__zdiv__mult__2,axiom,
% 2.39/2.79 ! [A: int,B: int] :
% 2.39/2.79 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 2.39/2.79 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 2.39/2.79 = ( divide_divide_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % neg_zdiv_mult_2
% 2.39/2.79 thf(fact_3639_minus__1__div__exp__eq__int,axiom,
% 2.39/2.79 ! [N: nat] :
% 2.39/2.79 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 2.39/2.79 = ( uminus_uminus_int @ one_one_int ) ) ).
% 2.39/2.79
% 2.39/2.79 % minus_1_div_exp_eq_int
% 2.39/2.79 thf(fact_3640_int__bit__induct,axiom,
% 2.39/2.79 ! [P2: int > $o,K: int] :
% 2.39/2.79 ( ( P2 @ zero_zero_int )
% 2.39/2.79 => ( ( P2 @ ( uminus_uminus_int @ one_one_int ) )
% 2.39/2.79 => ( ! [K2: int] :
% 2.39/2.79 ( ( P2 @ K2 )
% 2.39/2.79 => ( ( K2 != zero_zero_int )
% 2.39/2.79 => ( P2 @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) )
% 2.39/2.79 => ( ! [K2: int] :
% 2.39/2.79 ( ( P2 @ K2 )
% 2.39/2.79 => ( ( K2
% 2.39/2.79 != ( uminus_uminus_int @ one_one_int ) )
% 2.39/2.79 => ( P2 @ ( plus_plus_int @ one_one_int @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) )
% 2.39/2.79 => ( P2 @ K ) ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % int_bit_induct
% 2.39/2.79 thf(fact_3641_left__add__twice,axiom,
% 2.39/2.79 ! [A: nat,B: nat] :
% 2.39/2.79 ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 2.39/2.79 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 2.39/2.79
% 2.39/2.79 % left_add_twice
% 2.39/2.79 thf(fact_3642_left__add__twice,axiom,
% 2.39/2.79 ! [A: int,B: int] :
% 2.39/2.79 ( ( plus_plus_int @ A @ ( plus_plus_int @ A @ B ) )
% 2.39/2.79 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 2.39/2.79
% 2.39/2.79 % left_add_twice
% 2.39/2.79 thf(fact_3643_left__add__twice,axiom,
% 2.39/2.79 ! [A: rat,B: rat] :
% 2.39/2.79 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 2.39/2.79 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 2.39/2.79
% 2.39/2.79 % left_add_twice
% 2.39/2.79 thf(fact_3644_left__add__twice,axiom,
% 2.39/2.79 ! [A: code_integer,B: code_integer] :
% 2.39/2.79 ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 2.39/2.79 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 2.39/2.79
% 2.39/2.79 % left_add_twice
% 2.39/2.79 thf(fact_3645_left__add__twice,axiom,
% 2.39/2.79 ! [A: code_natural,B: code_natural] :
% 2.39/2.79 ( ( plus_p4538020629002901425atural @ A @ ( plus_p4538020629002901425atural @ A @ B ) )
% 2.39/2.79 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 2.39/2.79
% 2.39/2.79 % left_add_twice
% 2.39/2.79 thf(fact_3646_mult__2__right,axiom,
% 2.39/2.79 ! [Z: nat] :
% 2.39/2.79 ( ( times_times_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.79 = ( plus_plus_nat @ Z @ Z ) ) ).
% 2.39/2.79
% 2.39/2.79 % mult_2_right
% 2.39/2.79 thf(fact_3647_mult__2__right,axiom,
% 2.39/2.79 ! [Z: int] :
% 2.39/2.79 ( ( times_times_int @ Z @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 2.39/2.79 = ( plus_plus_int @ Z @ Z ) ) ).
% 2.39/2.79
% 2.39/2.79 % mult_2_right
% 2.39/2.79 thf(fact_3648_mult__2__right,axiom,
% 2.39/2.79 ! [Z: rat] :
% 2.39/2.79 ( ( times_times_rat @ Z @ ( numeral_numeral_rat @ ( bit0 @ one ) ) )
% 2.39/2.79 = ( plus_plus_rat @ Z @ Z ) ) ).
% 2.39/2.79
% 2.39/2.79 % mult_2_right
% 2.39/2.79 thf(fact_3649_mult__2__right,axiom,
% 2.39/2.79 ! [Z: code_integer] :
% 2.39/2.79 ( ( times_3573771949741848930nteger @ Z @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 2.39/2.79 = ( plus_p5714425477246183910nteger @ Z @ Z ) ) ).
% 2.39/2.79
% 2.39/2.79 % mult_2_right
% 2.39/2.79 thf(fact_3650_mult__2__right,axiom,
% 2.39/2.79 ! [Z: code_natural] :
% 2.39/2.79 ( ( times_2397367101498566445atural @ Z @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 2.39/2.79 = ( plus_p4538020629002901425atural @ Z @ Z ) ) ).
% 2.39/2.79
% 2.39/2.79 % mult_2_right
% 2.39/2.79 thf(fact_3651_mult__2,axiom,
% 2.39/2.79 ! [Z: nat] :
% 2.39/2.79 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z )
% 2.39/2.79 = ( plus_plus_nat @ Z @ Z ) ) ).
% 2.39/2.79
% 2.39/2.79 % mult_2
% 2.39/2.79 thf(fact_3652_mult__2,axiom,
% 2.39/2.79 ! [Z: int] :
% 2.39/2.79 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Z )
% 2.39/2.79 = ( plus_plus_int @ Z @ Z ) ) ).
% 2.39/2.79
% 2.39/2.79 % mult_2
% 2.39/2.79 thf(fact_3653_mult__2,axiom,
% 2.39/2.79 ! [Z: rat] :
% 2.39/2.79 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z )
% 2.39/2.79 = ( plus_plus_rat @ Z @ Z ) ) ).
% 2.39/2.79
% 2.39/2.79 % mult_2
% 2.39/2.79 thf(fact_3654_mult__2,axiom,
% 2.39/2.79 ! [Z: code_integer] :
% 2.39/2.79 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Z )
% 2.39/2.79 = ( plus_p5714425477246183910nteger @ Z @ Z ) ) ).
% 2.39/2.79
% 2.39/2.79 % mult_2
% 2.39/2.79 thf(fact_3655_mult__2,axiom,
% 2.39/2.79 ! [Z: code_natural] :
% 2.39/2.79 ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ Z )
% 2.39/2.79 = ( plus_p4538020629002901425atural @ Z @ Z ) ) ).
% 2.39/2.79
% 2.39/2.79 % mult_2
% 2.39/2.79 thf(fact_3656_power2__eq__square,axiom,
% 2.39/2.79 ! [A: assn] :
% 2.39/2.79 ( ( power_power_assn @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.79 = ( times_times_assn @ A @ A ) ) ).
% 2.39/2.79
% 2.39/2.79 % power2_eq_square
% 2.39/2.79 thf(fact_3657_power2__eq__square,axiom,
% 2.39/2.79 ! [A: nat] :
% 2.39/2.79 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.79 = ( times_times_nat @ A @ A ) ) ).
% 2.39/2.79
% 2.39/2.79 % power2_eq_square
% 2.39/2.79 thf(fact_3658_power2__eq__square,axiom,
% 2.39/2.79 ! [A: int] :
% 2.39/2.79 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.79 = ( times_times_int @ A @ A ) ) ).
% 2.39/2.79
% 2.39/2.79 % power2_eq_square
% 2.39/2.79 thf(fact_3659_power2__eq__square,axiom,
% 2.39/2.79 ! [A: code_integer] :
% 2.39/2.79 ( ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.79 = ( times_3573771949741848930nteger @ A @ A ) ) ).
% 2.39/2.79
% 2.39/2.79 % power2_eq_square
% 2.39/2.79 thf(fact_3660_power2__eq__square,axiom,
% 2.39/2.79 ! [A: code_natural] :
% 2.39/2.79 ( ( power_7079662738309270450atural @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.79 = ( times_2397367101498566445atural @ A @ A ) ) ).
% 2.39/2.79
% 2.39/2.79 % power2_eq_square
% 2.39/2.79 thf(fact_3661_power4__eq__xxxx,axiom,
% 2.39/2.79 ! [X: assn] :
% 2.39/2.79 ( ( power_power_assn @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 2.39/2.79 = ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ X @ X ) @ X ) @ X ) ) ).
% 2.39/2.79
% 2.39/2.79 % power4_eq_xxxx
% 2.39/2.79 thf(fact_3662_power4__eq__xxxx,axiom,
% 2.39/2.79 ! [X: nat] :
% 2.39/2.79 ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 2.39/2.79 = ( times_times_nat @ ( times_times_nat @ ( times_times_nat @ X @ X ) @ X ) @ X ) ) ).
% 2.39/2.79
% 2.39/2.79 % power4_eq_xxxx
% 2.39/2.79 thf(fact_3663_power4__eq__xxxx,axiom,
% 2.39/2.79 ! [X: int] :
% 2.39/2.79 ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 2.39/2.79 = ( times_times_int @ ( times_times_int @ ( times_times_int @ X @ X ) @ X ) @ X ) ) ).
% 2.39/2.79
% 2.39/2.79 % power4_eq_xxxx
% 2.39/2.79 thf(fact_3664_power4__eq__xxxx,axiom,
% 2.39/2.79 ! [X: code_integer] :
% 2.39/2.79 ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 2.39/2.79 = ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ X @ X ) @ X ) @ X ) ) ).
% 2.39/2.79
% 2.39/2.79 % power4_eq_xxxx
% 2.39/2.79 thf(fact_3665_power4__eq__xxxx,axiom,
% 2.39/2.79 ! [X: code_natural] :
% 2.39/2.79 ( ( power_7079662738309270450atural @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 2.39/2.79 = ( times_2397367101498566445atural @ ( times_2397367101498566445atural @ ( times_2397367101498566445atural @ X @ X ) @ X ) @ X ) ) ).
% 2.39/2.79
% 2.39/2.79 % power4_eq_xxxx
% 2.39/2.79 thf(fact_3666_one__power2,axiom,
% 2.39/2.79 ( ( power_8256067586552552935nteger @ one_one_Code_integer @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.79 = one_one_Code_integer ) ).
% 2.39/2.79
% 2.39/2.79 % one_power2
% 2.39/2.79 thf(fact_3667_one__power2,axiom,
% 2.39/2.79 ( ( power_power_rat @ one_one_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.79 = one_one_rat ) ).
% 2.39/2.79
% 2.39/2.79 % one_power2
% 2.39/2.79 thf(fact_3668_one__power2,axiom,
% 2.39/2.79 ( ( power_power_int @ one_one_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.79 = one_one_int ) ).
% 2.39/2.79
% 2.39/2.79 % one_power2
% 2.39/2.79 thf(fact_3669_one__power2,axiom,
% 2.39/2.79 ( ( power_power_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.79 = one_one_nat ) ).
% 2.39/2.79
% 2.39/2.79 % one_power2
% 2.39/2.79 thf(fact_3670_nat__1__add__1,axiom,
% 2.39/2.79 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 2.39/2.79 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % nat_1_add_1
% 2.39/2.79 thf(fact_3671_power2__eq__1__iff,axiom,
% 2.39/2.79 ! [A: int] :
% 2.39/2.79 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.79 = one_one_int )
% 2.39/2.79 = ( ( A = one_one_int )
% 2.39/2.79 | ( A
% 2.39/2.79 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % power2_eq_1_iff
% 2.39/2.79 thf(fact_3672_power2__eq__1__iff,axiom,
% 2.39/2.79 ! [A: rat] :
% 2.39/2.79 ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.79 = one_one_rat )
% 2.39/2.79 = ( ( A = one_one_rat )
% 2.39/2.79 | ( A
% 2.39/2.79 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % power2_eq_1_iff
% 2.39/2.79 thf(fact_3673_power2__eq__1__iff,axiom,
% 2.39/2.79 ! [A: code_integer] :
% 2.39/2.79 ( ( ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.79 = one_one_Code_integer )
% 2.39/2.79 = ( ( A = one_one_Code_integer )
% 2.39/2.79 | ( A
% 2.39/2.79 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % power2_eq_1_iff
% 2.39/2.79 thf(fact_3674_nat__induct2,axiom,
% 2.39/2.79 ! [P2: nat > $o,N: nat] :
% 2.39/2.79 ( ( P2 @ zero_zero_nat )
% 2.39/2.79 => ( ( P2 @ one_one_nat )
% 2.39/2.79 => ( ! [N4: nat] :
% 2.39/2.79 ( ( P2 @ N4 )
% 2.39/2.79 => ( P2 @ ( plus_plus_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 2.39/2.79 => ( P2 @ N ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % nat_induct2
% 2.39/2.79 thf(fact_3675_power2__sum,axiom,
% 2.39/2.79 ! [X: nat,Y: nat] :
% 2.39/2.79 ( ( power_power_nat @ ( plus_plus_nat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.79 = ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % power2_sum
% 2.39/2.79 thf(fact_3676_power2__sum,axiom,
% 2.39/2.79 ! [X: int,Y: int] :
% 2.39/2.79 ( ( power_power_int @ ( plus_plus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.79 = ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % power2_sum
% 2.39/2.79 thf(fact_3677_power2__sum,axiom,
% 2.39/2.79 ! [X: rat,Y: rat] :
% 2.39/2.79 ( ( power_power_rat @ ( plus_plus_rat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.79 = ( plus_plus_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % power2_sum
% 2.39/2.79 thf(fact_3678_power2__sum,axiom,
% 2.39/2.79 ! [X: code_integer,Y: code_integer] :
% 2.39/2.79 ( ( power_8256067586552552935nteger @ ( plus_p5714425477246183910nteger @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.79 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % power2_sum
% 2.39/2.79 thf(fact_3679_power2__sum,axiom,
% 2.39/2.79 ! [X: code_natural,Y: code_natural] :
% 2.39/2.79 ( ( power_7079662738309270450atural @ ( plus_p4538020629002901425atural @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.79 = ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( power_7079662738309270450atural @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_7079662738309270450atural @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_2397367101498566445atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % power2_sum
% 2.39/2.79 thf(fact_3680_square__le__1,axiom,
% 2.39/2.79 ! [X: code_integer] :
% 2.39/2.79 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X )
% 2.39/2.79 => ( ( ord_le3102999989581377725nteger @ X @ one_one_Code_integer )
% 2.39/2.79 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % square_le_1
% 2.39/2.79 thf(fact_3681_square__le__1,axiom,
% 2.39/2.79 ! [X: rat] :
% 2.39/2.79 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X )
% 2.39/2.79 => ( ( ord_less_eq_rat @ X @ one_one_rat )
% 2.39/2.79 => ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % square_le_1
% 2.39/2.79 thf(fact_3682_square__le__1,axiom,
% 2.39/2.79 ! [X: int] :
% 2.39/2.79 ( ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ X )
% 2.39/2.79 => ( ( ord_less_eq_int @ X @ one_one_int )
% 2.39/2.79 => ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % square_le_1
% 2.39/2.79 thf(fact_3683_minus__power__mult__self,axiom,
% 2.39/2.79 ! [A: int,N: nat] :
% 2.39/2.79 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 2.39/2.79 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % minus_power_mult_self
% 2.39/2.79 thf(fact_3684_minus__power__mult__self,axiom,
% 2.39/2.79 ! [A: rat,N: nat] :
% 2.39/2.79 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 2.39/2.79 = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % minus_power_mult_self
% 2.39/2.79 thf(fact_3685_minus__power__mult__self,axiom,
% 2.39/2.79 ! [A: code_integer,N: nat] :
% 2.39/2.79 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 2.39/2.79 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % minus_power_mult_self
% 2.39/2.79 thf(fact_3686_power__odd__eq,axiom,
% 2.39/2.79 ! [A: assn,N: nat] :
% 2.39/2.79 ( ( power_power_assn @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 2.39/2.79 = ( times_times_assn @ A @ ( power_power_assn @ ( power_power_assn @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % power_odd_eq
% 2.39/2.79 thf(fact_3687_power__odd__eq,axiom,
% 2.39/2.79 ! [A: nat,N: nat] :
% 2.39/2.79 ( ( power_power_nat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 2.39/2.79 = ( times_times_nat @ A @ ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % power_odd_eq
% 2.39/2.79 thf(fact_3688_power__odd__eq,axiom,
% 2.39/2.79 ! [A: int,N: nat] :
% 2.39/2.79 ( ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 2.39/2.79 = ( times_times_int @ A @ ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % power_odd_eq
% 2.39/2.79 thf(fact_3689_power__odd__eq,axiom,
% 2.39/2.79 ! [A: code_integer,N: nat] :
% 2.39/2.79 ( ( power_8256067586552552935nteger @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 2.39/2.79 = ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % power_odd_eq
% 2.39/2.79 thf(fact_3690_power__odd__eq,axiom,
% 2.39/2.79 ! [A: code_natural,N: nat] :
% 2.39/2.79 ( ( power_7079662738309270450atural @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 2.39/2.79 = ( times_2397367101498566445atural @ A @ ( power_7079662738309270450atural @ ( power_7079662738309270450atural @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % power_odd_eq
% 2.39/2.79 thf(fact_3691_ex__power__ivl2,axiom,
% 2.39/2.79 ! [B: nat,K: nat] :
% 2.39/2.79 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 2.39/2.79 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 2.39/2.79 => ? [N4: nat] :
% 2.39/2.79 ( ( ord_less_nat @ ( power_power_nat @ B @ N4 ) @ K )
% 2.39/2.79 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N4 @ one_one_nat ) ) ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % ex_power_ivl2
% 2.39/2.79 thf(fact_3692_ex__power__ivl1,axiom,
% 2.39/2.79 ! [B: nat,K: nat] :
% 2.39/2.79 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 2.39/2.79 => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 2.39/2.79 => ? [N4: nat] :
% 2.39/2.79 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N4 ) @ K )
% 2.39/2.79 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N4 @ one_one_nat ) ) ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % ex_power_ivl1
% 2.39/2.79 thf(fact_3693_divmod__step__eq,axiom,
% 2.39/2.79 ! [L: num,R2: nat,Q4: nat] :
% 2.39/2.79 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R2 )
% 2.39/2.79 => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q4 @ R2 ) )
% 2.39/2.79 = ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ one_one_nat ) @ ( minus_minus_nat @ R2 @ ( numeral_numeral_nat @ L ) ) ) ) )
% 2.39/2.79 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R2 )
% 2.39/2.79 => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q4 @ R2 ) )
% 2.39/2.79 = ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ R2 ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % divmod_step_eq
% 2.39/2.79 thf(fact_3694_divmod__step__eq,axiom,
% 2.39/2.79 ! [L: num,R2: int,Q4: int] :
% 2.39/2.79 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R2 )
% 2.39/2.79 => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q4 @ R2 ) )
% 2.39/2.79 = ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ one_one_int ) @ ( minus_minus_int @ R2 @ ( numeral_numeral_int @ L ) ) ) ) )
% 2.39/2.79 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R2 )
% 2.39/2.79 => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q4 @ R2 ) )
% 2.39/2.79 = ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ R2 ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % divmod_step_eq
% 2.39/2.79 thf(fact_3695_divmod__step__eq,axiom,
% 2.39/2.79 ! [L: num,R2: code_integer,Q4: code_integer] :
% 2.39/2.79 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R2 )
% 2.39/2.79 => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q4 @ R2 ) )
% 2.39/2.79 = ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R2 @ ( numera6620942414471956472nteger @ L ) ) ) ) )
% 2.39/2.79 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R2 )
% 2.39/2.79 => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q4 @ R2 ) )
% 2.39/2.79 = ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ R2 ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % divmod_step_eq
% 2.39/2.79 thf(fact_3696_set__bit__0,axiom,
% 2.39/2.79 ! [A: code_integer] :
% 2.39/2.79 ( ( bit_se2793503036327961859nteger @ zero_zero_nat @ A )
% 2.39/2.79 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % set_bit_0
% 2.39/2.79 thf(fact_3697_set__bit__0,axiom,
% 2.39/2.79 ! [A: code_natural] :
% 2.39/2.79 ( ( bit_se1617098188084679374atural @ zero_zero_nat @ A )
% 2.39/2.79 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % set_bit_0
% 2.39/2.79 thf(fact_3698_set__bit__0,axiom,
% 2.39/2.79 ! [A: nat] :
% 2.39/2.79 ( ( bit_se7882103937844011126it_nat @ zero_zero_nat @ A )
% 2.39/2.79 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % set_bit_0
% 2.39/2.79 thf(fact_3699_set__bit__0,axiom,
% 2.39/2.79 ! [A: int] :
% 2.39/2.79 ( ( bit_se7879613467334960850it_int @ zero_zero_nat @ A )
% 2.39/2.79 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % set_bit_0
% 2.39/2.79 thf(fact_3700_unset__bit__0,axiom,
% 2.39/2.79 ! [A: code_integer] :
% 2.39/2.79 ( ( bit_se8260200283734997820nteger @ zero_zero_nat @ A )
% 2.39/2.79 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % unset_bit_0
% 2.39/2.79 thf(fact_3701_unset__bit__0,axiom,
% 2.39/2.79 ! [A: nat] :
% 2.39/2.79 ( ( bit_se4205575877204974255it_nat @ zero_zero_nat @ A )
% 2.39/2.79 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % unset_bit_0
% 2.39/2.79 thf(fact_3702_unset__bit__0,axiom,
% 2.39/2.79 ! [A: code_natural] :
% 2.39/2.79 ( ( bit_se7083795435491715335atural @ zero_zero_nat @ A )
% 2.39/2.79 = ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % unset_bit_0
% 2.39/2.79 thf(fact_3703_unset__bit__0,axiom,
% 2.39/2.79 ! [A: int] :
% 2.39/2.79 ( ( bit_se4203085406695923979it_int @ zero_zero_nat @ A )
% 2.39/2.79 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % unset_bit_0
% 2.39/2.79 thf(fact_3704_dbl__simps_I4_J,axiom,
% 2.39/2.79 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ one_one_int ) )
% 2.39/2.79 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % dbl_simps(4)
% 2.39/2.79 thf(fact_3705_dbl__simps_I4_J,axiom,
% 2.39/2.79 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 2.39/2.79 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % dbl_simps(4)
% 2.39/2.79 thf(fact_3706_dbl__simps_I4_J,axiom,
% 2.39/2.79 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 2.39/2.79 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % dbl_simps(4)
% 2.39/2.79 thf(fact_3707_dbl__simps_I3_J,axiom,
% 2.39/2.79 ( ( neg_numeral_dbl_int @ one_one_int )
% 2.39/2.79 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % dbl_simps(3)
% 2.39/2.79 thf(fact_3708_dbl__simps_I3_J,axiom,
% 2.39/2.79 ( ( neg_numeral_dbl_rat @ one_one_rat )
% 2.39/2.79 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % dbl_simps(3)
% 2.39/2.79 thf(fact_3709_dbl__simps_I3_J,axiom,
% 2.39/2.79 ( ( neg_nu8804712462038260780nteger @ one_one_Code_integer )
% 2.39/2.79 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % dbl_simps(3)
% 2.39/2.79 thf(fact_3710_even__succ__div__exp,axiom,
% 2.39/2.79 ! [A: code_integer,N: nat] :
% 2.39/2.79 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 2.39/2.79 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.39/2.79 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 2.39/2.79 = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % even_succ_div_exp
% 2.39/2.79 thf(fact_3711_even__succ__div__exp,axiom,
% 2.39/2.79 ! [A: nat,N: nat] :
% 2.39/2.79 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 2.39/2.79 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.39/2.79 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 2.39/2.79 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % even_succ_div_exp
% 2.39/2.79 thf(fact_3712_even__succ__div__exp,axiom,
% 2.39/2.79 ! [A: int,N: nat] :
% 2.39/2.79 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 2.39/2.79 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.39/2.79 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 2.39/2.79 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % even_succ_div_exp
% 2.39/2.79 thf(fact_3713_even__succ__div__exp,axiom,
% 2.39/2.79 ! [A: code_natural,N: nat] :
% 2.39/2.79 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 2.39/2.79 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.39/2.79 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ one_one_Code_natural @ A ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 2.39/2.79 = ( divide5121882707175180666atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % even_succ_div_exp
% 2.39/2.79 thf(fact_3714_even__mult__exp__div__exp__iff,axiom,
% 2.39/2.79 ! [A: code_integer,M2: nat,N: nat] :
% 2.39/2.79 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 2.39/2.79 = ( ( ord_less_nat @ N @ M2 )
% 2.39/2.79 | ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 2.39/2.79 = zero_z3403309356797280102nteger )
% 2.39/2.79 | ( ( ord_less_eq_nat @ M2 @ N )
% 2.39/2.79 & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % even_mult_exp_div_exp_iff
% 2.39/2.79 thf(fact_3715_even__mult__exp__div__exp__iff,axiom,
% 2.39/2.79 ! [A: nat,M2: nat,N: nat] :
% 2.39/2.79 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 2.39/2.79 = ( ( ord_less_nat @ N @ M2 )
% 2.39/2.79 | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 2.39/2.79 = zero_zero_nat )
% 2.39/2.79 | ( ( ord_less_eq_nat @ M2 @ N )
% 2.39/2.79 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % even_mult_exp_div_exp_iff
% 2.39/2.79 thf(fact_3716_even__mult__exp__div__exp__iff,axiom,
% 2.39/2.79 ! [A: int,M2: nat,N: nat] :
% 2.39/2.79 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 2.39/2.79 = ( ( ord_less_nat @ N @ M2 )
% 2.39/2.79 | ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 2.39/2.79 = zero_zero_int )
% 2.39/2.79 | ( ( ord_less_eq_nat @ M2 @ N )
% 2.39/2.79 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % even_mult_exp_div_exp_iff
% 2.39/2.79 thf(fact_3717_even__mult__exp__div__exp__iff,axiom,
% 2.39/2.79 ! [A: code_natural,M2: nat,N: nat] :
% 2.39/2.79 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) ) )
% 2.39/2.79 = ( ( ord_less_nat @ N @ M2 )
% 2.39/2.79 | ( ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N )
% 2.39/2.79 = zero_z2226904508553997617atural )
% 2.39/2.79 | ( ( ord_less_eq_nat @ M2 @ N )
% 2.39/2.79 & ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % even_mult_exp_div_exp_iff
% 2.39/2.79 thf(fact_3718_divmod__digit__1_I1_J,axiom,
% 2.39/2.79 ! [A: code_integer,B: code_integer] :
% 2.39/2.79 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.79 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 2.39/2.79 => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 2.39/2.79 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_Code_integer )
% 2.39/2.79 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % divmod_digit_1(1)
% 2.39/2.79 thf(fact_3719_divmod__digit__1_I1_J,axiom,
% 2.39/2.79 ! [A: nat,B: nat] :
% 2.39/2.79 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 2.39/2.79 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 2.39/2.79 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 2.39/2.79 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_nat )
% 2.39/2.79 = ( divide_divide_nat @ A @ B ) ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % divmod_digit_1(1)
% 2.39/2.79 thf(fact_3720_divmod__digit__1_I1_J,axiom,
% 2.39/2.79 ! [A: int,B: int] :
% 2.39/2.79 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 2.39/2.79 => ( ( ord_less_int @ zero_zero_int @ B )
% 2.39/2.79 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 2.39/2.79 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_int )
% 2.39/2.79 = ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % divmod_digit_1(1)
% 2.39/2.79 thf(fact_3721_nat__dvd__1__iff__1,axiom,
% 2.39/2.79 ! [M2: nat] :
% 2.39/2.79 ( ( dvd_dvd_nat @ M2 @ one_one_nat )
% 2.39/2.79 = ( M2 = one_one_nat ) ) ).
% 2.39/2.79
% 2.39/2.79 % nat_dvd_1_iff_1
% 2.39/2.79 thf(fact_3722_dvd__times__right__cancel__iff,axiom,
% 2.39/2.79 ! [A: nat,B: nat,C: nat] :
% 2.39/2.79 ( ( A != zero_zero_nat )
% 2.39/2.79 => ( ( dvd_dvd_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) )
% 2.39/2.79 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % dvd_times_right_cancel_iff
% 2.39/2.79 thf(fact_3723_dvd__times__right__cancel__iff,axiom,
% 2.39/2.79 ! [A: int,B: int,C: int] :
% 2.39/2.79 ( ( A != zero_zero_int )
% 2.39/2.79 => ( ( dvd_dvd_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) )
% 2.39/2.79 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % dvd_times_right_cancel_iff
% 2.39/2.79 thf(fact_3724_dvd__times__right__cancel__iff,axiom,
% 2.39/2.79 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.79 ( ( A != zero_z3403309356797280102nteger )
% 2.39/2.79 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ A ) @ ( times_3573771949741848930nteger @ C @ A ) )
% 2.39/2.79 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % dvd_times_right_cancel_iff
% 2.39/2.79 thf(fact_3725_dvd__times__right__cancel__iff,axiom,
% 2.39/2.79 ! [A: code_natural,B: code_natural,C: code_natural] :
% 2.39/2.79 ( ( A != zero_z2226904508553997617atural )
% 2.39/2.79 => ( ( dvd_dvd_Code_natural @ ( times_2397367101498566445atural @ B @ A ) @ ( times_2397367101498566445atural @ C @ A ) )
% 2.39/2.79 = ( dvd_dvd_Code_natural @ B @ C ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % dvd_times_right_cancel_iff
% 2.39/2.79 thf(fact_3726_dvd__times__left__cancel__iff,axiom,
% 2.39/2.79 ! [A: nat,B: nat,C: nat] :
% 2.39/2.79 ( ( A != zero_zero_nat )
% 2.39/2.79 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
% 2.39/2.79 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % dvd_times_left_cancel_iff
% 2.39/2.79 thf(fact_3727_dvd__times__left__cancel__iff,axiom,
% 2.39/2.79 ! [A: int,B: int,C: int] :
% 2.39/2.79 ( ( A != zero_zero_int )
% 2.39/2.79 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
% 2.39/2.79 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % dvd_times_left_cancel_iff
% 2.39/2.79 thf(fact_3728_dvd__times__left__cancel__iff,axiom,
% 2.39/2.79 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.79 ( ( A != zero_z3403309356797280102nteger )
% 2.39/2.79 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) )
% 2.39/2.79 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % dvd_times_left_cancel_iff
% 2.39/2.79 thf(fact_3729_dvd__times__left__cancel__iff,axiom,
% 2.39/2.79 ! [A: code_natural,B: code_natural,C: code_natural] :
% 2.39/2.79 ( ( A != zero_z2226904508553997617atural )
% 2.39/2.79 => ( ( dvd_dvd_Code_natural @ ( times_2397367101498566445atural @ A @ B ) @ ( times_2397367101498566445atural @ A @ C ) )
% 2.39/2.79 = ( dvd_dvd_Code_natural @ B @ C ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % dvd_times_left_cancel_iff
% 2.39/2.79 thf(fact_3730_dvd__mult__cancel__right,axiom,
% 2.39/2.79 ! [A: rat,C: rat,B: rat] :
% 2.39/2.79 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 2.39/2.79 = ( ( C = zero_zero_rat )
% 2.39/2.79 | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % dvd_mult_cancel_right
% 2.39/2.79 thf(fact_3731_dvd__mult__cancel__right,axiom,
% 2.39/2.79 ! [A: int,C: int,B: int] :
% 2.39/2.79 ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 2.39/2.79 = ( ( C = zero_zero_int )
% 2.39/2.79 | ( dvd_dvd_int @ A @ B ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % dvd_mult_cancel_right
% 2.39/2.79 thf(fact_3732_dvd__mult__cancel__right,axiom,
% 2.39/2.79 ! [A: code_integer,C: code_integer,B: code_integer] :
% 2.39/2.79 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 2.39/2.79 = ( ( C = zero_z3403309356797280102nteger )
% 2.39/2.79 | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % dvd_mult_cancel_right
% 2.39/2.79 thf(fact_3733_dvd__mult__cancel__left,axiom,
% 2.39/2.79 ! [C: rat,A: rat,B: rat] :
% 2.39/2.79 ( ( dvd_dvd_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 2.39/2.79 = ( ( C = zero_zero_rat )
% 2.39/2.79 | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % dvd_mult_cancel_left
% 2.39/2.79 thf(fact_3734_dvd__mult__cancel__left,axiom,
% 2.39/2.79 ! [C: int,A: int,B: int] :
% 2.39/2.79 ( ( dvd_dvd_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 2.39/2.79 = ( ( C = zero_zero_int )
% 2.39/2.79 | ( dvd_dvd_int @ A @ B ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % dvd_mult_cancel_left
% 2.39/2.79 thf(fact_3735_dvd__mult__cancel__left,axiom,
% 2.39/2.79 ! [C: code_integer,A: code_integer,B: code_integer] :
% 2.39/2.79 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 2.39/2.79 = ( ( C = zero_z3403309356797280102nteger )
% 2.39/2.79 | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % dvd_mult_cancel_left
% 2.39/2.79 thf(fact_3736_dvd__add__times__triv__right__iff,axiom,
% 2.39/2.79 ! [A: rat,B: rat,C: rat] :
% 2.39/2.79 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ ( times_times_rat @ C @ A ) ) )
% 2.39/2.79 = ( dvd_dvd_rat @ A @ B ) ) ).
% 2.39/2.79
% 2.39/2.79 % dvd_add_times_triv_right_iff
% 2.39/2.79 thf(fact_3737_dvd__add__times__triv__right__iff,axiom,
% 2.39/2.79 ! [A: nat,B: nat,C: nat] :
% 2.39/2.79 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ ( times_times_nat @ C @ A ) ) )
% 2.39/2.79 = ( dvd_dvd_nat @ A @ B ) ) ).
% 2.39/2.79
% 2.39/2.79 % dvd_add_times_triv_right_iff
% 2.39/2.79 thf(fact_3738_dvd__add__times__triv__right__iff,axiom,
% 2.39/2.79 ! [A: int,B: int,C: int] :
% 2.39/2.79 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ C @ A ) ) )
% 2.39/2.79 = ( dvd_dvd_int @ A @ B ) ) ).
% 2.39/2.79
% 2.39/2.79 % dvd_add_times_triv_right_iff
% 2.39/2.79 thf(fact_3739_dvd__add__times__triv__right__iff,axiom,
% 2.39/2.79 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.79 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ ( times_3573771949741848930nteger @ C @ A ) ) )
% 2.39/2.79 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 2.39/2.79
% 2.39/2.79 % dvd_add_times_triv_right_iff
% 2.39/2.79 thf(fact_3740_dvd__add__times__triv__right__iff,axiom,
% 2.39/2.79 ! [A: code_natural,B: code_natural,C: code_natural] :
% 2.39/2.79 ( ( dvd_dvd_Code_natural @ A @ ( plus_p4538020629002901425atural @ B @ ( times_2397367101498566445atural @ C @ A ) ) )
% 2.39/2.79 = ( dvd_dvd_Code_natural @ A @ B ) ) ).
% 2.39/2.79
% 2.39/2.79 % dvd_add_times_triv_right_iff
% 2.39/2.79 thf(fact_3741_dvd__add__times__triv__left__iff,axiom,
% 2.39/2.79 ! [A: rat,C: rat,B: rat] :
% 2.39/2.79 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ ( times_times_rat @ C @ A ) @ B ) )
% 2.39/2.79 = ( dvd_dvd_rat @ A @ B ) ) ).
% 2.39/2.79
% 2.39/2.79 % dvd_add_times_triv_left_iff
% 2.39/2.79 thf(fact_3742_dvd__add__times__triv__left__iff,axiom,
% 2.39/2.79 ! [A: nat,C: nat,B: nat] :
% 2.39/2.79 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ B ) )
% 2.39/2.79 = ( dvd_dvd_nat @ A @ B ) ) ).
% 2.39/2.79
% 2.39/2.79 % dvd_add_times_triv_left_iff
% 2.39/2.79 thf(fact_3743_dvd__add__times__triv__left__iff,axiom,
% 2.39/2.79 ! [A: int,C: int,B: int] :
% 2.39/2.79 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ ( times_times_int @ C @ A ) @ B ) )
% 2.39/2.79 = ( dvd_dvd_int @ A @ B ) ) ).
% 2.39/2.79
% 2.39/2.79 % dvd_add_times_triv_left_iff
% 2.39/2.79 thf(fact_3744_dvd__add__times__triv__left__iff,axiom,
% 2.39/2.79 ! [A: code_integer,C: code_integer,B: code_integer] :
% 2.39/2.79 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ A ) @ B ) )
% 2.39/2.79 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 2.39/2.79
% 2.39/2.79 % dvd_add_times_triv_left_iff
% 2.39/2.79 thf(fact_3745_dvd__add__times__triv__left__iff,axiom,
% 2.39/2.79 ! [A: code_natural,C: code_natural,B: code_natural] :
% 2.39/2.79 ( ( dvd_dvd_Code_natural @ A @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ C @ A ) @ B ) )
% 2.39/2.79 = ( dvd_dvd_Code_natural @ A @ B ) ) ).
% 2.39/2.79
% 2.39/2.79 % dvd_add_times_triv_left_iff
% 2.39/2.79 thf(fact_3746_unit__prod,axiom,
% 2.39/2.79 ! [A: nat,B: nat] :
% 2.39/2.79 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 2.39/2.79 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 2.39/2.79 => ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % unit_prod
% 2.39/2.79 thf(fact_3747_unit__prod,axiom,
% 2.39/2.79 ! [A: int,B: int] :
% 2.39/2.79 ( ( dvd_dvd_int @ A @ one_one_int )
% 2.39/2.79 => ( ( dvd_dvd_int @ B @ one_one_int )
% 2.39/2.79 => ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % unit_prod
% 2.39/2.79 thf(fact_3748_unit__prod,axiom,
% 2.39/2.79 ! [A: code_integer,B: code_integer] :
% 2.39/2.79 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 2.39/2.79 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 2.39/2.79 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % unit_prod
% 2.39/2.79 thf(fact_3749_unit__prod,axiom,
% 2.39/2.79 ! [A: code_natural,B: code_natural] :
% 2.39/2.79 ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 2.39/2.79 => ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 2.39/2.79 => ( dvd_dvd_Code_natural @ ( times_2397367101498566445atural @ A @ B ) @ one_one_Code_natural ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % unit_prod
% 2.39/2.79 thf(fact_3750_mod__mult__self2__is__0,axiom,
% 2.39/2.79 ! [A: code_integer,B: code_integer] :
% 2.39/2.79 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ B )
% 2.39/2.79 = zero_z3403309356797280102nteger ) ).
% 2.39/2.79
% 2.39/2.79 % mod_mult_self2_is_0
% 2.39/2.79 thf(fact_3751_mod__mult__self2__is__0,axiom,
% 2.39/2.79 ! [A: nat,B: nat] :
% 2.39/2.79 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ B )
% 2.39/2.79 = zero_zero_nat ) ).
% 2.39/2.79
% 2.39/2.79 % mod_mult_self2_is_0
% 2.39/2.79 thf(fact_3752_mod__mult__self2__is__0,axiom,
% 2.39/2.79 ! [A: int,B: int] :
% 2.39/2.79 ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ B )
% 2.39/2.79 = zero_zero_int ) ).
% 2.39/2.79
% 2.39/2.79 % mod_mult_self2_is_0
% 2.39/2.79 thf(fact_3753_mod__mult__self2__is__0,axiom,
% 2.39/2.79 ! [A: code_natural,B: code_natural] :
% 2.39/2.79 ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ B ) @ B )
% 2.39/2.79 = zero_z2226904508553997617atural ) ).
% 2.39/2.79
% 2.39/2.79 % mod_mult_self2_is_0
% 2.39/2.79 thf(fact_3754_mod__mult__self1__is__0,axiom,
% 2.39/2.79 ! [B: code_integer,A: code_integer] :
% 2.39/2.79 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ B @ A ) @ B )
% 2.39/2.79 = zero_z3403309356797280102nteger ) ).
% 2.39/2.79
% 2.39/2.79 % mod_mult_self1_is_0
% 2.39/2.79 thf(fact_3755_mod__mult__self1__is__0,axiom,
% 2.39/2.79 ! [B: nat,A: nat] :
% 2.39/2.79 ( ( modulo_modulo_nat @ ( times_times_nat @ B @ A ) @ B )
% 2.39/2.79 = zero_zero_nat ) ).
% 2.39/2.79
% 2.39/2.79 % mod_mult_self1_is_0
% 2.39/2.79 thf(fact_3756_mod__mult__self1__is__0,axiom,
% 2.39/2.79 ! [B: int,A: int] :
% 2.39/2.79 ( ( modulo_modulo_int @ ( times_times_int @ B @ A ) @ B )
% 2.39/2.79 = zero_zero_int ) ).
% 2.39/2.79
% 2.39/2.79 % mod_mult_self1_is_0
% 2.39/2.79 thf(fact_3757_mod__mult__self1__is__0,axiom,
% 2.39/2.79 ! [B: code_natural,A: code_natural] :
% 2.39/2.79 ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ B @ A ) @ B )
% 2.39/2.79 = zero_z2226904508553997617atural ) ).
% 2.39/2.79
% 2.39/2.79 % mod_mult_self1_is_0
% 2.39/2.79 thf(fact_3758_mod__by__1,axiom,
% 2.39/2.79 ! [A: code_integer] :
% 2.39/2.79 ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 2.39/2.79 = zero_z3403309356797280102nteger ) ).
% 2.39/2.79
% 2.39/2.79 % mod_by_1
% 2.39/2.79 thf(fact_3759_mod__by__1,axiom,
% 2.39/2.79 ! [A: nat] :
% 2.39/2.79 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 2.39/2.79 = zero_zero_nat ) ).
% 2.39/2.79
% 2.39/2.79 % mod_by_1
% 2.39/2.79 thf(fact_3760_mod__by__1,axiom,
% 2.39/2.79 ! [A: int] :
% 2.39/2.79 ( ( modulo_modulo_int @ A @ one_one_int )
% 2.39/2.79 = zero_zero_int ) ).
% 2.39/2.79
% 2.39/2.79 % mod_by_1
% 2.39/2.79 thf(fact_3761_mod__by__1,axiom,
% 2.39/2.79 ! [A: code_natural] :
% 2.39/2.79 ( ( modulo8411746178871703098atural @ A @ one_one_Code_natural )
% 2.39/2.79 = zero_z2226904508553997617atural ) ).
% 2.39/2.79
% 2.39/2.79 % mod_by_1
% 2.39/2.79 thf(fact_3762_bits__mod__by__1,axiom,
% 2.39/2.79 ! [A: code_integer] :
% 2.39/2.79 ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 2.39/2.79 = zero_z3403309356797280102nteger ) ).
% 2.39/2.79
% 2.39/2.79 % bits_mod_by_1
% 2.39/2.79 thf(fact_3763_bits__mod__by__1,axiom,
% 2.39/2.79 ! [A: nat] :
% 2.39/2.79 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 2.39/2.79 = zero_zero_nat ) ).
% 2.39/2.79
% 2.39/2.79 % bits_mod_by_1
% 2.39/2.79 thf(fact_3764_bits__mod__by__1,axiom,
% 2.39/2.79 ! [A: int] :
% 2.39/2.79 ( ( modulo_modulo_int @ A @ one_one_int )
% 2.39/2.79 = zero_zero_int ) ).
% 2.39/2.79
% 2.39/2.79 % bits_mod_by_1
% 2.39/2.79 thf(fact_3765_bits__mod__by__1,axiom,
% 2.39/2.79 ! [A: code_natural] :
% 2.39/2.79 ( ( modulo8411746178871703098atural @ A @ one_one_Code_natural )
% 2.39/2.79 = zero_z2226904508553997617atural ) ).
% 2.39/2.79
% 2.39/2.79 % bits_mod_by_1
% 2.39/2.79 thf(fact_3766_mod__mult__self4,axiom,
% 2.39/2.79 ! [B: code_integer,C: code_integer,A: code_integer] :
% 2.39/2.79 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ C ) @ A ) @ B )
% 2.39/2.79 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 2.39/2.79
% 2.39/2.79 % mod_mult_self4
% 2.39/2.79 thf(fact_3767_mod__mult__self4,axiom,
% 2.39/2.79 ! [B: nat,C: nat,A: nat] :
% 2.39/2.79 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 2.39/2.79 = ( modulo_modulo_nat @ A @ B ) ) ).
% 2.39/2.79
% 2.39/2.79 % mod_mult_self4
% 2.39/2.79 thf(fact_3768_mod__mult__self4,axiom,
% 2.39/2.79 ! [B: int,C: int,A: int] :
% 2.39/2.79 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 2.39/2.79 = ( modulo_modulo_int @ A @ B ) ) ).
% 2.39/2.79
% 2.39/2.79 % mod_mult_self4
% 2.39/2.79 thf(fact_3769_mod__mult__self4,axiom,
% 2.39/2.79 ! [B: code_natural,C: code_natural,A: code_natural] :
% 2.39/2.79 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ C ) @ A ) @ B )
% 2.39/2.79 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 2.39/2.79
% 2.39/2.79 % mod_mult_self4
% 2.39/2.79 thf(fact_3770_mod__mult__self3,axiom,
% 2.39/2.79 ! [C: code_integer,B: code_integer,A: code_integer] :
% 2.39/2.79 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ B ) @ A ) @ B )
% 2.39/2.79 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 2.39/2.79
% 2.39/2.79 % mod_mult_self3
% 2.39/2.79 thf(fact_3771_mod__mult__self3,axiom,
% 2.39/2.79 ! [C: nat,B: nat,A: nat] :
% 2.39/2.79 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 2.39/2.79 = ( modulo_modulo_nat @ A @ B ) ) ).
% 2.39/2.79
% 2.39/2.79 % mod_mult_self3
% 2.39/2.79 thf(fact_3772_mod__mult__self3,axiom,
% 2.39/2.79 ! [C: int,B: int,A: int] :
% 2.39/2.79 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 2.39/2.79 = ( modulo_modulo_int @ A @ B ) ) ).
% 2.39/2.79
% 2.39/2.79 % mod_mult_self3
% 2.39/2.79 thf(fact_3773_mod__mult__self3,axiom,
% 2.39/2.79 ! [C: code_natural,B: code_natural,A: code_natural] :
% 2.39/2.79 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ C @ B ) @ A ) @ B )
% 2.39/2.79 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 2.39/2.79
% 2.39/2.79 % mod_mult_self3
% 2.39/2.79 thf(fact_3774_mod__mult__self2,axiom,
% 2.39/2.79 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.79 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) @ B )
% 2.39/2.79 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 2.39/2.79
% 2.39/2.79 % mod_mult_self2
% 2.39/2.79 thf(fact_3775_mod__mult__self2,axiom,
% 2.39/2.79 ! [A: nat,B: nat,C: nat] :
% 2.39/2.79 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 2.39/2.79 = ( modulo_modulo_nat @ A @ B ) ) ).
% 2.39/2.79
% 2.39/2.79 % mod_mult_self2
% 2.39/2.79 thf(fact_3776_mod__mult__self2,axiom,
% 2.39/2.79 ! [A: int,B: int,C: int] :
% 2.39/2.79 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 2.39/2.79 = ( modulo_modulo_int @ A @ B ) ) ).
% 2.39/2.79
% 2.39/2.79 % mod_mult_self2
% 2.39/2.79 thf(fact_3777_mod__mult__self2,axiom,
% 2.39/2.79 ! [A: code_natural,B: code_natural,C: code_natural] :
% 2.39/2.79 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ B @ C ) ) @ B )
% 2.39/2.79 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 2.39/2.79
% 2.39/2.79 % mod_mult_self2
% 2.39/2.79 thf(fact_3778_mod__mult__self1,axiom,
% 2.39/2.79 ! [A: code_integer,C: code_integer,B: code_integer] :
% 2.39/2.79 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ B ) ) @ B )
% 2.39/2.79 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 2.39/2.79
% 2.39/2.79 % mod_mult_self1
% 2.39/2.79 thf(fact_3779_mod__mult__self1,axiom,
% 2.39/2.79 ! [A: nat,C: nat,B: nat] :
% 2.39/2.79 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 2.39/2.79 = ( modulo_modulo_nat @ A @ B ) ) ).
% 2.39/2.79
% 2.39/2.79 % mod_mult_self1
% 2.39/2.79 thf(fact_3780_mod__mult__self1,axiom,
% 2.39/2.79 ! [A: int,C: int,B: int] :
% 2.39/2.79 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 2.39/2.79 = ( modulo_modulo_int @ A @ B ) ) ).
% 2.39/2.79
% 2.39/2.79 % mod_mult_self1
% 2.39/2.79 thf(fact_3781_mod__mult__self1,axiom,
% 2.39/2.79 ! [A: code_natural,C: code_natural,B: code_natural] :
% 2.39/2.79 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ C @ B ) ) @ B )
% 2.39/2.79 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 2.39/2.79
% 2.39/2.79 % mod_mult_self1
% 2.39/2.79 thf(fact_3782_dvd__div__mult__self,axiom,
% 2.39/2.79 ! [A: code_integer,B: code_integer] :
% 2.39/2.79 ( ( dvd_dvd_Code_integer @ A @ B )
% 2.39/2.79 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 2.39/2.79 = B ) ) ).
% 2.39/2.79
% 2.39/2.79 % dvd_div_mult_self
% 2.39/2.79 thf(fact_3783_dvd__div__mult__self,axiom,
% 2.39/2.79 ! [A: nat,B: nat] :
% 2.39/2.79 ( ( dvd_dvd_nat @ A @ B )
% 2.39/2.79 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 2.39/2.79 = B ) ) ).
% 2.39/2.79
% 2.39/2.79 % dvd_div_mult_self
% 2.39/2.79 thf(fact_3784_dvd__div__mult__self,axiom,
% 2.39/2.79 ! [A: int,B: int] :
% 2.39/2.79 ( ( dvd_dvd_int @ A @ B )
% 2.39/2.79 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 2.39/2.79 = B ) ) ).
% 2.39/2.79
% 2.39/2.79 % dvd_div_mult_self
% 2.39/2.79 thf(fact_3785_dvd__div__mult__self,axiom,
% 2.39/2.79 ! [A: code_natural,B: code_natural] :
% 2.39/2.79 ( ( dvd_dvd_Code_natural @ A @ B )
% 2.39/2.79 => ( ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ B @ A ) @ A )
% 2.39/2.79 = B ) ) ).
% 2.39/2.79
% 2.39/2.79 % dvd_div_mult_self
% 2.39/2.79 thf(fact_3786_dvd__mult__div__cancel,axiom,
% 2.39/2.79 ! [A: code_integer,B: code_integer] :
% 2.39/2.79 ( ( dvd_dvd_Code_integer @ A @ B )
% 2.39/2.79 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ A ) )
% 2.39/2.79 = B ) ) ).
% 2.39/2.79
% 2.39/2.79 % dvd_mult_div_cancel
% 2.39/2.79 thf(fact_3787_dvd__mult__div__cancel,axiom,
% 2.39/2.79 ! [A: nat,B: nat] :
% 2.39/2.79 ( ( dvd_dvd_nat @ A @ B )
% 2.39/2.79 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ A ) )
% 2.39/2.79 = B ) ) ).
% 2.39/2.79
% 2.39/2.79 % dvd_mult_div_cancel
% 2.39/2.79 thf(fact_3788_dvd__mult__div__cancel,axiom,
% 2.39/2.79 ! [A: int,B: int] :
% 2.39/2.79 ( ( dvd_dvd_int @ A @ B )
% 2.39/2.79 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ A ) )
% 2.39/2.79 = B ) ) ).
% 2.39/2.79
% 2.39/2.79 % dvd_mult_div_cancel
% 2.39/2.79 thf(fact_3789_dvd__mult__div__cancel,axiom,
% 2.39/2.79 ! [A: code_natural,B: code_natural] :
% 2.39/2.79 ( ( dvd_dvd_Code_natural @ A @ B )
% 2.39/2.79 => ( ( times_2397367101498566445atural @ A @ ( divide5121882707175180666atural @ B @ A ) )
% 2.39/2.79 = B ) ) ).
% 2.39/2.79
% 2.39/2.79 % dvd_mult_div_cancel
% 2.39/2.79 thf(fact_3790_unit__div,axiom,
% 2.39/2.79 ! [A: code_integer,B: code_integer] :
% 2.39/2.79 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 2.39/2.79 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 2.39/2.79 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % unit_div
% 2.39/2.79 thf(fact_3791_unit__div,axiom,
% 2.39/2.79 ! [A: nat,B: nat] :
% 2.39/2.79 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 2.39/2.79 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 2.39/2.79 => ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % unit_div
% 2.39/2.79 thf(fact_3792_unit__div,axiom,
% 2.39/2.79 ! [A: int,B: int] :
% 2.39/2.79 ( ( dvd_dvd_int @ A @ one_one_int )
% 2.39/2.79 => ( ( dvd_dvd_int @ B @ one_one_int )
% 2.39/2.79 => ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % unit_div
% 2.39/2.79 thf(fact_3793_unit__div,axiom,
% 2.39/2.79 ! [A: code_natural,B: code_natural] :
% 2.39/2.79 ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 2.39/2.79 => ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 2.39/2.79 => ( dvd_dvd_Code_natural @ ( divide5121882707175180666atural @ A @ B ) @ one_one_Code_natural ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % unit_div
% 2.39/2.79 thf(fact_3794_unit__div__1__unit,axiom,
% 2.39/2.79 ! [A: code_integer] :
% 2.39/2.79 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 2.39/2.79 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) @ one_one_Code_integer ) ) ).
% 2.39/2.79
% 2.39/2.79 % unit_div_1_unit
% 2.39/2.79 thf(fact_3795_unit__div__1__unit,axiom,
% 2.39/2.79 ! [A: nat] :
% 2.39/2.79 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 2.39/2.79 => ( dvd_dvd_nat @ ( divide_divide_nat @ one_one_nat @ A ) @ one_one_nat ) ) ).
% 2.39/2.79
% 2.39/2.79 % unit_div_1_unit
% 2.39/2.79 thf(fact_3796_unit__div__1__unit,axiom,
% 2.39/2.79 ! [A: int] :
% 2.39/2.79 ( ( dvd_dvd_int @ A @ one_one_int )
% 2.39/2.79 => ( dvd_dvd_int @ ( divide_divide_int @ one_one_int @ A ) @ one_one_int ) ) ).
% 2.39/2.79
% 2.39/2.79 % unit_div_1_unit
% 2.39/2.79 thf(fact_3797_unit__div__1__unit,axiom,
% 2.39/2.79 ! [A: code_natural] :
% 2.39/2.79 ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 2.39/2.79 => ( dvd_dvd_Code_natural @ ( divide5121882707175180666atural @ one_one_Code_natural @ A ) @ one_one_Code_natural ) ) ).
% 2.39/2.79
% 2.39/2.79 % unit_div_1_unit
% 2.39/2.79 thf(fact_3798_unit__div__1__div__1,axiom,
% 2.39/2.79 ! [A: code_integer] :
% 2.39/2.79 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 2.39/2.79 => ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 2.39/2.79 = A ) ) ).
% 2.39/2.79
% 2.39/2.79 % unit_div_1_div_1
% 2.39/2.79 thf(fact_3799_unit__div__1__div__1,axiom,
% 2.39/2.79 ! [A: nat] :
% 2.39/2.79 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 2.39/2.79 => ( ( divide_divide_nat @ one_one_nat @ ( divide_divide_nat @ one_one_nat @ A ) )
% 2.39/2.79 = A ) ) ).
% 2.39/2.79
% 2.39/2.79 % unit_div_1_div_1
% 2.39/2.79 thf(fact_3800_unit__div__1__div__1,axiom,
% 2.39/2.79 ! [A: int] :
% 2.39/2.79 ( ( dvd_dvd_int @ A @ one_one_int )
% 2.39/2.79 => ( ( divide_divide_int @ one_one_int @ ( divide_divide_int @ one_one_int @ A ) )
% 2.39/2.79 = A ) ) ).
% 2.39/2.79
% 2.39/2.79 % unit_div_1_div_1
% 2.39/2.79 thf(fact_3801_unit__div__1__div__1,axiom,
% 2.39/2.79 ! [A: code_natural] :
% 2.39/2.79 ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 2.39/2.79 => ( ( divide5121882707175180666atural @ one_one_Code_natural @ ( divide5121882707175180666atural @ one_one_Code_natural @ A ) )
% 2.39/2.79 = A ) ) ).
% 2.39/2.79
% 2.39/2.79 % unit_div_1_div_1
% 2.39/2.79 thf(fact_3802_unit__div__mult__self,axiom,
% 2.39/2.79 ! [A: code_integer,B: code_integer] :
% 2.39/2.79 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 2.39/2.79 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 2.39/2.79 = B ) ) ).
% 2.39/2.79
% 2.39/2.79 % unit_div_mult_self
% 2.39/2.79 thf(fact_3803_unit__div__mult__self,axiom,
% 2.39/2.79 ! [A: nat,B: nat] :
% 2.39/2.79 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 2.39/2.79 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 2.39/2.79 = B ) ) ).
% 2.39/2.79
% 2.39/2.79 % unit_div_mult_self
% 2.39/2.79 thf(fact_3804_unit__div__mult__self,axiom,
% 2.39/2.79 ! [A: int,B: int] :
% 2.39/2.79 ( ( dvd_dvd_int @ A @ one_one_int )
% 2.39/2.79 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 2.39/2.79 = B ) ) ).
% 2.39/2.79
% 2.39/2.79 % unit_div_mult_self
% 2.39/2.79 thf(fact_3805_unit__div__mult__self,axiom,
% 2.39/2.79 ! [A: code_natural,B: code_natural] :
% 2.39/2.79 ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 2.39/2.79 => ( ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ B @ A ) @ A )
% 2.39/2.79 = B ) ) ).
% 2.39/2.79
% 2.39/2.79 % unit_div_mult_self
% 2.39/2.79 thf(fact_3806_unit__mult__div__div,axiom,
% 2.39/2.79 ! [A: code_integer,B: code_integer] :
% 2.39/2.79 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 2.39/2.79 => ( ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 2.39/2.79 = ( divide6298287555418463151nteger @ B @ A ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % unit_mult_div_div
% 2.39/2.79 thf(fact_3807_unit__mult__div__div,axiom,
% 2.39/2.79 ! [A: nat,B: nat] :
% 2.39/2.79 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 2.39/2.79 => ( ( times_times_nat @ B @ ( divide_divide_nat @ one_one_nat @ A ) )
% 2.39/2.79 = ( divide_divide_nat @ B @ A ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % unit_mult_div_div
% 2.39/2.79 thf(fact_3808_unit__mult__div__div,axiom,
% 2.39/2.79 ! [A: int,B: int] :
% 2.39/2.79 ( ( dvd_dvd_int @ A @ one_one_int )
% 2.39/2.79 => ( ( times_times_int @ B @ ( divide_divide_int @ one_one_int @ A ) )
% 2.39/2.79 = ( divide_divide_int @ B @ A ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % unit_mult_div_div
% 2.39/2.79 thf(fact_3809_unit__mult__div__div,axiom,
% 2.39/2.79 ! [A: code_natural,B: code_natural] :
% 2.39/2.79 ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 2.39/2.79 => ( ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ one_one_Code_natural @ A ) )
% 2.39/2.79 = ( divide5121882707175180666atural @ B @ A ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % unit_mult_div_div
% 2.39/2.79 thf(fact_3810_mod__minus1__right,axiom,
% 2.39/2.79 ! [A: int] :
% 2.39/2.79 ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 2.39/2.79 = zero_zero_int ) ).
% 2.39/2.79
% 2.39/2.79 % mod_minus1_right
% 2.39/2.79 thf(fact_3811_mod__minus1__right,axiom,
% 2.39/2.79 ! [A: code_integer] :
% 2.39/2.79 ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 2.39/2.79 = zero_z3403309356797280102nteger ) ).
% 2.39/2.79
% 2.39/2.79 % mod_minus1_right
% 2.39/2.79 thf(fact_3812_Suc__times__numeral__mod__eq,axiom,
% 2.39/2.79 ! [K: num,N: nat] :
% 2.39/2.79 ( ( ( numeral_numeral_nat @ K )
% 2.39/2.79 != one_one_nat )
% 2.39/2.79 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K ) @ N ) ) @ ( numeral_numeral_nat @ K ) )
% 2.39/2.79 = one_one_nat ) ) ).
% 2.39/2.79
% 2.39/2.79 % Suc_times_numeral_mod_eq
% 2.39/2.79 thf(fact_3813_even__mult__iff,axiom,
% 2.39/2.79 ! [A: nat,B: nat] :
% 2.39/2.79 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ A @ B ) )
% 2.39/2.79 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 2.39/2.79 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % even_mult_iff
% 2.39/2.79 thf(fact_3814_even__mult__iff,axiom,
% 2.39/2.79 ! [A: int,B: int] :
% 2.39/2.79 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( times_times_int @ A @ B ) )
% 2.39/2.79 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 2.39/2.79 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % even_mult_iff
% 2.39/2.79 thf(fact_3815_even__mult__iff,axiom,
% 2.39/2.79 ! [A: code_integer,B: code_integer] :
% 2.39/2.79 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( times_3573771949741848930nteger @ A @ B ) )
% 2.39/2.79 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 2.39/2.79 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % even_mult_iff
% 2.39/2.79 thf(fact_3816_even__mult__iff,axiom,
% 2.39/2.79 ! [A: code_natural,B: code_natural] :
% 2.39/2.79 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( times_2397367101498566445atural @ A @ B ) )
% 2.39/2.79 = ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 2.39/2.79 | ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ B ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % even_mult_iff
% 2.39/2.79 thf(fact_3817_bits__one__mod__two__eq__one,axiom,
% 2.39/2.79 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 2.39/2.79 = one_one_Code_integer ) ).
% 2.39/2.79
% 2.39/2.79 % bits_one_mod_two_eq_one
% 2.39/2.79 thf(fact_3818_bits__one__mod__two__eq__one,axiom,
% 2.39/2.79 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.79 = one_one_nat ) ).
% 2.39/2.79
% 2.39/2.79 % bits_one_mod_two_eq_one
% 2.39/2.79 thf(fact_3819_bits__one__mod__two__eq__one,axiom,
% 2.39/2.79 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 2.39/2.79 = one_one_int ) ).
% 2.39/2.79
% 2.39/2.79 % bits_one_mod_two_eq_one
% 2.39/2.79 thf(fact_3820_bits__one__mod__two__eq__one,axiom,
% 2.39/2.79 ( ( modulo8411746178871703098atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 2.39/2.79 = one_one_Code_natural ) ).
% 2.39/2.79
% 2.39/2.79 % bits_one_mod_two_eq_one
% 2.39/2.79 thf(fact_3821_one__mod__two__eq__one,axiom,
% 2.39/2.79 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 2.39/2.79 = one_one_Code_integer ) ).
% 2.39/2.79
% 2.39/2.79 % one_mod_two_eq_one
% 2.39/2.79 thf(fact_3822_one__mod__two__eq__one,axiom,
% 2.39/2.79 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.79 = one_one_nat ) ).
% 2.39/2.79
% 2.39/2.79 % one_mod_two_eq_one
% 2.39/2.79 thf(fact_3823_one__mod__two__eq__one,axiom,
% 2.39/2.79 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 2.39/2.79 = one_one_int ) ).
% 2.39/2.79
% 2.39/2.79 % one_mod_two_eq_one
% 2.39/2.79 thf(fact_3824_one__mod__two__eq__one,axiom,
% 2.39/2.79 ( ( modulo8411746178871703098atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 2.39/2.79 = one_one_Code_natural ) ).
% 2.39/2.79
% 2.39/2.79 % one_mod_two_eq_one
% 2.39/2.79 thf(fact_3825_even__plus__one__iff,axiom,
% 2.39/2.79 ! [A: nat] :
% 2.39/2.79 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ one_one_nat ) )
% 2.39/2.79 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % even_plus_one_iff
% 2.39/2.79 thf(fact_3826_even__plus__one__iff,axiom,
% 2.39/2.79 ! [A: int] :
% 2.39/2.79 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ one_one_int ) )
% 2.39/2.79 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % even_plus_one_iff
% 2.39/2.79 thf(fact_3827_even__plus__one__iff,axiom,
% 2.39/2.79 ! [A: code_integer] :
% 2.39/2.79 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) )
% 2.39/2.79 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % even_plus_one_iff
% 2.39/2.79 thf(fact_3828_even__plus__one__iff,axiom,
% 2.39/2.79 ! [A: code_natural] :
% 2.39/2.79 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( plus_p4538020629002901425atural @ A @ one_one_Code_natural ) )
% 2.39/2.79 = ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) ) ).
% 2.39/2.79
% 2.39/2.79 % even_plus_one_iff
% 2.39/2.79 thf(fact_3829_not__mod__2__eq__0__eq__1,axiom,
% 2.39/2.79 ! [A: code_integer] :
% 2.39/2.79 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 2.39/2.79 != zero_z3403309356797280102nteger )
% 2.39/2.80 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 2.39/2.80 = one_one_Code_integer ) ) ).
% 2.39/2.80
% 2.39/2.80 % not_mod_2_eq_0_eq_1
% 2.39/2.80 thf(fact_3830_not__mod__2__eq__0__eq__1,axiom,
% 2.39/2.80 ! [A: nat] :
% 2.39/2.80 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.80 != zero_zero_nat )
% 2.39/2.80 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.80 = one_one_nat ) ) ).
% 2.39/2.80
% 2.39/2.80 % not_mod_2_eq_0_eq_1
% 2.39/2.80 thf(fact_3831_not__mod__2__eq__0__eq__1,axiom,
% 2.39/2.80 ! [A: int] :
% 2.39/2.80 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 2.39/2.80 != zero_zero_int )
% 2.39/2.80 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 2.39/2.80 = one_one_int ) ) ).
% 2.39/2.80
% 2.39/2.80 % not_mod_2_eq_0_eq_1
% 2.39/2.80 thf(fact_3832_not__mod__2__eq__0__eq__1,axiom,
% 2.39/2.80 ! [A: code_natural] :
% 2.39/2.80 ( ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 2.39/2.80 != zero_z2226904508553997617atural )
% 2.39/2.80 = ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 2.39/2.80 = one_one_Code_natural ) ) ).
% 2.39/2.80
% 2.39/2.80 % not_mod_2_eq_0_eq_1
% 2.39/2.80 thf(fact_3833_not__mod__2__eq__1__eq__0,axiom,
% 2.39/2.80 ! [A: code_integer] :
% 2.39/2.80 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 2.39/2.80 != one_one_Code_integer )
% 2.39/2.80 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 2.39/2.80 = zero_z3403309356797280102nteger ) ) ).
% 2.39/2.80
% 2.39/2.80 % not_mod_2_eq_1_eq_0
% 2.39/2.80 thf(fact_3834_not__mod__2__eq__1__eq__0,axiom,
% 2.39/2.80 ! [A: nat] :
% 2.39/2.80 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.80 != one_one_nat )
% 2.39/2.80 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.80 = zero_zero_nat ) ) ).
% 2.39/2.80
% 2.39/2.80 % not_mod_2_eq_1_eq_0
% 2.39/2.80 thf(fact_3835_not__mod__2__eq__1__eq__0,axiom,
% 2.39/2.80 ! [A: int] :
% 2.39/2.80 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 2.39/2.80 != one_one_int )
% 2.39/2.80 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 2.39/2.80 = zero_zero_int ) ) ).
% 2.39/2.80
% 2.39/2.80 % not_mod_2_eq_1_eq_0
% 2.39/2.80 thf(fact_3836_not__mod__2__eq__1__eq__0,axiom,
% 2.39/2.80 ! [A: code_natural] :
% 2.39/2.80 ( ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 2.39/2.80 != one_one_Code_natural )
% 2.39/2.80 = ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 2.39/2.80 = zero_z2226904508553997617atural ) ) ).
% 2.39/2.80
% 2.39/2.80 % not_mod_2_eq_1_eq_0
% 2.39/2.80 thf(fact_3837_bits__minus__1__mod__2__eq,axiom,
% 2.39/2.80 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 2.39/2.80 = one_one_int ) ).
% 2.39/2.80
% 2.39/2.80 % bits_minus_1_mod_2_eq
% 2.39/2.80 thf(fact_3838_bits__minus__1__mod__2__eq,axiom,
% 2.39/2.80 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 2.39/2.80 = one_one_Code_integer ) ).
% 2.39/2.80
% 2.39/2.80 % bits_minus_1_mod_2_eq
% 2.39/2.80 thf(fact_3839_minus__1__mod__2__eq,axiom,
% 2.39/2.80 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 2.39/2.80 = one_one_int ) ).
% 2.39/2.80
% 2.39/2.80 % minus_1_mod_2_eq
% 2.39/2.80 thf(fact_3840_minus__1__mod__2__eq,axiom,
% 2.39/2.80 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 2.39/2.80 = one_one_Code_integer ) ).
% 2.39/2.80
% 2.39/2.80 % minus_1_mod_2_eq
% 2.39/2.80 thf(fact_3841_neg__one__even__power,axiom,
% 2.39/2.80 ! [N: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 2.39/2.80 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 2.39/2.80 = one_one_int ) ) ).
% 2.39/2.80
% 2.39/2.80 % neg_one_even_power
% 2.39/2.80 thf(fact_3842_neg__one__even__power,axiom,
% 2.39/2.80 ! [N: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 2.39/2.80 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 2.39/2.80 = one_one_rat ) ) ).
% 2.39/2.80
% 2.39/2.80 % neg_one_even_power
% 2.39/2.80 thf(fact_3843_neg__one__even__power,axiom,
% 2.39/2.80 ! [N: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 2.39/2.80 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 2.39/2.80 = one_one_Code_integer ) ) ).
% 2.39/2.80
% 2.39/2.80 % neg_one_even_power
% 2.39/2.80 thf(fact_3844_neg__one__odd__power,axiom,
% 2.39/2.80 ! [N: nat] :
% 2.39/2.80 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 2.39/2.80 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 2.39/2.80 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % neg_one_odd_power
% 2.39/2.80 thf(fact_3845_neg__one__odd__power,axiom,
% 2.39/2.80 ! [N: nat] :
% 2.39/2.80 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 2.39/2.80 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 2.39/2.80 = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % neg_one_odd_power
% 2.39/2.80 thf(fact_3846_neg__one__odd__power,axiom,
% 2.39/2.80 ! [N: nat] :
% 2.39/2.80 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 2.39/2.80 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 2.39/2.80 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % neg_one_odd_power
% 2.39/2.80 thf(fact_3847_mod2__gr__0,axiom,
% 2.39/2.80 ! [M2: nat] :
% 2.39/2.80 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 2.39/2.80 = ( ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.80 = one_one_nat ) ) ).
% 2.39/2.80
% 2.39/2.80 % mod2_gr_0
% 2.39/2.80 thf(fact_3848_one__mod__numeral,axiom,
% 2.39/2.80 ! [N: num] :
% 2.39/2.80 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 2.39/2.80 = ( produc6174133586879617921nteger @ ( unique3479559517661332726nteger @ one @ N ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % one_mod_numeral
% 2.39/2.80 thf(fact_3849_one__mod__numeral,axiom,
% 2.39/2.80 ! [N: num] :
% 2.39/2.80 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 2.39/2.80 = ( product_snd_nat_nat @ ( unique5055182867167087721od_nat @ one @ N ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % one_mod_numeral
% 2.39/2.80 thf(fact_3850_one__mod__numeral,axiom,
% 2.39/2.80 ! [N: num] :
% 2.39/2.80 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 2.39/2.80 = ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % one_mod_numeral
% 2.39/2.80 thf(fact_3851_even__succ__div__2,axiom,
% 2.39/2.80 ! [A: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 2.39/2.80 = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % even_succ_div_2
% 2.39/2.80 thf(fact_3852_even__succ__div__2,axiom,
% 2.39/2.80 ! [A: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.80 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % even_succ_div_2
% 2.39/2.80 thf(fact_3853_even__succ__div__2,axiom,
% 2.39/2.80 ! [A: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 2.39/2.80 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % even_succ_div_2
% 2.39/2.80 thf(fact_3854_even__succ__div__2,axiom,
% 2.39/2.80 ! [A: code_natural] :
% 2.39/2.80 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ one_one_Code_natural @ A ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 2.39/2.80 = ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % even_succ_div_2
% 2.39/2.80 thf(fact_3855_odd__succ__div__two,axiom,
% 2.39/2.80 ! [A: code_integer] :
% 2.39/2.80 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 2.39/2.80 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % odd_succ_div_two
% 2.39/2.80 thf(fact_3856_odd__succ__div__two,axiom,
% 2.39/2.80 ! [A: nat] :
% 2.39/2.80 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.80 = ( plus_plus_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % odd_succ_div_two
% 2.39/2.80 thf(fact_3857_odd__succ__div__two,axiom,
% 2.39/2.80 ! [A: int] :
% 2.39/2.80 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 2.39/2.80 = ( plus_plus_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % odd_succ_div_two
% 2.39/2.80 thf(fact_3858_odd__succ__div__two,axiom,
% 2.39/2.80 ! [A: code_natural] :
% 2.39/2.80 ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ one_one_Code_natural ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 2.39/2.80 = ( plus_p4538020629002901425atural @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ one_one_Code_natural ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % odd_succ_div_two
% 2.39/2.80 thf(fact_3859_even__succ__div__two,axiom,
% 2.39/2.80 ! [A: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 2.39/2.80 = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % even_succ_div_two
% 2.39/2.80 thf(fact_3860_even__succ__div__two,axiom,
% 2.39/2.80 ! [A: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.80 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % even_succ_div_two
% 2.39/2.80 thf(fact_3861_even__succ__div__two,axiom,
% 2.39/2.80 ! [A: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 2.39/2.80 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % even_succ_div_two
% 2.39/2.80 thf(fact_3862_even__succ__div__two,axiom,
% 2.39/2.80 ! [A: code_natural] :
% 2.39/2.80 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ one_one_Code_natural ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 2.39/2.80 = ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % even_succ_div_two
% 2.39/2.80 thf(fact_3863_odd__two__times__div__two__nat,axiom,
% 2.39/2.80 ! [N: nat] :
% 2.39/2.80 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 2.39/2.80 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 2.39/2.80 = ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % odd_two_times_div_two_nat
% 2.39/2.80 thf(fact_3864_odd__two__times__div__two__succ,axiom,
% 2.39/2.80 ! [A: code_integer] :
% 2.39/2.80 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ one_one_Code_integer )
% 2.39/2.80 = A ) ) ).
% 2.39/2.80
% 2.39/2.80 % odd_two_times_div_two_succ
% 2.39/2.80 thf(fact_3865_odd__two__times__div__two__succ,axiom,
% 2.39/2.80 ! [A: nat] :
% 2.39/2.80 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 2.39/2.80 = A ) ) ).
% 2.39/2.80
% 2.39/2.80 % odd_two_times_div_two_succ
% 2.39/2.80 thf(fact_3866_odd__two__times__div__two__succ,axiom,
% 2.39/2.80 ! [A: int] :
% 2.39/2.80 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ one_one_int )
% 2.39/2.80 = A ) ) ).
% 2.39/2.80
% 2.39/2.80 % odd_two_times_div_two_succ
% 2.39/2.80 thf(fact_3867_odd__two__times__div__two__succ,axiom,
% 2.39/2.80 ! [A: code_natural] :
% 2.39/2.80 ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ( ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) @ one_one_Code_natural )
% 2.39/2.80 = A ) ) ).
% 2.39/2.80
% 2.39/2.80 % odd_two_times_div_two_succ
% 2.39/2.80 thf(fact_3868_semiring__parity__class_Oeven__mask__iff,axiom,
% 2.39/2.80 ! [N: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) )
% 2.39/2.80 = ( N = zero_zero_nat ) ) ).
% 2.39/2.80
% 2.39/2.80 % semiring_parity_class.even_mask_iff
% 2.39/2.80 thf(fact_3869_semiring__parity__class_Oeven__mask__iff,axiom,
% 2.39/2.80 ! [N: nat] :
% 2.39/2.80 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 2.39/2.80 = ( N = zero_zero_nat ) ) ).
% 2.39/2.80
% 2.39/2.80 % semiring_parity_class.even_mask_iff
% 2.39/2.80 thf(fact_3870_semiring__parity__class_Oeven__mask__iff,axiom,
% 2.39/2.80 ! [N: nat] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) )
% 2.39/2.80 = ( N = zero_zero_nat ) ) ).
% 2.39/2.80
% 2.39/2.80 % semiring_parity_class.even_mask_iff
% 2.39/2.80 thf(fact_3871_semiring__parity__class_Oeven__mask__iff,axiom,
% 2.39/2.80 ! [N: nat] :
% 2.39/2.80 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( minus_7197305767214868737atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) @ one_one_Code_natural ) )
% 2.39/2.80 = ( N = zero_zero_nat ) ) ).
% 2.39/2.80
% 2.39/2.80 % semiring_parity_class.even_mask_iff
% 2.39/2.80 thf(fact_3872_even__succ__mod__exp,axiom,
% 2.39/2.80 ! [A: code_integer,N: nat] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.39/2.80 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 2.39/2.80 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % even_succ_mod_exp
% 2.39/2.80 thf(fact_3873_even__succ__mod__exp,axiom,
% 2.39/2.80 ! [A: nat,N: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.39/2.80 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 2.39/2.80 = ( plus_plus_nat @ one_one_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % even_succ_mod_exp
% 2.39/2.80 thf(fact_3874_even__succ__mod__exp,axiom,
% 2.39/2.80 ! [A: int,N: nat] :
% 2.39/2.80 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.39/2.80 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 2.39/2.80 = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % even_succ_mod_exp
% 2.39/2.80 thf(fact_3875_even__succ__mod__exp,axiom,
% 2.39/2.80 ! [A: code_natural,N: nat] :
% 2.39/2.80 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.39/2.80 => ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ one_one_Code_natural @ A ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 2.39/2.80 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( modulo8411746178871703098atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % even_succ_mod_exp
% 2.39/2.80 thf(fact_3876_div__pos__neg__trivial,axiom,
% 2.39/2.80 ! [K: int,L: int] :
% 2.39/2.80 ( ( ord_less_int @ zero_zero_int @ K )
% 2.39/2.80 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 2.39/2.80 => ( ( divide_divide_int @ K @ L )
% 2.39/2.80 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % div_pos_neg_trivial
% 2.39/2.80 thf(fact_3877_minus__mod__int__eq,axiom,
% 2.39/2.80 ! [L: int,K: int] :
% 2.39/2.80 ( ( ord_less_eq_int @ zero_zero_int @ L )
% 2.39/2.80 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
% 2.39/2.80 = ( minus_minus_int @ ( minus_minus_int @ L @ one_one_int ) @ ( modulo_modulo_int @ ( minus_minus_int @ K @ one_one_int ) @ L ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % minus_mod_int_eq
% 2.39/2.80 thf(fact_3878_zmod__minus1,axiom,
% 2.39/2.80 ! [B: int] :
% 2.39/2.80 ( ( ord_less_int @ zero_zero_int @ B )
% 2.39/2.80 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 2.39/2.80 = ( minus_minus_int @ B @ one_one_int ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % zmod_minus1
% 2.39/2.80 thf(fact_3879_div__pos__geq,axiom,
% 2.39/2.80 ! [L: int,K: int] :
% 2.39/2.80 ( ( ord_less_int @ zero_zero_int @ L )
% 2.39/2.80 => ( ( ord_less_eq_int @ L @ K )
% 2.39/2.80 => ( ( divide_divide_int @ K @ L )
% 2.39/2.80 = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K @ L ) @ L ) @ one_one_int ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % div_pos_geq
% 2.39/2.80 thf(fact_3880_int__div__less__self,axiom,
% 2.39/2.80 ! [X: int,K: int] :
% 2.39/2.80 ( ( ord_less_int @ zero_zero_int @ X )
% 2.39/2.80 => ( ( ord_less_int @ one_one_int @ K )
% 2.39/2.80 => ( ord_less_int @ ( divide_divide_int @ X @ K ) @ X ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % int_div_less_self
% 2.39/2.80 thf(fact_3881_div__eq__minus1,axiom,
% 2.39/2.80 ! [B: int] :
% 2.39/2.80 ( ( ord_less_int @ zero_zero_int @ B )
% 2.39/2.80 => ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 2.39/2.80 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % div_eq_minus1
% 2.39/2.80 thf(fact_3882_zdiv__zminus1__eq__if,axiom,
% 2.39/2.80 ! [B: int,A: int] :
% 2.39/2.80 ( ( B != zero_zero_int )
% 2.39/2.80 => ( ( ( ( modulo_modulo_int @ A @ B )
% 2.39/2.80 = zero_zero_int )
% 2.39/2.80 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 2.39/2.80 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 2.39/2.80 & ( ( ( modulo_modulo_int @ A @ B )
% 2.39/2.80 != zero_zero_int )
% 2.39/2.80 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 2.39/2.80 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % zdiv_zminus1_eq_if
% 2.39/2.80 thf(fact_3883_zdiv__zminus2__eq__if,axiom,
% 2.39/2.80 ! [B: int,A: int] :
% 2.39/2.80 ( ( B != zero_zero_int )
% 2.39/2.80 => ( ( ( ( modulo_modulo_int @ A @ B )
% 2.39/2.80 = zero_zero_int )
% 2.39/2.80 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 2.39/2.80 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 2.39/2.80 & ( ( ( modulo_modulo_int @ A @ B )
% 2.39/2.80 != zero_zero_int )
% 2.39/2.80 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 2.39/2.80 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % zdiv_zminus2_eq_if
% 2.39/2.80 thf(fact_3884_unit__imp__mod__eq__0,axiom,
% 2.39/2.80 ! [B: code_integer,A: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 2.39/2.80 => ( ( modulo364778990260209775nteger @ A @ B )
% 2.39/2.80 = zero_z3403309356797280102nteger ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_imp_mod_eq_0
% 2.39/2.80 thf(fact_3885_unit__imp__mod__eq__0,axiom,
% 2.39/2.80 ! [B: nat,A: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 2.39/2.80 => ( ( modulo_modulo_nat @ A @ B )
% 2.39/2.80 = zero_zero_nat ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_imp_mod_eq_0
% 2.39/2.80 thf(fact_3886_unit__imp__mod__eq__0,axiom,
% 2.39/2.80 ! [B: int,A: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ B @ one_one_int )
% 2.39/2.80 => ( ( modulo_modulo_int @ A @ B )
% 2.39/2.80 = zero_zero_int ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_imp_mod_eq_0
% 2.39/2.80 thf(fact_3887_unit__imp__mod__eq__0,axiom,
% 2.39/2.80 ! [B: code_natural,A: code_natural] :
% 2.39/2.80 ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 2.39/2.80 => ( ( modulo8411746178871703098atural @ A @ B )
% 2.39/2.80 = zero_z2226904508553997617atural ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_imp_mod_eq_0
% 2.39/2.80 thf(fact_3888_mod__mult__right__eq,axiom,
% 2.39/2.80 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.80 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 2.39/2.80 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 2.39/2.80
% 2.39/2.80 % mod_mult_right_eq
% 2.39/2.80 thf(fact_3889_mod__mult__right__eq,axiom,
% 2.39/2.80 ! [A: nat,B: nat,C: nat] :
% 2.39/2.80 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 2.39/2.80 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 2.39/2.80
% 2.39/2.80 % mod_mult_right_eq
% 2.39/2.80 thf(fact_3890_mod__mult__right__eq,axiom,
% 2.39/2.80 ! [A: int,B: int,C: int] :
% 2.39/2.80 ( ( modulo_modulo_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 2.39/2.80 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 2.39/2.80
% 2.39/2.80 % mod_mult_right_eq
% 2.39/2.80 thf(fact_3891_mod__mult__right__eq,axiom,
% 2.39/2.80 ! [A: code_natural,B: code_natural,C: code_natural] :
% 2.39/2.80 ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ ( modulo8411746178871703098atural @ B @ C ) ) @ C )
% 2.39/2.80 = ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ B ) @ C ) ) ).
% 2.39/2.80
% 2.39/2.80 % mod_mult_right_eq
% 2.39/2.80 thf(fact_3892_mod__mult__left__eq,axiom,
% 2.39/2.80 ! [A: code_integer,C: code_integer,B: code_integer] :
% 2.39/2.80 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 2.39/2.80 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 2.39/2.80
% 2.39/2.80 % mod_mult_left_eq
% 2.39/2.80 thf(fact_3893_mod__mult__left__eq,axiom,
% 2.39/2.80 ! [A: nat,C: nat,B: nat] :
% 2.39/2.80 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 2.39/2.80 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 2.39/2.80
% 2.39/2.80 % mod_mult_left_eq
% 2.39/2.80 thf(fact_3894_mod__mult__left__eq,axiom,
% 2.39/2.80 ! [A: int,C: int,B: int] :
% 2.39/2.80 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 2.39/2.80 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 2.39/2.80
% 2.39/2.80 % mod_mult_left_eq
% 2.39/2.80 thf(fact_3895_mod__mult__left__eq,axiom,
% 2.39/2.80 ! [A: code_natural,C: code_natural,B: code_natural] :
% 2.39/2.80 ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ A @ C ) @ B ) @ C )
% 2.39/2.80 = ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ B ) @ C ) ) ).
% 2.39/2.80
% 2.39/2.80 % mod_mult_left_eq
% 2.39/2.80 thf(fact_3896_mult__mod__right,axiom,
% 2.39/2.80 ! [C: code_integer,A: code_integer,B: code_integer] :
% 2.39/2.80 ( ( times_3573771949741848930nteger @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 2.39/2.80 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % mult_mod_right
% 2.39/2.80 thf(fact_3897_mult__mod__right,axiom,
% 2.39/2.80 ! [C: nat,A: nat,B: nat] :
% 2.39/2.80 ( ( times_times_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 2.39/2.80 = ( modulo_modulo_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % mult_mod_right
% 2.39/2.80 thf(fact_3898_mult__mod__right,axiom,
% 2.39/2.80 ! [C: int,A: int,B: int] :
% 2.39/2.80 ( ( times_times_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 2.39/2.80 = ( modulo_modulo_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % mult_mod_right
% 2.39/2.80 thf(fact_3899_mult__mod__right,axiom,
% 2.39/2.80 ! [C: code_natural,A: code_natural,B: code_natural] :
% 2.39/2.80 ( ( times_2397367101498566445atural @ C @ ( modulo8411746178871703098atural @ A @ B ) )
% 2.39/2.80 = ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ C @ A ) @ ( times_2397367101498566445atural @ C @ B ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % mult_mod_right
% 2.39/2.80 thf(fact_3900_mod__mult__mult2,axiom,
% 2.39/2.80 ! [A: code_integer,C: code_integer,B: code_integer] :
% 2.39/2.80 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 2.39/2.80 = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ B ) @ C ) ) ).
% 2.39/2.80
% 2.39/2.80 % mod_mult_mult2
% 2.39/2.80 thf(fact_3901_mod__mult__mult2,axiom,
% 2.39/2.80 ! [A: nat,C: nat,B: nat] :
% 2.39/2.80 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 2.39/2.80 = ( times_times_nat @ ( modulo_modulo_nat @ A @ B ) @ C ) ) ).
% 2.39/2.80
% 2.39/2.80 % mod_mult_mult2
% 2.39/2.80 thf(fact_3902_mod__mult__mult2,axiom,
% 2.39/2.80 ! [A: int,C: int,B: int] :
% 2.39/2.80 ( ( modulo_modulo_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 2.39/2.80 = ( times_times_int @ ( modulo_modulo_int @ A @ B ) @ C ) ) ).
% 2.39/2.80
% 2.39/2.80 % mod_mult_mult2
% 2.39/2.80 thf(fact_3903_mod__mult__mult2,axiom,
% 2.39/2.80 ! [A: code_natural,C: code_natural,B: code_natural] :
% 2.39/2.80 ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ C ) )
% 2.39/2.80 = ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ A @ B ) @ C ) ) ).
% 2.39/2.80
% 2.39/2.80 % mod_mult_mult2
% 2.39/2.80 thf(fact_3904_mod__mult__cong,axiom,
% 2.39/2.80 ! [A: code_integer,C: code_integer,A5: code_integer,B: code_integer,B6: code_integer] :
% 2.39/2.80 ( ( ( modulo364778990260209775nteger @ A @ C )
% 2.39/2.80 = ( modulo364778990260209775nteger @ A5 @ C ) )
% 2.39/2.80 => ( ( ( modulo364778990260209775nteger @ B @ C )
% 2.39/2.80 = ( modulo364778990260209775nteger @ B6 @ C ) )
% 2.39/2.80 => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 2.39/2.80 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A5 @ B6 ) @ C ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % mod_mult_cong
% 2.39/2.80 thf(fact_3905_mod__mult__cong,axiom,
% 2.39/2.80 ! [A: nat,C: nat,A5: nat,B: nat,B6: nat] :
% 2.39/2.80 ( ( ( modulo_modulo_nat @ A @ C )
% 2.39/2.80 = ( modulo_modulo_nat @ A5 @ C ) )
% 2.39/2.80 => ( ( ( modulo_modulo_nat @ B @ C )
% 2.39/2.80 = ( modulo_modulo_nat @ B6 @ C ) )
% 2.39/2.80 => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C )
% 2.39/2.80 = ( modulo_modulo_nat @ ( times_times_nat @ A5 @ B6 ) @ C ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % mod_mult_cong
% 2.39/2.80 thf(fact_3906_mod__mult__cong,axiom,
% 2.39/2.80 ! [A: int,C: int,A5: int,B: int,B6: int] :
% 2.39/2.80 ( ( ( modulo_modulo_int @ A @ C )
% 2.39/2.80 = ( modulo_modulo_int @ A5 @ C ) )
% 2.39/2.80 => ( ( ( modulo_modulo_int @ B @ C )
% 2.39/2.80 = ( modulo_modulo_int @ B6 @ C ) )
% 2.39/2.80 => ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C )
% 2.39/2.80 = ( modulo_modulo_int @ ( times_times_int @ A5 @ B6 ) @ C ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % mod_mult_cong
% 2.39/2.80 thf(fact_3907_mod__mult__cong,axiom,
% 2.39/2.80 ! [A: code_natural,C: code_natural,A5: code_natural,B: code_natural,B6: code_natural] :
% 2.39/2.80 ( ( ( modulo8411746178871703098atural @ A @ C )
% 2.39/2.80 = ( modulo8411746178871703098atural @ A5 @ C ) )
% 2.39/2.80 => ( ( ( modulo8411746178871703098atural @ B @ C )
% 2.39/2.80 = ( modulo8411746178871703098atural @ B6 @ C ) )
% 2.39/2.80 => ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ B ) @ C )
% 2.39/2.80 = ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A5 @ B6 ) @ C ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % mod_mult_cong
% 2.39/2.80 thf(fact_3908_mod__mult__eq,axiom,
% 2.39/2.80 ! [A: code_integer,C: code_integer,B: code_integer] :
% 2.39/2.80 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 2.39/2.80 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 2.39/2.80
% 2.39/2.80 % mod_mult_eq
% 2.39/2.80 thf(fact_3909_mod__mult__eq,axiom,
% 2.39/2.80 ! [A: nat,C: nat,B: nat] :
% 2.39/2.80 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 2.39/2.80 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 2.39/2.80
% 2.39/2.80 % mod_mult_eq
% 2.39/2.80 thf(fact_3910_mod__mult__eq,axiom,
% 2.39/2.80 ! [A: int,C: int,B: int] :
% 2.39/2.80 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 2.39/2.80 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 2.39/2.80
% 2.39/2.80 % mod_mult_eq
% 2.39/2.80 thf(fact_3911_mod__mult__eq,axiom,
% 2.39/2.80 ! [A: code_natural,C: code_natural,B: code_natural] :
% 2.39/2.80 ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ A @ C ) @ ( modulo8411746178871703098atural @ B @ C ) ) @ C )
% 2.39/2.80 = ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ B ) @ C ) ) ).
% 2.39/2.80
% 2.39/2.80 % mod_mult_eq
% 2.39/2.80 thf(fact_3912_dvd__triv__right,axiom,
% 2.39/2.80 ! [A: assn,B: assn] : ( dvd_dvd_assn @ A @ ( times_times_assn @ B @ A ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_triv_right
% 2.39/2.80 thf(fact_3913_dvd__triv__right,axiom,
% 2.39/2.80 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ A ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_triv_right
% 2.39/2.80 thf(fact_3914_dvd__triv__right,axiom,
% 2.39/2.80 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ B @ A ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_triv_right
% 2.39/2.80 thf(fact_3915_dvd__triv__right,axiom,
% 2.39/2.80 ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ A ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_triv_right
% 2.39/2.80 thf(fact_3916_dvd__triv__right,axiom,
% 2.39/2.80 ! [A: code_natural,B: code_natural] : ( dvd_dvd_Code_natural @ A @ ( times_2397367101498566445atural @ B @ A ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_triv_right
% 2.39/2.80 thf(fact_3917_dvd__mult__right,axiom,
% 2.39/2.80 ! [A: assn,B: assn,C: assn] :
% 2.39/2.80 ( ( dvd_dvd_assn @ ( times_times_assn @ A @ B ) @ C )
% 2.39/2.80 => ( dvd_dvd_assn @ B @ C ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_mult_right
% 2.39/2.80 thf(fact_3918_dvd__mult__right,axiom,
% 2.39/2.80 ! [A: nat,B: nat,C: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 2.39/2.80 => ( dvd_dvd_nat @ B @ C ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_mult_right
% 2.39/2.80 thf(fact_3919_dvd__mult__right,axiom,
% 2.39/2.80 ! [A: int,B: int,C: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 2.39/2.80 => ( dvd_dvd_int @ B @ C ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_mult_right
% 2.39/2.80 thf(fact_3920_dvd__mult__right,axiom,
% 2.39/2.80 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 2.39/2.80 => ( dvd_dvd_Code_integer @ B @ C ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_mult_right
% 2.39/2.80 thf(fact_3921_dvd__mult__right,axiom,
% 2.39/2.80 ! [A: code_natural,B: code_natural,C: code_natural] :
% 2.39/2.80 ( ( dvd_dvd_Code_natural @ ( times_2397367101498566445atural @ A @ B ) @ C )
% 2.39/2.80 => ( dvd_dvd_Code_natural @ B @ C ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_mult_right
% 2.39/2.80 thf(fact_3922_mult__dvd__mono,axiom,
% 2.39/2.80 ! [A: assn,B: assn,C: assn,D2: assn] :
% 2.39/2.80 ( ( dvd_dvd_assn @ A @ B )
% 2.39/2.80 => ( ( dvd_dvd_assn @ C @ D2 )
% 2.39/2.80 => ( dvd_dvd_assn @ ( times_times_assn @ A @ C ) @ ( times_times_assn @ B @ D2 ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % mult_dvd_mono
% 2.39/2.80 thf(fact_3923_mult__dvd__mono,axiom,
% 2.39/2.80 ! [A: nat,B: nat,C: nat,D2: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ A @ B )
% 2.39/2.80 => ( ( dvd_dvd_nat @ C @ D2 )
% 2.39/2.80 => ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % mult_dvd_mono
% 2.39/2.80 thf(fact_3924_mult__dvd__mono,axiom,
% 2.39/2.80 ! [A: int,B: int,C: int,D2: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ A @ B )
% 2.39/2.80 => ( ( dvd_dvd_int @ C @ D2 )
% 2.39/2.80 => ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % mult_dvd_mono
% 2.39/2.80 thf(fact_3925_mult__dvd__mono,axiom,
% 2.39/2.80 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ A @ B )
% 2.39/2.80 => ( ( dvd_dvd_Code_integer @ C @ D2 )
% 2.39/2.80 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % mult_dvd_mono
% 2.39/2.80 thf(fact_3926_mult__dvd__mono,axiom,
% 2.39/2.80 ! [A: code_natural,B: code_natural,C: code_natural,D2: code_natural] :
% 2.39/2.80 ( ( dvd_dvd_Code_natural @ A @ B )
% 2.39/2.80 => ( ( dvd_dvd_Code_natural @ C @ D2 )
% 2.39/2.80 => ( dvd_dvd_Code_natural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ D2 ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % mult_dvd_mono
% 2.39/2.80 thf(fact_3927_dvd__triv__left,axiom,
% 2.39/2.80 ! [A: assn,B: assn] : ( dvd_dvd_assn @ A @ ( times_times_assn @ A @ B ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_triv_left
% 2.39/2.80 thf(fact_3928_dvd__triv__left,axiom,
% 2.39/2.80 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ A @ B ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_triv_left
% 2.39/2.80 thf(fact_3929_dvd__triv__left,axiom,
% 2.39/2.80 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ A @ B ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_triv_left
% 2.39/2.80 thf(fact_3930_dvd__triv__left,axiom,
% 2.39/2.80 ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ A @ B ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_triv_left
% 2.39/2.80 thf(fact_3931_dvd__triv__left,axiom,
% 2.39/2.80 ! [A: code_natural,B: code_natural] : ( dvd_dvd_Code_natural @ A @ ( times_2397367101498566445atural @ A @ B ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_triv_left
% 2.39/2.80 thf(fact_3932_dvd__mult__left,axiom,
% 2.39/2.80 ! [A: assn,B: assn,C: assn] :
% 2.39/2.80 ( ( dvd_dvd_assn @ ( times_times_assn @ A @ B ) @ C )
% 2.39/2.80 => ( dvd_dvd_assn @ A @ C ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_mult_left
% 2.39/2.80 thf(fact_3933_dvd__mult__left,axiom,
% 2.39/2.80 ! [A: nat,B: nat,C: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 2.39/2.80 => ( dvd_dvd_nat @ A @ C ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_mult_left
% 2.39/2.80 thf(fact_3934_dvd__mult__left,axiom,
% 2.39/2.80 ! [A: int,B: int,C: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 2.39/2.80 => ( dvd_dvd_int @ A @ C ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_mult_left
% 2.39/2.80 thf(fact_3935_dvd__mult__left,axiom,
% 2.39/2.80 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 2.39/2.80 => ( dvd_dvd_Code_integer @ A @ C ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_mult_left
% 2.39/2.80 thf(fact_3936_dvd__mult__left,axiom,
% 2.39/2.80 ! [A: code_natural,B: code_natural,C: code_natural] :
% 2.39/2.80 ( ( dvd_dvd_Code_natural @ ( times_2397367101498566445atural @ A @ B ) @ C )
% 2.39/2.80 => ( dvd_dvd_Code_natural @ A @ C ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_mult_left
% 2.39/2.80 thf(fact_3937_dvd__mult2,axiom,
% 2.39/2.80 ! [A: assn,B: assn,C: assn] :
% 2.39/2.80 ( ( dvd_dvd_assn @ A @ B )
% 2.39/2.80 => ( dvd_dvd_assn @ A @ ( times_times_assn @ B @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_mult2
% 2.39/2.80 thf(fact_3938_dvd__mult2,axiom,
% 2.39/2.80 ! [A: nat,B: nat,C: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ A @ B )
% 2.39/2.80 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_mult2
% 2.39/2.80 thf(fact_3939_dvd__mult2,axiom,
% 2.39/2.80 ! [A: int,B: int,C: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ A @ B )
% 2.39/2.80 => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_mult2
% 2.39/2.80 thf(fact_3940_dvd__mult2,axiom,
% 2.39/2.80 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ A @ B )
% 2.39/2.80 => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_mult2
% 2.39/2.80 thf(fact_3941_dvd__mult2,axiom,
% 2.39/2.80 ! [A: code_natural,B: code_natural,C: code_natural] :
% 2.39/2.80 ( ( dvd_dvd_Code_natural @ A @ B )
% 2.39/2.80 => ( dvd_dvd_Code_natural @ A @ ( times_2397367101498566445atural @ B @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_mult2
% 2.39/2.80 thf(fact_3942_dvd__mult,axiom,
% 2.39/2.80 ! [A: assn,C: assn,B: assn] :
% 2.39/2.80 ( ( dvd_dvd_assn @ A @ C )
% 2.39/2.80 => ( dvd_dvd_assn @ A @ ( times_times_assn @ B @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_mult
% 2.39/2.80 thf(fact_3943_dvd__mult,axiom,
% 2.39/2.80 ! [A: nat,C: nat,B: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ A @ C )
% 2.39/2.80 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_mult
% 2.39/2.80 thf(fact_3944_dvd__mult,axiom,
% 2.39/2.80 ! [A: int,C: int,B: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ A @ C )
% 2.39/2.80 => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_mult
% 2.39/2.80 thf(fact_3945_dvd__mult,axiom,
% 2.39/2.80 ! [A: code_integer,C: code_integer,B: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ A @ C )
% 2.39/2.80 => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_mult
% 2.39/2.80 thf(fact_3946_dvd__mult,axiom,
% 2.39/2.80 ! [A: code_natural,C: code_natural,B: code_natural] :
% 2.39/2.80 ( ( dvd_dvd_Code_natural @ A @ C )
% 2.39/2.80 => ( dvd_dvd_Code_natural @ A @ ( times_2397367101498566445atural @ B @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_mult
% 2.39/2.80 thf(fact_3947_dvd__def,axiom,
% 2.39/2.80 ( dvd_dvd_assn
% 2.39/2.80 = ( ^ [B2: assn,A2: assn] :
% 2.39/2.80 ? [K4: assn] :
% 2.39/2.80 ( A2
% 2.39/2.80 = ( times_times_assn @ B2 @ K4 ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_def
% 2.39/2.80 thf(fact_3948_dvd__def,axiom,
% 2.39/2.80 ( dvd_dvd_nat
% 2.39/2.80 = ( ^ [B2: nat,A2: nat] :
% 2.39/2.80 ? [K4: nat] :
% 2.39/2.80 ( A2
% 2.39/2.80 = ( times_times_nat @ B2 @ K4 ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_def
% 2.39/2.80 thf(fact_3949_dvd__def,axiom,
% 2.39/2.80 ( dvd_dvd_int
% 2.39/2.80 = ( ^ [B2: int,A2: int] :
% 2.39/2.80 ? [K4: int] :
% 2.39/2.80 ( A2
% 2.39/2.80 = ( times_times_int @ B2 @ K4 ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_def
% 2.39/2.80 thf(fact_3950_dvd__def,axiom,
% 2.39/2.80 ( dvd_dvd_Code_integer
% 2.39/2.80 = ( ^ [B2: code_integer,A2: code_integer] :
% 2.39/2.80 ? [K4: code_integer] :
% 2.39/2.80 ( A2
% 2.39/2.80 = ( times_3573771949741848930nteger @ B2 @ K4 ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_def
% 2.39/2.80 thf(fact_3951_dvd__def,axiom,
% 2.39/2.80 ( dvd_dvd_Code_natural
% 2.39/2.80 = ( ^ [B2: code_natural,A2: code_natural] :
% 2.39/2.80 ? [K4: code_natural] :
% 2.39/2.80 ( A2
% 2.39/2.80 = ( times_2397367101498566445atural @ B2 @ K4 ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_def
% 2.39/2.80 thf(fact_3952_dvdI,axiom,
% 2.39/2.80 ! [A: assn,B: assn,K: assn] :
% 2.39/2.80 ( ( A
% 2.39/2.80 = ( times_times_assn @ B @ K ) )
% 2.39/2.80 => ( dvd_dvd_assn @ B @ A ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvdI
% 2.39/2.80 thf(fact_3953_dvdI,axiom,
% 2.39/2.80 ! [A: nat,B: nat,K: nat] :
% 2.39/2.80 ( ( A
% 2.39/2.80 = ( times_times_nat @ B @ K ) )
% 2.39/2.80 => ( dvd_dvd_nat @ B @ A ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvdI
% 2.39/2.80 thf(fact_3954_dvdI,axiom,
% 2.39/2.80 ! [A: int,B: int,K: int] :
% 2.39/2.80 ( ( A
% 2.39/2.80 = ( times_times_int @ B @ K ) )
% 2.39/2.80 => ( dvd_dvd_int @ B @ A ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvdI
% 2.39/2.80 thf(fact_3955_dvdI,axiom,
% 2.39/2.80 ! [A: code_integer,B: code_integer,K: code_integer] :
% 2.39/2.80 ( ( A
% 2.39/2.80 = ( times_3573771949741848930nteger @ B @ K ) )
% 2.39/2.80 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvdI
% 2.39/2.80 thf(fact_3956_dvdI,axiom,
% 2.39/2.80 ! [A: code_natural,B: code_natural,K: code_natural] :
% 2.39/2.80 ( ( A
% 2.39/2.80 = ( times_2397367101498566445atural @ B @ K ) )
% 2.39/2.80 => ( dvd_dvd_Code_natural @ B @ A ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvdI
% 2.39/2.80 thf(fact_3957_dvdE,axiom,
% 2.39/2.80 ! [B: assn,A: assn] :
% 2.39/2.80 ( ( dvd_dvd_assn @ B @ A )
% 2.39/2.80 => ~ ! [K2: assn] :
% 2.39/2.80 ( A
% 2.39/2.80 != ( times_times_assn @ B @ K2 ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvdE
% 2.39/2.80 thf(fact_3958_dvdE,axiom,
% 2.39/2.80 ! [B: nat,A: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ B @ A )
% 2.39/2.80 => ~ ! [K2: nat] :
% 2.39/2.80 ( A
% 2.39/2.80 != ( times_times_nat @ B @ K2 ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvdE
% 2.39/2.80 thf(fact_3959_dvdE,axiom,
% 2.39/2.80 ! [B: int,A: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ B @ A )
% 2.39/2.80 => ~ ! [K2: int] :
% 2.39/2.80 ( A
% 2.39/2.80 != ( times_times_int @ B @ K2 ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvdE
% 2.39/2.80 thf(fact_3960_dvdE,axiom,
% 2.39/2.80 ! [B: code_integer,A: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ B @ A )
% 2.39/2.80 => ~ ! [K2: code_integer] :
% 2.39/2.80 ( A
% 2.39/2.80 != ( times_3573771949741848930nteger @ B @ K2 ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvdE
% 2.39/2.80 thf(fact_3961_dvdE,axiom,
% 2.39/2.80 ! [B: code_natural,A: code_natural] :
% 2.39/2.80 ( ( dvd_dvd_Code_natural @ B @ A )
% 2.39/2.80 => ~ ! [K2: code_natural] :
% 2.39/2.80 ( A
% 2.39/2.80 != ( times_2397367101498566445atural @ B @ K2 ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvdE
% 2.39/2.80 thf(fact_3962_dvd__unit__imp__unit,axiom,
% 2.39/2.80 ! [A: code_integer,B: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ A @ B )
% 2.39/2.80 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 2.39/2.80 => ( dvd_dvd_Code_integer @ A @ one_one_Code_integer ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_unit_imp_unit
% 2.39/2.80 thf(fact_3963_dvd__unit__imp__unit,axiom,
% 2.39/2.80 ! [A: nat,B: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ A @ B )
% 2.39/2.80 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 2.39/2.80 => ( dvd_dvd_nat @ A @ one_one_nat ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_unit_imp_unit
% 2.39/2.80 thf(fact_3964_dvd__unit__imp__unit,axiom,
% 2.39/2.80 ! [A: int,B: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ A @ B )
% 2.39/2.80 => ( ( dvd_dvd_int @ B @ one_one_int )
% 2.39/2.80 => ( dvd_dvd_int @ A @ one_one_int ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_unit_imp_unit
% 2.39/2.80 thf(fact_3965_unit__imp__dvd,axiom,
% 2.39/2.80 ! [B: code_integer,A: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 2.39/2.80 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_imp_dvd
% 2.39/2.80 thf(fact_3966_unit__imp__dvd,axiom,
% 2.39/2.80 ! [B: nat,A: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 2.39/2.80 => ( dvd_dvd_nat @ B @ A ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_imp_dvd
% 2.39/2.80 thf(fact_3967_unit__imp__dvd,axiom,
% 2.39/2.80 ! [B: int,A: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ B @ one_one_int )
% 2.39/2.80 => ( dvd_dvd_int @ B @ A ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_imp_dvd
% 2.39/2.80 thf(fact_3968_one__dvd,axiom,
% 2.39/2.80 ! [A: code_integer] : ( dvd_dvd_Code_integer @ one_one_Code_integer @ A ) ).
% 2.39/2.80
% 2.39/2.80 % one_dvd
% 2.39/2.80 thf(fact_3969_one__dvd,axiom,
% 2.39/2.80 ! [A: assn] : ( dvd_dvd_assn @ one_one_assn @ A ) ).
% 2.39/2.80
% 2.39/2.80 % one_dvd
% 2.39/2.80 thf(fact_3970_one__dvd,axiom,
% 2.39/2.80 ! [A: rat] : ( dvd_dvd_rat @ one_one_rat @ A ) ).
% 2.39/2.80
% 2.39/2.80 % one_dvd
% 2.39/2.80 thf(fact_3971_one__dvd,axiom,
% 2.39/2.80 ! [A: nat] : ( dvd_dvd_nat @ one_one_nat @ A ) ).
% 2.39/2.80
% 2.39/2.80 % one_dvd
% 2.39/2.80 thf(fact_3972_one__dvd,axiom,
% 2.39/2.80 ! [A: int] : ( dvd_dvd_int @ one_one_int @ A ) ).
% 2.39/2.80
% 2.39/2.80 % one_dvd
% 2.39/2.80 thf(fact_3973_odd__iff__mod__2__eq__one,axiom,
% 2.39/2.80 ! [A: code_integer] :
% 2.39/2.80 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 2.39/2.80 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 2.39/2.80 = one_one_Code_integer ) ) ).
% 2.39/2.80
% 2.39/2.80 % odd_iff_mod_2_eq_one
% 2.39/2.80 thf(fact_3974_odd__iff__mod__2__eq__one,axiom,
% 2.39/2.80 ! [A: nat] :
% 2.39/2.80 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 2.39/2.80 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.80 = one_one_nat ) ) ).
% 2.39/2.80
% 2.39/2.80 % odd_iff_mod_2_eq_one
% 2.39/2.80 thf(fact_3975_odd__iff__mod__2__eq__one,axiom,
% 2.39/2.80 ! [A: int] :
% 2.39/2.80 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 2.39/2.80 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 2.39/2.80 = one_one_int ) ) ).
% 2.39/2.80
% 2.39/2.80 % odd_iff_mod_2_eq_one
% 2.39/2.80 thf(fact_3976_odd__iff__mod__2__eq__one,axiom,
% 2.39/2.80 ! [A: code_natural] :
% 2.39/2.80 ( ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) )
% 2.39/2.80 = ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 2.39/2.80 = one_one_Code_natural ) ) ).
% 2.39/2.80
% 2.39/2.80 % odd_iff_mod_2_eq_one
% 2.39/2.80 thf(fact_3977_mod__eqE,axiom,
% 2.39/2.80 ! [A: code_integer,C: code_integer,B: code_integer] :
% 2.39/2.80 ( ( ( modulo364778990260209775nteger @ A @ C )
% 2.39/2.80 = ( modulo364778990260209775nteger @ B @ C ) )
% 2.39/2.80 => ~ ! [D3: code_integer] :
% 2.39/2.80 ( B
% 2.39/2.80 != ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ D3 ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % mod_eqE
% 2.39/2.80 thf(fact_3978_mod__eqE,axiom,
% 2.39/2.80 ! [A: int,C: int,B: int] :
% 2.39/2.80 ( ( ( modulo_modulo_int @ A @ C )
% 2.39/2.80 = ( modulo_modulo_int @ B @ C ) )
% 2.39/2.80 => ~ ! [D3: int] :
% 2.39/2.80 ( B
% 2.39/2.80 != ( plus_plus_int @ A @ ( times_times_int @ C @ D3 ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % mod_eqE
% 2.39/2.80 thf(fact_3979_pos__zmod__mult__2,axiom,
% 2.39/2.80 ! [A: int,B: int] :
% 2.39/2.80 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 2.39/2.80 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 2.39/2.80 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ A ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % pos_zmod_mult_2
% 2.39/2.80 thf(fact_3980_neg__zmod__mult__2,axiom,
% 2.39/2.80 ! [A: int,B: int] :
% 2.39/2.80 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 2.39/2.80 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 2.39/2.80 = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) @ one_one_int ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % neg_zmod_mult_2
% 2.39/2.80 thf(fact_3981_not__is__unit__0,axiom,
% 2.39/2.80 ~ ( dvd_dvd_nat @ zero_zero_nat @ one_one_nat ) ).
% 2.39/2.80
% 2.39/2.80 % not_is_unit_0
% 2.39/2.80 thf(fact_3982_not__is__unit__0,axiom,
% 2.39/2.80 ~ ( dvd_dvd_int @ zero_zero_int @ one_one_int ) ).
% 2.39/2.80
% 2.39/2.80 % not_is_unit_0
% 2.39/2.80 thf(fact_3983_not__is__unit__0,axiom,
% 2.39/2.80 ~ ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer ) ).
% 2.39/2.80
% 2.39/2.80 % not_is_unit_0
% 2.39/2.80 thf(fact_3984_not__is__unit__0,axiom,
% 2.39/2.80 ~ ( dvd_dvd_Code_natural @ zero_z2226904508553997617atural @ one_one_Code_natural ) ).
% 2.39/2.80
% 2.39/2.80 % not_is_unit_0
% 2.39/2.80 thf(fact_3985_unit__mult__right__cancel,axiom,
% 2.39/2.80 ! [A: nat,B: nat,C: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 2.39/2.80 => ( ( ( times_times_nat @ B @ A )
% 2.39/2.80 = ( times_times_nat @ C @ A ) )
% 2.39/2.80 = ( B = C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_mult_right_cancel
% 2.39/2.80 thf(fact_3986_unit__mult__right__cancel,axiom,
% 2.39/2.80 ! [A: int,B: int,C: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ A @ one_one_int )
% 2.39/2.80 => ( ( ( times_times_int @ B @ A )
% 2.39/2.80 = ( times_times_int @ C @ A ) )
% 2.39/2.80 = ( B = C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_mult_right_cancel
% 2.39/2.80 thf(fact_3987_unit__mult__right__cancel,axiom,
% 2.39/2.80 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 2.39/2.80 => ( ( ( times_3573771949741848930nteger @ B @ A )
% 2.39/2.80 = ( times_3573771949741848930nteger @ C @ A ) )
% 2.39/2.80 = ( B = C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_mult_right_cancel
% 2.39/2.80 thf(fact_3988_unit__mult__right__cancel,axiom,
% 2.39/2.80 ! [A: code_natural,B: code_natural,C: code_natural] :
% 2.39/2.80 ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 2.39/2.80 => ( ( ( times_2397367101498566445atural @ B @ A )
% 2.39/2.80 = ( times_2397367101498566445atural @ C @ A ) )
% 2.39/2.80 = ( B = C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_mult_right_cancel
% 2.39/2.80 thf(fact_3989_unit__mult__left__cancel,axiom,
% 2.39/2.80 ! [A: nat,B: nat,C: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 2.39/2.80 => ( ( ( times_times_nat @ A @ B )
% 2.39/2.80 = ( times_times_nat @ A @ C ) )
% 2.39/2.80 = ( B = C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_mult_left_cancel
% 2.39/2.80 thf(fact_3990_unit__mult__left__cancel,axiom,
% 2.39/2.80 ! [A: int,B: int,C: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ A @ one_one_int )
% 2.39/2.80 => ( ( ( times_times_int @ A @ B )
% 2.39/2.80 = ( times_times_int @ A @ C ) )
% 2.39/2.80 = ( B = C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_mult_left_cancel
% 2.39/2.80 thf(fact_3991_unit__mult__left__cancel,axiom,
% 2.39/2.80 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 2.39/2.80 => ( ( ( times_3573771949741848930nteger @ A @ B )
% 2.39/2.80 = ( times_3573771949741848930nteger @ A @ C ) )
% 2.39/2.80 = ( B = C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_mult_left_cancel
% 2.39/2.80 thf(fact_3992_unit__mult__left__cancel,axiom,
% 2.39/2.80 ! [A: code_natural,B: code_natural,C: code_natural] :
% 2.39/2.80 ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 2.39/2.80 => ( ( ( times_2397367101498566445atural @ A @ B )
% 2.39/2.80 = ( times_2397367101498566445atural @ A @ C ) )
% 2.39/2.80 = ( B = C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_mult_left_cancel
% 2.39/2.80 thf(fact_3993_mult__unit__dvd__iff_H,axiom,
% 2.39/2.80 ! [A: nat,B: nat,C: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 2.39/2.80 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 2.39/2.80 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % mult_unit_dvd_iff'
% 2.39/2.80 thf(fact_3994_mult__unit__dvd__iff_H,axiom,
% 2.39/2.80 ! [A: int,B: int,C: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ A @ one_one_int )
% 2.39/2.80 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 2.39/2.80 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % mult_unit_dvd_iff'
% 2.39/2.80 thf(fact_3995_mult__unit__dvd__iff_H,axiom,
% 2.39/2.80 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 2.39/2.80 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 2.39/2.80 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % mult_unit_dvd_iff'
% 2.39/2.80 thf(fact_3996_mult__unit__dvd__iff_H,axiom,
% 2.39/2.80 ! [A: code_natural,B: code_natural,C: code_natural] :
% 2.39/2.80 ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 2.39/2.80 => ( ( dvd_dvd_Code_natural @ ( times_2397367101498566445atural @ A @ B ) @ C )
% 2.39/2.80 = ( dvd_dvd_Code_natural @ B @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % mult_unit_dvd_iff'
% 2.39/2.80 thf(fact_3997_dvd__mult__unit__iff_H,axiom,
% 2.39/2.80 ! [B: nat,A: nat,C: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 2.39/2.80 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 2.39/2.80 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_mult_unit_iff'
% 2.39/2.80 thf(fact_3998_dvd__mult__unit__iff_H,axiom,
% 2.39/2.80 ! [B: int,A: int,C: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ B @ one_one_int )
% 2.39/2.80 => ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 2.39/2.80 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_mult_unit_iff'
% 2.39/2.80 thf(fact_3999_dvd__mult__unit__iff_H,axiom,
% 2.39/2.80 ! [B: code_integer,A: code_integer,C: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 2.39/2.80 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 2.39/2.80 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_mult_unit_iff'
% 2.39/2.80 thf(fact_4000_dvd__mult__unit__iff_H,axiom,
% 2.39/2.80 ! [B: code_natural,A: code_natural,C: code_natural] :
% 2.39/2.80 ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 2.39/2.80 => ( ( dvd_dvd_Code_natural @ A @ ( times_2397367101498566445atural @ B @ C ) )
% 2.39/2.80 = ( dvd_dvd_Code_natural @ A @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_mult_unit_iff'
% 2.39/2.80 thf(fact_4001_mult__unit__dvd__iff,axiom,
% 2.39/2.80 ! [B: nat,A: nat,C: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 2.39/2.80 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 2.39/2.80 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % mult_unit_dvd_iff
% 2.39/2.80 thf(fact_4002_mult__unit__dvd__iff,axiom,
% 2.39/2.80 ! [B: int,A: int,C: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ B @ one_one_int )
% 2.39/2.80 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 2.39/2.80 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % mult_unit_dvd_iff
% 2.39/2.80 thf(fact_4003_mult__unit__dvd__iff,axiom,
% 2.39/2.80 ! [B: code_integer,A: code_integer,C: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 2.39/2.80 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 2.39/2.80 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % mult_unit_dvd_iff
% 2.39/2.80 thf(fact_4004_mult__unit__dvd__iff,axiom,
% 2.39/2.80 ! [B: code_natural,A: code_natural,C: code_natural] :
% 2.39/2.80 ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 2.39/2.80 => ( ( dvd_dvd_Code_natural @ ( times_2397367101498566445atural @ A @ B ) @ C )
% 2.39/2.80 = ( dvd_dvd_Code_natural @ A @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % mult_unit_dvd_iff
% 2.39/2.80 thf(fact_4005_dvd__mult__unit__iff,axiom,
% 2.39/2.80 ! [B: nat,A: nat,C: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 2.39/2.80 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) )
% 2.39/2.80 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_mult_unit_iff
% 2.39/2.80 thf(fact_4006_dvd__mult__unit__iff,axiom,
% 2.39/2.80 ! [B: int,A: int,C: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ B @ one_one_int )
% 2.39/2.80 => ( ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) )
% 2.39/2.80 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_mult_unit_iff
% 2.39/2.80 thf(fact_4007_dvd__mult__unit__iff,axiom,
% 2.39/2.80 ! [B: code_integer,A: code_integer,C: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 2.39/2.80 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) )
% 2.39/2.80 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_mult_unit_iff
% 2.39/2.80 thf(fact_4008_dvd__mult__unit__iff,axiom,
% 2.39/2.80 ! [B: code_natural,A: code_natural,C: code_natural] :
% 2.39/2.80 ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 2.39/2.80 => ( ( dvd_dvd_Code_natural @ A @ ( times_2397367101498566445atural @ C @ B ) )
% 2.39/2.80 = ( dvd_dvd_Code_natural @ A @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_mult_unit_iff
% 2.39/2.80 thf(fact_4009_is__unit__mult__iff,axiom,
% 2.39/2.80 ! [A: nat,B: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat )
% 2.39/2.80 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 2.39/2.80 & ( dvd_dvd_nat @ B @ one_one_nat ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % is_unit_mult_iff
% 2.39/2.80 thf(fact_4010_is__unit__mult__iff,axiom,
% 2.39/2.80 ! [A: int,B: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int )
% 2.39/2.80 = ( ( dvd_dvd_int @ A @ one_one_int )
% 2.39/2.80 & ( dvd_dvd_int @ B @ one_one_int ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % is_unit_mult_iff
% 2.39/2.80 thf(fact_4011_is__unit__mult__iff,axiom,
% 2.39/2.80 ! [A: code_integer,B: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer )
% 2.39/2.80 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 2.39/2.80 & ( dvd_dvd_Code_integer @ B @ one_one_Code_integer ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % is_unit_mult_iff
% 2.39/2.80 thf(fact_4012_is__unit__mult__iff,axiom,
% 2.39/2.80 ! [A: code_natural,B: code_natural] :
% 2.39/2.80 ( ( dvd_dvd_Code_natural @ ( times_2397367101498566445atural @ A @ B ) @ one_one_Code_natural )
% 2.39/2.80 = ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 2.39/2.80 & ( dvd_dvd_Code_natural @ B @ one_one_Code_natural ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % is_unit_mult_iff
% 2.39/2.80 thf(fact_4013_dvd__div__mult,axiom,
% 2.39/2.80 ! [C: code_integer,B: code_integer,A: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ C @ B )
% 2.39/2.80 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ C ) @ A )
% 2.39/2.80 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ B @ A ) @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_div_mult
% 2.39/2.80 thf(fact_4014_dvd__div__mult,axiom,
% 2.39/2.80 ! [C: nat,B: nat,A: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ C @ B )
% 2.39/2.80 => ( ( times_times_nat @ ( divide_divide_nat @ B @ C ) @ A )
% 2.39/2.80 = ( divide_divide_nat @ ( times_times_nat @ B @ A ) @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_div_mult
% 2.39/2.80 thf(fact_4015_dvd__div__mult,axiom,
% 2.39/2.80 ! [C: int,B: int,A: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ C @ B )
% 2.39/2.80 => ( ( times_times_int @ ( divide_divide_int @ B @ C ) @ A )
% 2.39/2.80 = ( divide_divide_int @ ( times_times_int @ B @ A ) @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_div_mult
% 2.39/2.80 thf(fact_4016_dvd__div__mult,axiom,
% 2.39/2.80 ! [C: code_natural,B: code_natural,A: code_natural] :
% 2.39/2.80 ( ( dvd_dvd_Code_natural @ C @ B )
% 2.39/2.80 => ( ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ B @ C ) @ A )
% 2.39/2.80 = ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ B @ A ) @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_div_mult
% 2.39/2.80 thf(fact_4017_div__mult__swap,axiom,
% 2.39/2.80 ! [C: code_integer,B: code_integer,A: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ C @ B )
% 2.39/2.80 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 2.39/2.80 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % div_mult_swap
% 2.39/2.80 thf(fact_4018_div__mult__swap,axiom,
% 2.39/2.80 ! [C: nat,B: nat,A: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ C @ B )
% 2.39/2.80 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 2.39/2.80 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % div_mult_swap
% 2.39/2.80 thf(fact_4019_div__mult__swap,axiom,
% 2.39/2.80 ! [C: int,B: int,A: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ C @ B )
% 2.39/2.80 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 2.39/2.80 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % div_mult_swap
% 2.39/2.80 thf(fact_4020_div__mult__swap,axiom,
% 2.39/2.80 ! [C: code_natural,B: code_natural,A: code_natural] :
% 2.39/2.80 ( ( dvd_dvd_Code_natural @ C @ B )
% 2.39/2.80 => ( ( times_2397367101498566445atural @ A @ ( divide5121882707175180666atural @ B @ C ) )
% 2.39/2.80 = ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ B ) @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % div_mult_swap
% 2.39/2.80 thf(fact_4021_div__div__eq__right,axiom,
% 2.39/2.80 ! [C: code_integer,B: code_integer,A: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ C @ B )
% 2.39/2.80 => ( ( dvd_dvd_Code_integer @ B @ A )
% 2.39/2.80 => ( ( divide6298287555418463151nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 2.39/2.80 = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % div_div_eq_right
% 2.39/2.80 thf(fact_4022_div__div__eq__right,axiom,
% 2.39/2.80 ! [C: nat,B: nat,A: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ C @ B )
% 2.39/2.80 => ( ( dvd_dvd_nat @ B @ A )
% 2.39/2.80 => ( ( divide_divide_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 2.39/2.80 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % div_div_eq_right
% 2.39/2.80 thf(fact_4023_div__div__eq__right,axiom,
% 2.39/2.80 ! [C: int,B: int,A: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ C @ B )
% 2.39/2.80 => ( ( dvd_dvd_int @ B @ A )
% 2.39/2.80 => ( ( divide_divide_int @ A @ ( divide_divide_int @ B @ C ) )
% 2.39/2.80 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % div_div_eq_right
% 2.39/2.80 thf(fact_4024_div__div__eq__right,axiom,
% 2.39/2.80 ! [C: code_natural,B: code_natural,A: code_natural] :
% 2.39/2.80 ( ( dvd_dvd_Code_natural @ C @ B )
% 2.39/2.80 => ( ( dvd_dvd_Code_natural @ B @ A )
% 2.39/2.80 => ( ( divide5121882707175180666atural @ A @ ( divide5121882707175180666atural @ B @ C ) )
% 2.39/2.80 = ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ C ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % div_div_eq_right
% 2.39/2.80 thf(fact_4025_dvd__div__mult2__eq,axiom,
% 2.39/2.80 ! [B: code_integer,C: code_integer,A: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ C ) @ A )
% 2.39/2.80 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 2.39/2.80 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_div_mult2_eq
% 2.39/2.80 thf(fact_4026_dvd__div__mult2__eq,axiom,
% 2.39/2.80 ! [B: nat,C: nat,A: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ ( times_times_nat @ B @ C ) @ A )
% 2.39/2.80 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 2.39/2.80 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_div_mult2_eq
% 2.39/2.80 thf(fact_4027_dvd__div__mult2__eq,axiom,
% 2.39/2.80 ! [B: int,C: int,A: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ ( times_times_int @ B @ C ) @ A )
% 2.39/2.80 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 2.39/2.80 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_div_mult2_eq
% 2.39/2.80 thf(fact_4028_dvd__div__mult2__eq,axiom,
% 2.39/2.80 ! [B: code_natural,C: code_natural,A: code_natural] :
% 2.39/2.80 ( ( dvd_dvd_Code_natural @ ( times_2397367101498566445atural @ B @ C ) @ A )
% 2.39/2.80 => ( ( divide5121882707175180666atural @ A @ ( times_2397367101498566445atural @ B @ C ) )
% 2.39/2.80 = ( divide5121882707175180666atural @ ( divide5121882707175180666atural @ A @ B ) @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_div_mult2_eq
% 2.39/2.80 thf(fact_4029_dvd__mult__imp__div,axiom,
% 2.39/2.80 ! [A: code_integer,C: code_integer,B: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B )
% 2.39/2.80 => ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_mult_imp_div
% 2.39/2.80 thf(fact_4030_dvd__mult__imp__div,axiom,
% 2.39/2.80 ! [A: nat,C: nat,B: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B )
% 2.39/2.80 => ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_mult_imp_div
% 2.39/2.80 thf(fact_4031_dvd__mult__imp__div,axiom,
% 2.39/2.80 ! [A: int,C: int,B: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B )
% 2.39/2.80 => ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_mult_imp_div
% 2.39/2.80 thf(fact_4032_dvd__mult__imp__div,axiom,
% 2.39/2.80 ! [A: code_natural,C: code_natural,B: code_natural] :
% 2.39/2.80 ( ( dvd_dvd_Code_natural @ ( times_2397367101498566445atural @ A @ C ) @ B )
% 2.39/2.80 => ( dvd_dvd_Code_natural @ A @ ( divide5121882707175180666atural @ B @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_mult_imp_div
% 2.39/2.80 thf(fact_4033_div__mult__div__if__dvd,axiom,
% 2.39/2.80 ! [B: code_integer,A: code_integer,D2: code_integer,C: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ B @ A )
% 2.39/2.80 => ( ( dvd_dvd_Code_integer @ D2 @ C )
% 2.39/2.80 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ ( divide6298287555418463151nteger @ C @ D2 ) )
% 2.39/2.80 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % div_mult_div_if_dvd
% 2.39/2.80 thf(fact_4034_div__mult__div__if__dvd,axiom,
% 2.39/2.80 ! [B: nat,A: nat,D2: nat,C: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ B @ A )
% 2.39/2.80 => ( ( dvd_dvd_nat @ D2 @ C )
% 2.39/2.80 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ ( divide_divide_nat @ C @ D2 ) )
% 2.39/2.80 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % div_mult_div_if_dvd
% 2.39/2.80 thf(fact_4035_div__mult__div__if__dvd,axiom,
% 2.39/2.80 ! [B: int,A: int,D2: int,C: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ B @ A )
% 2.39/2.80 => ( ( dvd_dvd_int @ D2 @ C )
% 2.39/2.80 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ C @ D2 ) )
% 2.39/2.80 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % div_mult_div_if_dvd
% 2.39/2.80 thf(fact_4036_div__mult__div__if__dvd,axiom,
% 2.39/2.80 ! [B: code_natural,A: code_natural,D2: code_natural,C: code_natural] :
% 2.39/2.80 ( ( dvd_dvd_Code_natural @ B @ A )
% 2.39/2.80 => ( ( dvd_dvd_Code_natural @ D2 @ C )
% 2.39/2.80 => ( ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ ( divide5121882707175180666atural @ C @ D2 ) )
% 2.39/2.80 = ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ D2 ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % div_mult_div_if_dvd
% 2.39/2.80 thf(fact_4037_dvd__div__unit__iff,axiom,
% 2.39/2.80 ! [B: code_integer,A: code_integer,C: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 2.39/2.80 => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ C @ B ) )
% 2.39/2.80 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_div_unit_iff
% 2.39/2.80 thf(fact_4038_dvd__div__unit__iff,axiom,
% 2.39/2.80 ! [B: nat,A: nat,C: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 2.39/2.80 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ C @ B ) )
% 2.39/2.80 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_div_unit_iff
% 2.39/2.80 thf(fact_4039_dvd__div__unit__iff,axiom,
% 2.39/2.80 ! [B: int,A: int,C: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ B @ one_one_int )
% 2.39/2.80 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ C @ B ) )
% 2.39/2.80 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_div_unit_iff
% 2.39/2.80 thf(fact_4040_dvd__div__unit__iff,axiom,
% 2.39/2.80 ! [B: code_natural,A: code_natural,C: code_natural] :
% 2.39/2.80 ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 2.39/2.80 => ( ( dvd_dvd_Code_natural @ A @ ( divide5121882707175180666atural @ C @ B ) )
% 2.39/2.80 = ( dvd_dvd_Code_natural @ A @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_div_unit_iff
% 2.39/2.80 thf(fact_4041_div__unit__dvd__iff,axiom,
% 2.39/2.80 ! [B: code_integer,A: code_integer,C: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 2.39/2.80 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 2.39/2.80 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % div_unit_dvd_iff
% 2.39/2.80 thf(fact_4042_div__unit__dvd__iff,axiom,
% 2.39/2.80 ! [B: nat,A: nat,C: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 2.39/2.80 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 2.39/2.80 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % div_unit_dvd_iff
% 2.39/2.80 thf(fact_4043_div__unit__dvd__iff,axiom,
% 2.39/2.80 ! [B: int,A: int,C: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ B @ one_one_int )
% 2.39/2.80 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 2.39/2.80 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % div_unit_dvd_iff
% 2.39/2.80 thf(fact_4044_div__unit__dvd__iff,axiom,
% 2.39/2.80 ! [B: code_natural,A: code_natural,C: code_natural] :
% 2.39/2.80 ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 2.39/2.80 => ( ( dvd_dvd_Code_natural @ ( divide5121882707175180666atural @ A @ B ) @ C )
% 2.39/2.80 = ( dvd_dvd_Code_natural @ A @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % div_unit_dvd_iff
% 2.39/2.80 thf(fact_4045_unit__div__cancel,axiom,
% 2.39/2.80 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 2.39/2.80 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 2.39/2.80 = ( divide6298287555418463151nteger @ C @ A ) )
% 2.39/2.80 = ( B = C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_div_cancel
% 2.39/2.80 thf(fact_4046_unit__div__cancel,axiom,
% 2.39/2.80 ! [A: nat,B: nat,C: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 2.39/2.80 => ( ( ( divide_divide_nat @ B @ A )
% 2.39/2.80 = ( divide_divide_nat @ C @ A ) )
% 2.39/2.80 = ( B = C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_div_cancel
% 2.39/2.80 thf(fact_4047_unit__div__cancel,axiom,
% 2.39/2.80 ! [A: int,B: int,C: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ A @ one_one_int )
% 2.39/2.80 => ( ( ( divide_divide_int @ B @ A )
% 2.39/2.80 = ( divide_divide_int @ C @ A ) )
% 2.39/2.80 = ( B = C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_div_cancel
% 2.39/2.80 thf(fact_4048_unit__div__cancel,axiom,
% 2.39/2.80 ! [A: code_natural,B: code_natural,C: code_natural] :
% 2.39/2.80 ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 2.39/2.80 => ( ( ( divide5121882707175180666atural @ B @ A )
% 2.39/2.80 = ( divide5121882707175180666atural @ C @ A ) )
% 2.39/2.80 = ( B = C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_div_cancel
% 2.39/2.80 thf(fact_4049_mod2__eq__if,axiom,
% 2.39/2.80 ! [A: code_integer] :
% 2.39/2.80 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 2.39/2.80 = zero_z3403309356797280102nteger ) )
% 2.39/2.80 & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 2.39/2.80 = one_one_Code_integer ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % mod2_eq_if
% 2.39/2.80 thf(fact_4050_mod2__eq__if,axiom,
% 2.39/2.80 ! [A: nat] :
% 2.39/2.80 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.80 = zero_zero_nat ) )
% 2.39/2.80 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.80 = one_one_nat ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % mod2_eq_if
% 2.39/2.80 thf(fact_4051_mod2__eq__if,axiom,
% 2.39/2.80 ! [A: int] :
% 2.39/2.80 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 2.39/2.80 = zero_zero_int ) )
% 2.39/2.80 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 2.39/2.80 = one_one_int ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % mod2_eq_if
% 2.39/2.80 thf(fact_4052_mod2__eq__if,axiom,
% 2.39/2.80 ! [A: code_natural] :
% 2.39/2.80 ( ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 2.39/2.80 = zero_z2226904508553997617atural ) )
% 2.39/2.80 & ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 2.39/2.80 = one_one_Code_natural ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % mod2_eq_if
% 2.39/2.80 thf(fact_4053_parity__cases,axiom,
% 2.39/2.80 ! [A: code_integer] :
% 2.39/2.80 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 2.39/2.80 != zero_z3403309356797280102nteger ) )
% 2.39/2.80 => ~ ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 2.39/2.80 != one_one_Code_integer ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % parity_cases
% 2.39/2.80 thf(fact_4054_parity__cases,axiom,
% 2.39/2.80 ! [A: nat] :
% 2.39/2.80 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.80 != zero_zero_nat ) )
% 2.39/2.80 => ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.80 != one_one_nat ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % parity_cases
% 2.39/2.80 thf(fact_4055_parity__cases,axiom,
% 2.39/2.80 ! [A: int] :
% 2.39/2.80 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 2.39/2.80 != zero_zero_int ) )
% 2.39/2.80 => ~ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 2.39/2.80 != one_one_int ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % parity_cases
% 2.39/2.80 thf(fact_4056_parity__cases,axiom,
% 2.39/2.80 ! [A: code_natural] :
% 2.39/2.80 ( ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 2.39/2.80 != zero_z2226904508553997617atural ) )
% 2.39/2.80 => ~ ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 2.39/2.80 != one_one_Code_natural ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % parity_cases
% 2.39/2.80 thf(fact_4057_cancel__div__mod__rules_I2_J,axiom,
% 2.39/2.80 ! [B: code_integer,A: code_integer,C: code_integer] :
% 2.39/2.80 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 2.39/2.80 = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 2.39/2.80
% 2.39/2.80 % cancel_div_mod_rules(2)
% 2.39/2.80 thf(fact_4058_cancel__div__mod__rules_I2_J,axiom,
% 2.39/2.80 ! [B: nat,A: nat,C: nat] :
% 2.39/2.80 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 2.39/2.80 = ( plus_plus_nat @ A @ C ) ) ).
% 2.39/2.80
% 2.39/2.80 % cancel_div_mod_rules(2)
% 2.39/2.80 thf(fact_4059_cancel__div__mod__rules_I2_J,axiom,
% 2.39/2.80 ! [B: int,A: int,C: int] :
% 2.39/2.80 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 2.39/2.80 = ( plus_plus_int @ A @ C ) ) ).
% 2.39/2.80
% 2.39/2.80 % cancel_div_mod_rules(2)
% 2.39/2.80 thf(fact_4060_cancel__div__mod__rules_I2_J,axiom,
% 2.39/2.80 ! [B: code_natural,A: code_natural,C: code_natural] :
% 2.39/2.80 ( ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) @ ( modulo8411746178871703098atural @ A @ B ) ) @ C )
% 2.39/2.80 = ( plus_p4538020629002901425atural @ A @ C ) ) ).
% 2.39/2.80
% 2.39/2.80 % cancel_div_mod_rules(2)
% 2.39/2.80 thf(fact_4061_cancel__div__mod__rules_I1_J,axiom,
% 2.39/2.80 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.80 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 2.39/2.80 = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 2.39/2.80
% 2.39/2.80 % cancel_div_mod_rules(1)
% 2.39/2.80 thf(fact_4062_cancel__div__mod__rules_I1_J,axiom,
% 2.39/2.80 ! [A: nat,B: nat,C: nat] :
% 2.39/2.80 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 2.39/2.80 = ( plus_plus_nat @ A @ C ) ) ).
% 2.39/2.80
% 2.39/2.80 % cancel_div_mod_rules(1)
% 2.39/2.80 thf(fact_4063_cancel__div__mod__rules_I1_J,axiom,
% 2.39/2.80 ! [A: int,B: int,C: int] :
% 2.39/2.80 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 2.39/2.80 = ( plus_plus_int @ A @ C ) ) ).
% 2.39/2.80
% 2.39/2.80 % cancel_div_mod_rules(1)
% 2.39/2.80 thf(fact_4064_cancel__div__mod__rules_I1_J,axiom,
% 2.39/2.80 ! [A: code_natural,B: code_natural,C: code_natural] :
% 2.39/2.80 ( ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) @ ( modulo8411746178871703098atural @ A @ B ) ) @ C )
% 2.39/2.80 = ( plus_p4538020629002901425atural @ A @ C ) ) ).
% 2.39/2.80
% 2.39/2.80 % cancel_div_mod_rules(1)
% 2.39/2.80 thf(fact_4065_mod__div__decomp,axiom,
% 2.39/2.80 ! [A: code_integer,B: code_integer] :
% 2.39/2.80 ( A
% 2.39/2.80 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % mod_div_decomp
% 2.39/2.80 thf(fact_4066_mod__div__decomp,axiom,
% 2.39/2.80 ! [A: nat,B: nat] :
% 2.39/2.80 ( A
% 2.39/2.80 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % mod_div_decomp
% 2.39/2.80 thf(fact_4067_mod__div__decomp,axiom,
% 2.39/2.80 ! [A: int,B: int] :
% 2.39/2.80 ( A
% 2.39/2.80 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % mod_div_decomp
% 2.39/2.80 thf(fact_4068_mod__div__decomp,axiom,
% 2.39/2.80 ! [A: code_natural,B: code_natural] :
% 2.39/2.80 ( A
% 2.39/2.80 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) @ ( modulo8411746178871703098atural @ A @ B ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % mod_div_decomp
% 2.39/2.80 thf(fact_4069_div__mult__mod__eq,axiom,
% 2.39/2.80 ! [A: code_integer,B: code_integer] :
% 2.39/2.80 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 2.39/2.80 = A ) ).
% 2.39/2.80
% 2.39/2.80 % div_mult_mod_eq
% 2.39/2.80 thf(fact_4070_div__mult__mod__eq,axiom,
% 2.39/2.80 ! [A: nat,B: nat] :
% 2.39/2.80 ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) )
% 2.39/2.80 = A ) ).
% 2.39/2.80
% 2.39/2.80 % div_mult_mod_eq
% 2.39/2.80 thf(fact_4071_div__mult__mod__eq,axiom,
% 2.39/2.80 ! [A: int,B: int] :
% 2.39/2.80 ( ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) )
% 2.39/2.80 = A ) ).
% 2.39/2.80
% 2.39/2.80 % div_mult_mod_eq
% 2.39/2.80 thf(fact_4072_div__mult__mod__eq,axiom,
% 2.39/2.80 ! [A: code_natural,B: code_natural] :
% 2.39/2.80 ( ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) @ ( modulo8411746178871703098atural @ A @ B ) )
% 2.39/2.80 = A ) ).
% 2.39/2.80
% 2.39/2.80 % div_mult_mod_eq
% 2.39/2.80 thf(fact_4073_mod__div__mult__eq,axiom,
% 2.39/2.80 ! [A: code_integer,B: code_integer] :
% 2.39/2.80 ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 2.39/2.80 = A ) ).
% 2.39/2.80
% 2.39/2.80 % mod_div_mult_eq
% 2.39/2.80 thf(fact_4074_mod__div__mult__eq,axiom,
% 2.39/2.80 ! [A: nat,B: nat] :
% 2.39/2.80 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 2.39/2.80 = A ) ).
% 2.39/2.80
% 2.39/2.80 % mod_div_mult_eq
% 2.39/2.80 thf(fact_4075_mod__div__mult__eq,axiom,
% 2.39/2.80 ! [A: int,B: int] :
% 2.39/2.80 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 2.39/2.80 = A ) ).
% 2.39/2.80
% 2.39/2.80 % mod_div_mult_eq
% 2.39/2.80 thf(fact_4076_mod__div__mult__eq,axiom,
% 2.39/2.80 ! [A: code_natural,B: code_natural] :
% 2.39/2.80 ( ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ B ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) )
% 2.39/2.80 = A ) ).
% 2.39/2.80
% 2.39/2.80 % mod_div_mult_eq
% 2.39/2.80 thf(fact_4077_mod__mult__div__eq,axiom,
% 2.39/2.80 ! [A: code_integer,B: code_integer] :
% 2.39/2.80 ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 2.39/2.80 = A ) ).
% 2.39/2.80
% 2.39/2.80 % mod_mult_div_eq
% 2.39/2.80 thf(fact_4078_mod__mult__div__eq,axiom,
% 2.39/2.80 ! [A: nat,B: nat] :
% 2.39/2.80 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 2.39/2.80 = A ) ).
% 2.39/2.80
% 2.39/2.80 % mod_mult_div_eq
% 2.39/2.80 thf(fact_4079_mod__mult__div__eq,axiom,
% 2.39/2.80 ! [A: int,B: int] :
% 2.39/2.80 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 2.39/2.80 = A ) ).
% 2.39/2.80
% 2.39/2.80 % mod_mult_div_eq
% 2.39/2.80 thf(fact_4080_mod__mult__div__eq,axiom,
% 2.39/2.80 ! [A: code_natural,B: code_natural] :
% 2.39/2.80 ( ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ B ) @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) )
% 2.39/2.80 = A ) ).
% 2.39/2.80
% 2.39/2.80 % mod_mult_div_eq
% 2.39/2.80 thf(fact_4081_mult__div__mod__eq,axiom,
% 2.39/2.80 ! [B: code_integer,A: code_integer] :
% 2.39/2.80 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 2.39/2.80 = A ) ).
% 2.39/2.80
% 2.39/2.80 % mult_div_mod_eq
% 2.39/2.80 thf(fact_4082_mult__div__mod__eq,axiom,
% 2.39/2.80 ! [B: nat,A: nat] :
% 2.39/2.80 ( ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) )
% 2.39/2.80 = A ) ).
% 2.39/2.80
% 2.39/2.80 % mult_div_mod_eq
% 2.39/2.80 thf(fact_4083_mult__div__mod__eq,axiom,
% 2.39/2.80 ! [B: int,A: int] :
% 2.39/2.80 ( ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) )
% 2.39/2.80 = A ) ).
% 2.39/2.80
% 2.39/2.80 % mult_div_mod_eq
% 2.39/2.80 thf(fact_4084_mult__div__mod__eq,axiom,
% 2.39/2.80 ! [B: code_natural,A: code_natural] :
% 2.39/2.80 ( ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) @ ( modulo8411746178871703098atural @ A @ B ) )
% 2.39/2.80 = A ) ).
% 2.39/2.80
% 2.39/2.80 % mult_div_mod_eq
% 2.39/2.80 thf(fact_4085_div__mult1__eq,axiom,
% 2.39/2.80 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.80 ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 2.39/2.80 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % div_mult1_eq
% 2.39/2.80 thf(fact_4086_div__mult1__eq,axiom,
% 2.39/2.80 ! [A: nat,B: nat,C: nat] :
% 2.39/2.80 ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C )
% 2.39/2.80 = ( plus_plus_nat @ ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % div_mult1_eq
% 2.39/2.80 thf(fact_4087_div__mult1__eq,axiom,
% 2.39/2.80 ! [A: int,B: int,C: int] :
% 2.39/2.80 ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ C )
% 2.39/2.80 = ( plus_plus_int @ ( times_times_int @ A @ ( divide_divide_int @ B @ C ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % div_mult1_eq
% 2.39/2.80 thf(fact_4088_div__mult1__eq,axiom,
% 2.39/2.80 ! [A: code_natural,B: code_natural,C: code_natural] :
% 2.39/2.80 ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ B ) @ C )
% 2.39/2.80 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ A @ ( divide5121882707175180666atural @ B @ C ) ) @ ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ ( modulo8411746178871703098atural @ B @ C ) ) @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % div_mult1_eq
% 2.39/2.80 thf(fact_4089_minus__div__mult__eq__mod,axiom,
% 2.39/2.80 ! [A: code_integer,B: code_integer] :
% 2.39/2.80 ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 2.39/2.80 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 2.39/2.80
% 2.39/2.80 % minus_div_mult_eq_mod
% 2.39/2.80 thf(fact_4090_minus__div__mult__eq__mod,axiom,
% 2.39/2.80 ! [A: nat,B: nat] :
% 2.39/2.80 ( ( minus_minus_nat @ A @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 2.39/2.80 = ( modulo_modulo_nat @ A @ B ) ) ).
% 2.39/2.80
% 2.39/2.80 % minus_div_mult_eq_mod
% 2.39/2.80 thf(fact_4091_minus__div__mult__eq__mod,axiom,
% 2.39/2.80 ! [A: int,B: int] :
% 2.39/2.80 ( ( minus_minus_int @ A @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 2.39/2.80 = ( modulo_modulo_int @ A @ B ) ) ).
% 2.39/2.80
% 2.39/2.80 % minus_div_mult_eq_mod
% 2.39/2.80 thf(fact_4092_minus__div__mult__eq__mod,axiom,
% 2.39/2.80 ! [A: code_natural,B: code_natural] :
% 2.39/2.80 ( ( minus_7197305767214868737atural @ A @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) )
% 2.39/2.80 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 2.39/2.80
% 2.39/2.80 % minus_div_mult_eq_mod
% 2.39/2.80 thf(fact_4093_minus__mod__eq__div__mult,axiom,
% 2.39/2.80 ! [A: code_integer,B: code_integer] :
% 2.39/2.80 ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 2.39/2.80 = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) ) ).
% 2.39/2.80
% 2.39/2.80 % minus_mod_eq_div_mult
% 2.39/2.80 thf(fact_4094_minus__mod__eq__div__mult,axiom,
% 2.39/2.80 ! [A: nat,B: nat] :
% 2.39/2.80 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 2.39/2.80 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) ) ).
% 2.39/2.80
% 2.39/2.80 % minus_mod_eq_div_mult
% 2.39/2.80 thf(fact_4095_minus__mod__eq__div__mult,axiom,
% 2.39/2.80 ! [A: int,B: int] :
% 2.39/2.80 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 2.39/2.80 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) ) ).
% 2.39/2.80
% 2.39/2.80 % minus_mod_eq_div_mult
% 2.39/2.80 thf(fact_4096_minus__mod__eq__div__mult,axiom,
% 2.39/2.80 ! [A: code_natural,B: code_natural] :
% 2.39/2.80 ( ( minus_7197305767214868737atural @ A @ ( modulo8411746178871703098atural @ A @ B ) )
% 2.39/2.80 = ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) ) ).
% 2.39/2.80
% 2.39/2.80 % minus_mod_eq_div_mult
% 2.39/2.80 thf(fact_4097_minus__mod__eq__mult__div,axiom,
% 2.39/2.80 ! [A: code_integer,B: code_integer] :
% 2.39/2.80 ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 2.39/2.80 = ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % minus_mod_eq_mult_div
% 2.39/2.80 thf(fact_4098_minus__mod__eq__mult__div,axiom,
% 2.39/2.80 ! [A: nat,B: nat] :
% 2.39/2.80 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 2.39/2.80 = ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % minus_mod_eq_mult_div
% 2.39/2.80 thf(fact_4099_minus__mod__eq__mult__div,axiom,
% 2.39/2.80 ! [A: int,B: int] :
% 2.39/2.80 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 2.39/2.80 = ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % minus_mod_eq_mult_div
% 2.39/2.80 thf(fact_4100_minus__mod__eq__mult__div,axiom,
% 2.39/2.80 ! [A: code_natural,B: code_natural] :
% 2.39/2.80 ( ( minus_7197305767214868737atural @ A @ ( modulo8411746178871703098atural @ A @ B ) )
% 2.39/2.80 = ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % minus_mod_eq_mult_div
% 2.39/2.80 thf(fact_4101_minus__mult__div__eq__mod,axiom,
% 2.39/2.80 ! [A: code_integer,B: code_integer] :
% 2.39/2.80 ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 2.39/2.80 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 2.39/2.80
% 2.39/2.80 % minus_mult_div_eq_mod
% 2.39/2.80 thf(fact_4102_minus__mult__div__eq__mod,axiom,
% 2.39/2.80 ! [A: nat,B: nat] :
% 2.39/2.80 ( ( minus_minus_nat @ A @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 2.39/2.80 = ( modulo_modulo_nat @ A @ B ) ) ).
% 2.39/2.80
% 2.39/2.80 % minus_mult_div_eq_mod
% 2.39/2.80 thf(fact_4103_minus__mult__div__eq__mod,axiom,
% 2.39/2.80 ! [A: int,B: int] :
% 2.39/2.80 ( ( minus_minus_int @ A @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 2.39/2.80 = ( modulo_modulo_int @ A @ B ) ) ).
% 2.39/2.80
% 2.39/2.80 % minus_mult_div_eq_mod
% 2.39/2.80 thf(fact_4104_minus__mult__div__eq__mod,axiom,
% 2.39/2.80 ! [A: code_natural,B: code_natural] :
% 2.39/2.80 ( ( minus_7197305767214868737atural @ A @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) )
% 2.39/2.80 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 2.39/2.80
% 2.39/2.80 % minus_mult_div_eq_mod
% 2.39/2.80 thf(fact_4105_unity__coeff__ex,axiom,
% 2.39/2.80 ! [P2: rat > $o,L: rat] :
% 2.39/2.80 ( ( ? [X2: rat] : ( P2 @ ( times_times_rat @ L @ X2 ) ) )
% 2.39/2.80 = ( ? [X2: rat] :
% 2.39/2.80 ( ( dvd_dvd_rat @ L @ ( plus_plus_rat @ X2 @ zero_zero_rat ) )
% 2.39/2.80 & ( P2 @ X2 ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unity_coeff_ex
% 2.39/2.80 thf(fact_4106_unity__coeff__ex,axiom,
% 2.39/2.80 ! [P2: nat > $o,L: nat] :
% 2.39/2.80 ( ( ? [X2: nat] : ( P2 @ ( times_times_nat @ L @ X2 ) ) )
% 2.39/2.80 = ( ? [X2: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ L @ ( plus_plus_nat @ X2 @ zero_zero_nat ) )
% 2.39/2.80 & ( P2 @ X2 ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unity_coeff_ex
% 2.39/2.80 thf(fact_4107_unity__coeff__ex,axiom,
% 2.39/2.80 ! [P2: int > $o,L: int] :
% 2.39/2.80 ( ( ? [X2: int] : ( P2 @ ( times_times_int @ L @ X2 ) ) )
% 2.39/2.80 = ( ? [X2: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ L @ ( plus_plus_int @ X2 @ zero_zero_int ) )
% 2.39/2.80 & ( P2 @ X2 ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unity_coeff_ex
% 2.39/2.80 thf(fact_4108_unity__coeff__ex,axiom,
% 2.39/2.80 ! [P2: code_integer > $o,L: code_integer] :
% 2.39/2.80 ( ( ? [X2: code_integer] : ( P2 @ ( times_3573771949741848930nteger @ L @ X2 ) ) )
% 2.39/2.80 = ( ? [X2: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ L @ ( plus_p5714425477246183910nteger @ X2 @ zero_z3403309356797280102nteger ) )
% 2.39/2.80 & ( P2 @ X2 ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unity_coeff_ex
% 2.39/2.80 thf(fact_4109_unity__coeff__ex,axiom,
% 2.39/2.80 ! [P2: code_natural > $o,L: code_natural] :
% 2.39/2.80 ( ( ? [X2: code_natural] : ( P2 @ ( times_2397367101498566445atural @ L @ X2 ) ) )
% 2.39/2.80 = ( ? [X2: code_natural] :
% 2.39/2.80 ( ( dvd_dvd_Code_natural @ L @ ( plus_p4538020629002901425atural @ X2 @ zero_z2226904508553997617atural ) )
% 2.39/2.80 & ( P2 @ X2 ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unity_coeff_ex
% 2.39/2.80 thf(fact_4110_unit__dvdE,axiom,
% 2.39/2.80 ! [A: nat,B: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 2.39/2.80 => ~ ( ( A != zero_zero_nat )
% 2.39/2.80 => ! [C3: nat] :
% 2.39/2.80 ( B
% 2.39/2.80 != ( times_times_nat @ A @ C3 ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_dvdE
% 2.39/2.80 thf(fact_4111_unit__dvdE,axiom,
% 2.39/2.80 ! [A: int,B: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ A @ one_one_int )
% 2.39/2.80 => ~ ( ( A != zero_zero_int )
% 2.39/2.80 => ! [C3: int] :
% 2.39/2.80 ( B
% 2.39/2.80 != ( times_times_int @ A @ C3 ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_dvdE
% 2.39/2.80 thf(fact_4112_unit__dvdE,axiom,
% 2.39/2.80 ! [A: code_integer,B: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 2.39/2.80 => ~ ( ( A != zero_z3403309356797280102nteger )
% 2.39/2.80 => ! [C3: code_integer] :
% 2.39/2.80 ( B
% 2.39/2.80 != ( times_3573771949741848930nteger @ A @ C3 ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_dvdE
% 2.39/2.80 thf(fact_4113_unit__dvdE,axiom,
% 2.39/2.80 ! [A: code_natural,B: code_natural] :
% 2.39/2.80 ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 2.39/2.80 => ~ ( ( A != zero_z2226904508553997617atural )
% 2.39/2.80 => ! [C3: code_natural] :
% 2.39/2.80 ( B
% 2.39/2.80 != ( times_2397367101498566445atural @ A @ C3 ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_dvdE
% 2.39/2.80 thf(fact_4114_inf__period_I3_J,axiom,
% 2.39/2.80 ! [D2: rat,D: rat,T3: rat] :
% 2.39/2.80 ( ( dvd_dvd_rat @ D2 @ D )
% 2.39/2.80 => ! [X4: rat,K3: rat] :
% 2.39/2.80 ( ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X4 @ T3 ) )
% 2.39/2.80 = ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K3 @ D ) ) @ T3 ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % inf_period(3)
% 2.39/2.80 thf(fact_4115_inf__period_I3_J,axiom,
% 2.39/2.80 ! [D2: int,D: int,T3: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ D2 @ D )
% 2.39/2.80 => ! [X4: int,K3: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X4 @ T3 ) )
% 2.39/2.80 = ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D ) ) @ T3 ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % inf_period(3)
% 2.39/2.80 thf(fact_4116_inf__period_I3_J,axiom,
% 2.39/2.80 ! [D2: code_integer,D: code_integer,T3: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ D2 @ D )
% 2.39/2.80 => ! [X4: code_integer,K3: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X4 @ T3 ) )
% 2.39/2.80 = ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X4 @ ( times_3573771949741848930nteger @ K3 @ D ) ) @ T3 ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % inf_period(3)
% 2.39/2.80 thf(fact_4117_inf__period_I4_J,axiom,
% 2.39/2.80 ! [D2: rat,D: rat,T3: rat] :
% 2.39/2.80 ( ( dvd_dvd_rat @ D2 @ D )
% 2.39/2.80 => ! [X4: rat,K3: rat] :
% 2.39/2.80 ( ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X4 @ T3 ) ) )
% 2.39/2.80 = ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K3 @ D ) ) @ T3 ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % inf_period(4)
% 2.39/2.80 thf(fact_4118_inf__period_I4_J,axiom,
% 2.39/2.80 ! [D2: int,D: int,T3: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ D2 @ D )
% 2.39/2.80 => ! [X4: int,K3: int] :
% 2.39/2.80 ( ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X4 @ T3 ) ) )
% 2.39/2.80 = ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D ) ) @ T3 ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % inf_period(4)
% 2.39/2.80 thf(fact_4119_inf__period_I4_J,axiom,
% 2.39/2.80 ! [D2: code_integer,D: code_integer,T3: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ D2 @ D )
% 2.39/2.80 => ! [X4: code_integer,K3: code_integer] :
% 2.39/2.80 ( ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X4 @ T3 ) ) )
% 2.39/2.80 = ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X4 @ ( times_3573771949741848930nteger @ K3 @ D ) ) @ T3 ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % inf_period(4)
% 2.39/2.80 thf(fact_4120_dvd__div__eq__mult,axiom,
% 2.39/2.80 ! [A: code_integer,B: code_integer,C: code_integer] :
% 2.39/2.80 ( ( A != zero_z3403309356797280102nteger )
% 2.39/2.80 => ( ( dvd_dvd_Code_integer @ A @ B )
% 2.39/2.80 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 2.39/2.80 = C )
% 2.39/2.80 = ( B
% 2.39/2.80 = ( times_3573771949741848930nteger @ C @ A ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_div_eq_mult
% 2.39/2.80 thf(fact_4121_dvd__div__eq__mult,axiom,
% 2.39/2.80 ! [A: nat,B: nat,C: nat] :
% 2.39/2.80 ( ( A != zero_zero_nat )
% 2.39/2.80 => ( ( dvd_dvd_nat @ A @ B )
% 2.39/2.80 => ( ( ( divide_divide_nat @ B @ A )
% 2.39/2.80 = C )
% 2.39/2.80 = ( B
% 2.39/2.80 = ( times_times_nat @ C @ A ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_div_eq_mult
% 2.39/2.80 thf(fact_4122_dvd__div__eq__mult,axiom,
% 2.39/2.80 ! [A: int,B: int,C: int] :
% 2.39/2.80 ( ( A != zero_zero_int )
% 2.39/2.80 => ( ( dvd_dvd_int @ A @ B )
% 2.39/2.80 => ( ( ( divide_divide_int @ B @ A )
% 2.39/2.80 = C )
% 2.39/2.80 = ( B
% 2.39/2.80 = ( times_times_int @ C @ A ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_div_eq_mult
% 2.39/2.80 thf(fact_4123_dvd__div__eq__mult,axiom,
% 2.39/2.80 ! [A: code_natural,B: code_natural,C: code_natural] :
% 2.39/2.80 ( ( A != zero_z2226904508553997617atural )
% 2.39/2.80 => ( ( dvd_dvd_Code_natural @ A @ B )
% 2.39/2.80 => ( ( ( divide5121882707175180666atural @ B @ A )
% 2.39/2.80 = C )
% 2.39/2.80 = ( B
% 2.39/2.80 = ( times_2397367101498566445atural @ C @ A ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_div_eq_mult
% 2.39/2.80 thf(fact_4124_div__dvd__iff__mult,axiom,
% 2.39/2.80 ! [B: code_integer,A: code_integer,C: code_integer] :
% 2.39/2.80 ( ( B != zero_z3403309356797280102nteger )
% 2.39/2.80 => ( ( dvd_dvd_Code_integer @ B @ A )
% 2.39/2.80 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 2.39/2.80 = ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % div_dvd_iff_mult
% 2.39/2.80 thf(fact_4125_div__dvd__iff__mult,axiom,
% 2.39/2.80 ! [B: nat,A: nat,C: nat] :
% 2.39/2.80 ( ( B != zero_zero_nat )
% 2.39/2.80 => ( ( dvd_dvd_nat @ B @ A )
% 2.39/2.80 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 2.39/2.80 = ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % div_dvd_iff_mult
% 2.39/2.80 thf(fact_4126_div__dvd__iff__mult,axiom,
% 2.39/2.80 ! [B: int,A: int,C: int] :
% 2.39/2.80 ( ( B != zero_zero_int )
% 2.39/2.80 => ( ( dvd_dvd_int @ B @ A )
% 2.39/2.80 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 2.39/2.80 = ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % div_dvd_iff_mult
% 2.39/2.80 thf(fact_4127_div__dvd__iff__mult,axiom,
% 2.39/2.80 ! [B: code_natural,A: code_natural,C: code_natural] :
% 2.39/2.80 ( ( B != zero_z2226904508553997617atural )
% 2.39/2.80 => ( ( dvd_dvd_Code_natural @ B @ A )
% 2.39/2.80 => ( ( dvd_dvd_Code_natural @ ( divide5121882707175180666atural @ A @ B ) @ C )
% 2.39/2.80 = ( dvd_dvd_Code_natural @ A @ ( times_2397367101498566445atural @ C @ B ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % div_dvd_iff_mult
% 2.39/2.80 thf(fact_4128_dvd__div__iff__mult,axiom,
% 2.39/2.80 ! [C: code_integer,B: code_integer,A: code_integer] :
% 2.39/2.80 ( ( C != zero_z3403309356797280102nteger )
% 2.39/2.80 => ( ( dvd_dvd_Code_integer @ C @ B )
% 2.39/2.80 => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 2.39/2.80 = ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_div_iff_mult
% 2.39/2.80 thf(fact_4129_dvd__div__iff__mult,axiom,
% 2.39/2.80 ! [C: nat,B: nat,A: nat] :
% 2.39/2.80 ( ( C != zero_zero_nat )
% 2.39/2.80 => ( ( dvd_dvd_nat @ C @ B )
% 2.39/2.80 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 2.39/2.80 = ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_div_iff_mult
% 2.39/2.80 thf(fact_4130_dvd__div__iff__mult,axiom,
% 2.39/2.80 ! [C: int,B: int,A: int] :
% 2.39/2.80 ( ( C != zero_zero_int )
% 2.39/2.80 => ( ( dvd_dvd_int @ C @ B )
% 2.39/2.80 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) )
% 2.39/2.80 = ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_div_iff_mult
% 2.39/2.80 thf(fact_4131_dvd__div__iff__mult,axiom,
% 2.39/2.80 ! [C: code_natural,B: code_natural,A: code_natural] :
% 2.39/2.80 ( ( C != zero_z2226904508553997617atural )
% 2.39/2.80 => ( ( dvd_dvd_Code_natural @ C @ B )
% 2.39/2.80 => ( ( dvd_dvd_Code_natural @ A @ ( divide5121882707175180666atural @ B @ C ) )
% 2.39/2.80 = ( dvd_dvd_Code_natural @ ( times_2397367101498566445atural @ A @ C ) @ B ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_div_iff_mult
% 2.39/2.80 thf(fact_4132_dvd__div__div__eq__mult,axiom,
% 2.39/2.80 ! [A: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 2.39/2.80 ( ( A != zero_z3403309356797280102nteger )
% 2.39/2.80 => ( ( C != zero_z3403309356797280102nteger )
% 2.39/2.80 => ( ( dvd_dvd_Code_integer @ A @ B )
% 2.39/2.80 => ( ( dvd_dvd_Code_integer @ C @ D2 )
% 2.39/2.80 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 2.39/2.80 = ( divide6298287555418463151nteger @ D2 @ C ) )
% 2.39/2.80 = ( ( times_3573771949741848930nteger @ B @ C )
% 2.39/2.80 = ( times_3573771949741848930nteger @ A @ D2 ) ) ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_div_div_eq_mult
% 2.39/2.80 thf(fact_4133_dvd__div__div__eq__mult,axiom,
% 2.39/2.80 ! [A: nat,C: nat,B: nat,D2: nat] :
% 2.39/2.80 ( ( A != zero_zero_nat )
% 2.39/2.80 => ( ( C != zero_zero_nat )
% 2.39/2.80 => ( ( dvd_dvd_nat @ A @ B )
% 2.39/2.80 => ( ( dvd_dvd_nat @ C @ D2 )
% 2.39/2.80 => ( ( ( divide_divide_nat @ B @ A )
% 2.39/2.80 = ( divide_divide_nat @ D2 @ C ) )
% 2.39/2.80 = ( ( times_times_nat @ B @ C )
% 2.39/2.80 = ( times_times_nat @ A @ D2 ) ) ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_div_div_eq_mult
% 2.39/2.80 thf(fact_4134_dvd__div__div__eq__mult,axiom,
% 2.39/2.80 ! [A: int,C: int,B: int,D2: int] :
% 2.39/2.80 ( ( A != zero_zero_int )
% 2.39/2.80 => ( ( C != zero_zero_int )
% 2.39/2.80 => ( ( dvd_dvd_int @ A @ B )
% 2.39/2.80 => ( ( dvd_dvd_int @ C @ D2 )
% 2.39/2.80 => ( ( ( divide_divide_int @ B @ A )
% 2.39/2.80 = ( divide_divide_int @ D2 @ C ) )
% 2.39/2.80 = ( ( times_times_int @ B @ C )
% 2.39/2.80 = ( times_times_int @ A @ D2 ) ) ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_div_div_eq_mult
% 2.39/2.80 thf(fact_4135_dvd__div__div__eq__mult,axiom,
% 2.39/2.80 ! [A: code_natural,C: code_natural,B: code_natural,D2: code_natural] :
% 2.39/2.80 ( ( A != zero_z2226904508553997617atural )
% 2.39/2.80 => ( ( C != zero_z2226904508553997617atural )
% 2.39/2.80 => ( ( dvd_dvd_Code_natural @ A @ B )
% 2.39/2.80 => ( ( dvd_dvd_Code_natural @ C @ D2 )
% 2.39/2.80 => ( ( ( divide5121882707175180666atural @ B @ A )
% 2.39/2.80 = ( divide5121882707175180666atural @ D2 @ C ) )
% 2.39/2.80 = ( ( times_2397367101498566445atural @ B @ C )
% 2.39/2.80 = ( times_2397367101498566445atural @ A @ D2 ) ) ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_div_div_eq_mult
% 2.39/2.80 thf(fact_4136_unit__div__eq__0__iff,axiom,
% 2.39/2.80 ! [B: code_integer,A: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 2.39/2.80 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 2.39/2.80 = zero_z3403309356797280102nteger )
% 2.39/2.80 = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_div_eq_0_iff
% 2.39/2.80 thf(fact_4137_unit__div__eq__0__iff,axiom,
% 2.39/2.80 ! [B: nat,A: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 2.39/2.80 => ( ( ( divide_divide_nat @ A @ B )
% 2.39/2.80 = zero_zero_nat )
% 2.39/2.80 = ( A = zero_zero_nat ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_div_eq_0_iff
% 2.39/2.80 thf(fact_4138_unit__div__eq__0__iff,axiom,
% 2.39/2.80 ! [B: int,A: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ B @ one_one_int )
% 2.39/2.80 => ( ( ( divide_divide_int @ A @ B )
% 2.39/2.80 = zero_zero_int )
% 2.39/2.80 = ( A = zero_zero_int ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_div_eq_0_iff
% 2.39/2.80 thf(fact_4139_unit__div__eq__0__iff,axiom,
% 2.39/2.80 ! [B: code_natural,A: code_natural] :
% 2.39/2.80 ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 2.39/2.80 => ( ( ( divide5121882707175180666atural @ A @ B )
% 2.39/2.80 = zero_z2226904508553997617atural )
% 2.39/2.80 = ( A = zero_z2226904508553997617atural ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_div_eq_0_iff
% 2.39/2.80 thf(fact_4140_is__unit__div__mult2__eq,axiom,
% 2.39/2.80 ! [B: code_integer,C: code_integer,A: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 2.39/2.80 => ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 2.39/2.80 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 2.39/2.80 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % is_unit_div_mult2_eq
% 2.39/2.80 thf(fact_4141_is__unit__div__mult2__eq,axiom,
% 2.39/2.80 ! [B: nat,C: nat,A: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 2.39/2.80 => ( ( dvd_dvd_nat @ C @ one_one_nat )
% 2.39/2.80 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 2.39/2.80 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % is_unit_div_mult2_eq
% 2.39/2.80 thf(fact_4142_is__unit__div__mult2__eq,axiom,
% 2.39/2.80 ! [B: int,C: int,A: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ B @ one_one_int )
% 2.39/2.80 => ( ( dvd_dvd_int @ C @ one_one_int )
% 2.39/2.80 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 2.39/2.80 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % is_unit_div_mult2_eq
% 2.39/2.80 thf(fact_4143_is__unit__div__mult2__eq,axiom,
% 2.39/2.80 ! [B: code_natural,C: code_natural,A: code_natural] :
% 2.39/2.80 ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 2.39/2.80 => ( ( dvd_dvd_Code_natural @ C @ one_one_Code_natural )
% 2.39/2.80 => ( ( divide5121882707175180666atural @ A @ ( times_2397367101498566445atural @ B @ C ) )
% 2.39/2.80 = ( divide5121882707175180666atural @ ( divide5121882707175180666atural @ A @ B ) @ C ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % is_unit_div_mult2_eq
% 2.39/2.80 thf(fact_4144_unit__div__mult__swap,axiom,
% 2.39/2.80 ! [C: code_integer,A: code_integer,B: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 2.39/2.80 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 2.39/2.80 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_div_mult_swap
% 2.39/2.80 thf(fact_4145_unit__div__mult__swap,axiom,
% 2.39/2.80 ! [C: nat,A: nat,B: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 2.39/2.80 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 2.39/2.80 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_div_mult_swap
% 2.39/2.80 thf(fact_4146_unit__div__mult__swap,axiom,
% 2.39/2.80 ! [C: int,A: int,B: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ C @ one_one_int )
% 2.39/2.80 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 2.39/2.80 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_div_mult_swap
% 2.39/2.80 thf(fact_4147_unit__div__mult__swap,axiom,
% 2.39/2.80 ! [C: code_natural,A: code_natural,B: code_natural] :
% 2.39/2.80 ( ( dvd_dvd_Code_natural @ C @ one_one_Code_natural )
% 2.39/2.80 => ( ( times_2397367101498566445atural @ A @ ( divide5121882707175180666atural @ B @ C ) )
% 2.39/2.80 = ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ B ) @ C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_div_mult_swap
% 2.39/2.80 thf(fact_4148_unit__div__commute,axiom,
% 2.39/2.80 ! [B: code_integer,A: code_integer,C: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 2.39/2.80 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 2.39/2.80 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_div_commute
% 2.39/2.80 thf(fact_4149_unit__div__commute,axiom,
% 2.39/2.80 ! [B: nat,A: nat,C: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 2.39/2.80 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 2.39/2.80 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_div_commute
% 2.39/2.80 thf(fact_4150_unit__div__commute,axiom,
% 2.39/2.80 ! [B: int,A: int,C: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ B @ one_one_int )
% 2.39/2.80 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ C )
% 2.39/2.80 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ B ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_div_commute
% 2.39/2.80 thf(fact_4151_unit__div__commute,axiom,
% 2.39/2.80 ! [B: code_natural,A: code_natural,C: code_natural] :
% 2.39/2.80 ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 2.39/2.80 => ( ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ C )
% 2.39/2.80 = ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ C ) @ B ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_div_commute
% 2.39/2.80 thf(fact_4152_div__mult__unit2,axiom,
% 2.39/2.80 ! [C: code_integer,B: code_integer,A: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 2.39/2.80 => ( ( dvd_dvd_Code_integer @ B @ A )
% 2.39/2.80 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 2.39/2.80 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % div_mult_unit2
% 2.39/2.80 thf(fact_4153_div__mult__unit2,axiom,
% 2.39/2.80 ! [C: nat,B: nat,A: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 2.39/2.80 => ( ( dvd_dvd_nat @ B @ A )
% 2.39/2.80 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 2.39/2.80 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % div_mult_unit2
% 2.39/2.80 thf(fact_4154_div__mult__unit2,axiom,
% 2.39/2.80 ! [C: int,B: int,A: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ C @ one_one_int )
% 2.39/2.80 => ( ( dvd_dvd_int @ B @ A )
% 2.39/2.80 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 2.39/2.80 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % div_mult_unit2
% 2.39/2.80 thf(fact_4155_div__mult__unit2,axiom,
% 2.39/2.80 ! [C: code_natural,B: code_natural,A: code_natural] :
% 2.39/2.80 ( ( dvd_dvd_Code_natural @ C @ one_one_Code_natural )
% 2.39/2.80 => ( ( dvd_dvd_Code_natural @ B @ A )
% 2.39/2.80 => ( ( divide5121882707175180666atural @ A @ ( times_2397367101498566445atural @ B @ C ) )
% 2.39/2.80 = ( divide5121882707175180666atural @ ( divide5121882707175180666atural @ A @ B ) @ C ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % div_mult_unit2
% 2.39/2.80 thf(fact_4156_unit__eq__div2,axiom,
% 2.39/2.80 ! [B: code_integer,A: code_integer,C: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 2.39/2.80 => ( ( A
% 2.39/2.80 = ( divide6298287555418463151nteger @ C @ B ) )
% 2.39/2.80 = ( ( times_3573771949741848930nteger @ A @ B )
% 2.39/2.80 = C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_eq_div2
% 2.39/2.80 thf(fact_4157_unit__eq__div2,axiom,
% 2.39/2.80 ! [B: nat,A: nat,C: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 2.39/2.80 => ( ( A
% 2.39/2.80 = ( divide_divide_nat @ C @ B ) )
% 2.39/2.80 = ( ( times_times_nat @ A @ B )
% 2.39/2.80 = C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_eq_div2
% 2.39/2.80 thf(fact_4158_unit__eq__div2,axiom,
% 2.39/2.80 ! [B: int,A: int,C: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ B @ one_one_int )
% 2.39/2.80 => ( ( A
% 2.39/2.80 = ( divide_divide_int @ C @ B ) )
% 2.39/2.80 = ( ( times_times_int @ A @ B )
% 2.39/2.80 = C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_eq_div2
% 2.39/2.80 thf(fact_4159_unit__eq__div2,axiom,
% 2.39/2.80 ! [B: code_natural,A: code_natural,C: code_natural] :
% 2.39/2.80 ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 2.39/2.80 => ( ( A
% 2.39/2.80 = ( divide5121882707175180666atural @ C @ B ) )
% 2.39/2.80 = ( ( times_2397367101498566445atural @ A @ B )
% 2.39/2.80 = C ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_eq_div2
% 2.39/2.80 thf(fact_4160_unit__eq__div1,axiom,
% 2.39/2.80 ! [B: code_integer,A: code_integer,C: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 2.39/2.80 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 2.39/2.80 = C )
% 2.39/2.80 = ( A
% 2.39/2.80 = ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_eq_div1
% 2.39/2.80 thf(fact_4161_unit__eq__div1,axiom,
% 2.39/2.80 ! [B: nat,A: nat,C: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 2.39/2.80 => ( ( ( divide_divide_nat @ A @ B )
% 2.39/2.80 = C )
% 2.39/2.80 = ( A
% 2.39/2.80 = ( times_times_nat @ C @ B ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_eq_div1
% 2.39/2.80 thf(fact_4162_unit__eq__div1,axiom,
% 2.39/2.80 ! [B: int,A: int,C: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ B @ one_one_int )
% 2.39/2.80 => ( ( ( divide_divide_int @ A @ B )
% 2.39/2.80 = C )
% 2.39/2.80 = ( A
% 2.39/2.80 = ( times_times_int @ C @ B ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_eq_div1
% 2.39/2.80 thf(fact_4163_unit__eq__div1,axiom,
% 2.39/2.80 ! [B: code_natural,A: code_natural,C: code_natural] :
% 2.39/2.80 ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 2.39/2.80 => ( ( ( divide5121882707175180666atural @ A @ B )
% 2.39/2.80 = C )
% 2.39/2.80 = ( A
% 2.39/2.80 = ( times_2397367101498566445atural @ C @ B ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unit_eq_div1
% 2.39/2.80 thf(fact_4164_is__unit__power__iff,axiom,
% 2.39/2.80 ! [A: code_integer,N: nat] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) @ one_one_Code_integer )
% 2.39/2.80 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 2.39/2.80 | ( N = zero_zero_nat ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % is_unit_power_iff
% 2.39/2.80 thf(fact_4165_is__unit__power__iff,axiom,
% 2.39/2.80 ! [A: int,N: nat] :
% 2.39/2.80 ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ one_one_int )
% 2.39/2.80 = ( ( dvd_dvd_int @ A @ one_one_int )
% 2.39/2.80 | ( N = zero_zero_nat ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % is_unit_power_iff
% 2.39/2.80 thf(fact_4166_is__unit__power__iff,axiom,
% 2.39/2.80 ! [A: nat,N: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ one_one_nat )
% 2.39/2.80 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 2.39/2.80 | ( N = zero_zero_nat ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % is_unit_power_iff
% 2.39/2.80 thf(fact_4167_power__dvd__imp__le,axiom,
% 2.39/2.80 ! [I2: nat,M2: nat,N: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ ( power_power_nat @ I2 @ M2 ) @ ( power_power_nat @ I2 @ N ) )
% 2.39/2.80 => ( ( ord_less_nat @ one_one_nat @ I2 )
% 2.39/2.80 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % power_dvd_imp_le
% 2.39/2.80 thf(fact_4168_is__unitE,axiom,
% 2.39/2.80 ! [A: code_integer,C: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 2.39/2.80 => ~ ( ( A != zero_z3403309356797280102nteger )
% 2.39/2.80 => ! [B5: code_integer] :
% 2.39/2.80 ( ( B5 != zero_z3403309356797280102nteger )
% 2.39/2.80 => ( ( dvd_dvd_Code_integer @ B5 @ one_one_Code_integer )
% 2.39/2.80 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ A )
% 2.39/2.80 = B5 )
% 2.39/2.80 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ B5 )
% 2.39/2.80 = A )
% 2.39/2.80 => ( ( ( times_3573771949741848930nteger @ A @ B5 )
% 2.39/2.80 = one_one_Code_integer )
% 2.39/2.80 => ( ( divide6298287555418463151nteger @ C @ A )
% 2.39/2.80 != ( times_3573771949741848930nteger @ C @ B5 ) ) ) ) ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % is_unitE
% 2.39/2.80 thf(fact_4169_is__unitE,axiom,
% 2.39/2.80 ! [A: nat,C: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 2.39/2.80 => ~ ( ( A != zero_zero_nat )
% 2.39/2.80 => ! [B5: nat] :
% 2.39/2.80 ( ( B5 != zero_zero_nat )
% 2.39/2.80 => ( ( dvd_dvd_nat @ B5 @ one_one_nat )
% 2.39/2.80 => ( ( ( divide_divide_nat @ one_one_nat @ A )
% 2.39/2.80 = B5 )
% 2.39/2.80 => ( ( ( divide_divide_nat @ one_one_nat @ B5 )
% 2.39/2.80 = A )
% 2.39/2.80 => ( ( ( times_times_nat @ A @ B5 )
% 2.39/2.80 = one_one_nat )
% 2.39/2.80 => ( ( divide_divide_nat @ C @ A )
% 2.39/2.80 != ( times_times_nat @ C @ B5 ) ) ) ) ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % is_unitE
% 2.39/2.80 thf(fact_4170_is__unitE,axiom,
% 2.39/2.80 ! [A: int,C: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ A @ one_one_int )
% 2.39/2.80 => ~ ( ( A != zero_zero_int )
% 2.39/2.80 => ! [B5: int] :
% 2.39/2.80 ( ( B5 != zero_zero_int )
% 2.39/2.80 => ( ( dvd_dvd_int @ B5 @ one_one_int )
% 2.39/2.80 => ( ( ( divide_divide_int @ one_one_int @ A )
% 2.39/2.80 = B5 )
% 2.39/2.80 => ( ( ( divide_divide_int @ one_one_int @ B5 )
% 2.39/2.80 = A )
% 2.39/2.80 => ( ( ( times_times_int @ A @ B5 )
% 2.39/2.80 = one_one_int )
% 2.39/2.80 => ( ( divide_divide_int @ C @ A )
% 2.39/2.80 != ( times_times_int @ C @ B5 ) ) ) ) ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % is_unitE
% 2.39/2.80 thf(fact_4171_is__unitE,axiom,
% 2.39/2.80 ! [A: code_natural,C: code_natural] :
% 2.39/2.80 ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 2.39/2.80 => ~ ( ( A != zero_z2226904508553997617atural )
% 2.39/2.80 => ! [B5: code_natural] :
% 2.39/2.80 ( ( B5 != zero_z2226904508553997617atural )
% 2.39/2.80 => ( ( dvd_dvd_Code_natural @ B5 @ one_one_Code_natural )
% 2.39/2.80 => ( ( ( divide5121882707175180666atural @ one_one_Code_natural @ A )
% 2.39/2.80 = B5 )
% 2.39/2.80 => ( ( ( divide5121882707175180666atural @ one_one_Code_natural @ B5 )
% 2.39/2.80 = A )
% 2.39/2.80 => ( ( ( times_2397367101498566445atural @ A @ B5 )
% 2.39/2.80 = one_one_Code_natural )
% 2.39/2.80 => ( ( divide5121882707175180666atural @ C @ A )
% 2.39/2.80 != ( times_2397367101498566445atural @ C @ B5 ) ) ) ) ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % is_unitE
% 2.39/2.80 thf(fact_4172_is__unit__div__mult__cancel__left,axiom,
% 2.39/2.80 ! [A: code_integer,B: code_integer] :
% 2.39/2.80 ( ( A != zero_z3403309356797280102nteger )
% 2.39/2.80 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 2.39/2.80 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ A @ B ) )
% 2.39/2.80 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % is_unit_div_mult_cancel_left
% 2.39/2.80 thf(fact_4173_is__unit__div__mult__cancel__left,axiom,
% 2.39/2.80 ! [A: nat,B: nat] :
% 2.39/2.80 ( ( A != zero_zero_nat )
% 2.39/2.80 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 2.39/2.80 => ( ( divide_divide_nat @ A @ ( times_times_nat @ A @ B ) )
% 2.39/2.80 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % is_unit_div_mult_cancel_left
% 2.39/2.80 thf(fact_4174_is__unit__div__mult__cancel__left,axiom,
% 2.39/2.80 ! [A: int,B: int] :
% 2.39/2.80 ( ( A != zero_zero_int )
% 2.39/2.80 => ( ( dvd_dvd_int @ B @ one_one_int )
% 2.39/2.80 => ( ( divide_divide_int @ A @ ( times_times_int @ A @ B ) )
% 2.39/2.80 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % is_unit_div_mult_cancel_left
% 2.39/2.80 thf(fact_4175_is__unit__div__mult__cancel__left,axiom,
% 2.39/2.80 ! [A: code_natural,B: code_natural] :
% 2.39/2.80 ( ( A != zero_z2226904508553997617atural )
% 2.39/2.80 => ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 2.39/2.80 => ( ( divide5121882707175180666atural @ A @ ( times_2397367101498566445atural @ A @ B ) )
% 2.39/2.80 = ( divide5121882707175180666atural @ one_one_Code_natural @ B ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % is_unit_div_mult_cancel_left
% 2.39/2.80 thf(fact_4176_is__unit__div__mult__cancel__right,axiom,
% 2.39/2.80 ! [A: code_integer,B: code_integer] :
% 2.39/2.80 ( ( A != zero_z3403309356797280102nteger )
% 2.39/2.80 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 2.39/2.80 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ A ) )
% 2.39/2.80 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % is_unit_div_mult_cancel_right
% 2.39/2.80 thf(fact_4177_is__unit__div__mult__cancel__right,axiom,
% 2.39/2.80 ! [A: nat,B: nat] :
% 2.39/2.80 ( ( A != zero_zero_nat )
% 2.39/2.80 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 2.39/2.80 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ A ) )
% 2.39/2.80 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % is_unit_div_mult_cancel_right
% 2.39/2.80 thf(fact_4178_is__unit__div__mult__cancel__right,axiom,
% 2.39/2.80 ! [A: int,B: int] :
% 2.39/2.80 ( ( A != zero_zero_int )
% 2.39/2.80 => ( ( dvd_dvd_int @ B @ one_one_int )
% 2.39/2.80 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ A ) )
% 2.39/2.80 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % is_unit_div_mult_cancel_right
% 2.39/2.80 thf(fact_4179_is__unit__div__mult__cancel__right,axiom,
% 2.39/2.80 ! [A: code_natural,B: code_natural] :
% 2.39/2.80 ( ( A != zero_z2226904508553997617atural )
% 2.39/2.80 => ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 2.39/2.80 => ( ( divide5121882707175180666atural @ A @ ( times_2397367101498566445atural @ B @ A ) )
% 2.39/2.80 = ( divide5121882707175180666atural @ one_one_Code_natural @ B ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % is_unit_div_mult_cancel_right
% 2.39/2.80 thf(fact_4180_evenE,axiom,
% 2.39/2.80 ! [A: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ~ ! [B5: nat] :
% 2.39/2.80 ( A
% 2.39/2.80 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B5 ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % evenE
% 2.39/2.80 thf(fact_4181_evenE,axiom,
% 2.39/2.80 ! [A: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ~ ! [B5: int] :
% 2.39/2.80 ( A
% 2.39/2.80 != ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B5 ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % evenE
% 2.39/2.80 thf(fact_4182_evenE,axiom,
% 2.39/2.80 ! [A: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ~ ! [B5: code_integer] :
% 2.39/2.80 ( A
% 2.39/2.80 != ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B5 ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % evenE
% 2.39/2.80 thf(fact_4183_evenE,axiom,
% 2.39/2.80 ! [A: code_natural] :
% 2.39/2.80 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ~ ! [B5: code_natural] :
% 2.39/2.80 ( A
% 2.39/2.80 != ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ B5 ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % evenE
% 2.39/2.80 thf(fact_4184_odd__one,axiom,
% 2.39/2.80 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ one_one_nat ) ).
% 2.39/2.80
% 2.39/2.80 % odd_one
% 2.39/2.80 thf(fact_4185_odd__one,axiom,
% 2.39/2.80 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ one_one_int ) ).
% 2.39/2.80
% 2.39/2.80 % odd_one
% 2.39/2.80 thf(fact_4186_odd__one,axiom,
% 2.39/2.80 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ one_one_Code_integer ) ).
% 2.39/2.80
% 2.39/2.80 % odd_one
% 2.39/2.80 thf(fact_4187_odd__one,axiom,
% 2.39/2.80 ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ one_one_Code_natural ) ).
% 2.39/2.80
% 2.39/2.80 % odd_one
% 2.39/2.80 thf(fact_4188_dvd__power__iff,axiom,
% 2.39/2.80 ! [X: code_integer,M2: nat,N: nat] :
% 2.39/2.80 ( ( X != zero_z3403309356797280102nteger )
% 2.39/2.80 => ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ M2 ) @ ( power_8256067586552552935nteger @ X @ N ) )
% 2.39/2.80 = ( ( dvd_dvd_Code_integer @ X @ one_one_Code_integer )
% 2.39/2.80 | ( ord_less_eq_nat @ M2 @ N ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_power_iff
% 2.39/2.80 thf(fact_4189_dvd__power__iff,axiom,
% 2.39/2.80 ! [X: code_natural,M2: nat,N: nat] :
% 2.39/2.80 ( ( X != zero_z2226904508553997617atural )
% 2.39/2.80 => ( ( dvd_dvd_Code_natural @ ( power_7079662738309270450atural @ X @ M2 ) @ ( power_7079662738309270450atural @ X @ N ) )
% 2.39/2.80 = ( ( dvd_dvd_Code_natural @ X @ one_one_Code_natural )
% 2.39/2.80 | ( ord_less_eq_nat @ M2 @ N ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_power_iff
% 2.39/2.80 thf(fact_4190_dvd__power__iff,axiom,
% 2.39/2.80 ! [X: int,M2: nat,N: nat] :
% 2.39/2.80 ( ( X != zero_zero_int )
% 2.39/2.80 => ( ( dvd_dvd_int @ ( power_power_int @ X @ M2 ) @ ( power_power_int @ X @ N ) )
% 2.39/2.80 = ( ( dvd_dvd_int @ X @ one_one_int )
% 2.39/2.80 | ( ord_less_eq_nat @ M2 @ N ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_power_iff
% 2.39/2.80 thf(fact_4191_dvd__power__iff,axiom,
% 2.39/2.80 ! [X: nat,M2: nat,N: nat] :
% 2.39/2.80 ( ( X != zero_zero_nat )
% 2.39/2.80 => ( ( dvd_dvd_nat @ ( power_power_nat @ X @ M2 ) @ ( power_power_nat @ X @ N ) )
% 2.39/2.80 = ( ( dvd_dvd_nat @ X @ one_one_nat )
% 2.39/2.80 | ( ord_less_eq_nat @ M2 @ N ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_power_iff
% 2.39/2.80 thf(fact_4192_dvd__power,axiom,
% 2.39/2.80 ! [N: nat,X: code_integer] :
% 2.39/2.80 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.39/2.80 | ( X = one_one_Code_integer ) )
% 2.39/2.80 => ( dvd_dvd_Code_integer @ X @ ( power_8256067586552552935nteger @ X @ N ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_power
% 2.39/2.80 thf(fact_4193_dvd__power,axiom,
% 2.39/2.80 ! [N: nat,X: rat] :
% 2.39/2.80 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.39/2.80 | ( X = one_one_rat ) )
% 2.39/2.80 => ( dvd_dvd_rat @ X @ ( power_power_rat @ X @ N ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_power
% 2.39/2.80 thf(fact_4194_dvd__power,axiom,
% 2.39/2.80 ! [N: nat,X: int] :
% 2.39/2.80 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.39/2.80 | ( X = one_one_int ) )
% 2.39/2.80 => ( dvd_dvd_int @ X @ ( power_power_int @ X @ N ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_power
% 2.39/2.80 thf(fact_4195_dvd__power,axiom,
% 2.39/2.80 ! [N: nat,X: nat] :
% 2.39/2.80 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.39/2.80 | ( X = one_one_nat ) )
% 2.39/2.80 => ( dvd_dvd_nat @ X @ ( power_power_nat @ X @ N ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_power
% 2.39/2.80 thf(fact_4196_dvd__mult__cancel2,axiom,
% 2.39/2.80 ! [M2: nat,N: nat] :
% 2.39/2.80 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 2.39/2.80 => ( ( dvd_dvd_nat @ ( times_times_nat @ N @ M2 ) @ M2 )
% 2.39/2.80 = ( N = one_one_nat ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_mult_cancel2
% 2.39/2.80 thf(fact_4197_dvd__mult__cancel1,axiom,
% 2.39/2.80 ! [M2: nat,N: nat] :
% 2.39/2.80 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 2.39/2.80 => ( ( dvd_dvd_nat @ ( times_times_nat @ M2 @ N ) @ M2 )
% 2.39/2.80 = ( N = one_one_nat ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % dvd_mult_cancel1
% 2.39/2.80 thf(fact_4198_set__bit__Suc,axiom,
% 2.39/2.80 ! [N: nat,A: code_integer] :
% 2.39/2.80 ( ( bit_se2793503036327961859nteger @ ( suc @ N ) @ A )
% 2.39/2.80 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % set_bit_Suc
% 2.39/2.80 thf(fact_4199_set__bit__Suc,axiom,
% 2.39/2.80 ! [N: nat,A: code_natural] :
% 2.39/2.80 ( ( bit_se1617098188084679374atural @ ( suc @ N ) @ A )
% 2.39/2.80 = ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se1617098188084679374atural @ N @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % set_bit_Suc
% 2.39/2.80 thf(fact_4200_set__bit__Suc,axiom,
% 2.39/2.80 ! [N: nat,A: nat] :
% 2.39/2.80 ( ( bit_se7882103937844011126it_nat @ ( suc @ N ) @ A )
% 2.39/2.80 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % set_bit_Suc
% 2.39/2.80 thf(fact_4201_set__bit__Suc,axiom,
% 2.39/2.80 ! [N: nat,A: int] :
% 2.39/2.80 ( ( bit_se7879613467334960850it_int @ ( suc @ N ) @ A )
% 2.39/2.80 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % set_bit_Suc
% 2.39/2.80 thf(fact_4202_unset__bit__Suc,axiom,
% 2.39/2.80 ! [N: nat,A: code_integer] :
% 2.39/2.80 ( ( bit_se8260200283734997820nteger @ ( suc @ N ) @ A )
% 2.39/2.80 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unset_bit_Suc
% 2.39/2.80 thf(fact_4203_unset__bit__Suc,axiom,
% 2.39/2.80 ! [N: nat,A: nat] :
% 2.39/2.80 ( ( bit_se4205575877204974255it_nat @ ( suc @ N ) @ A )
% 2.39/2.80 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unset_bit_Suc
% 2.39/2.80 thf(fact_4204_unset__bit__Suc,axiom,
% 2.39/2.80 ! [N: nat,A: code_natural] :
% 2.39/2.80 ( ( bit_se7083795435491715335atural @ ( suc @ N ) @ A )
% 2.39/2.80 = ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se7083795435491715335atural @ N @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unset_bit_Suc
% 2.39/2.80 thf(fact_4205_unset__bit__Suc,axiom,
% 2.39/2.80 ! [N: nat,A: int] :
% 2.39/2.80 ( ( bit_se4203085406695923979it_int @ ( suc @ N ) @ A )
% 2.39/2.80 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unset_bit_Suc
% 2.39/2.80 thf(fact_4206_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 2.39/2.80 ! [C: code_integer,A: code_integer,B: code_integer] :
% 2.39/2.80 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 2.39/2.80 => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 2.39/2.80 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 2.39/2.80 thf(fact_4207_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 2.39/2.80 ! [C: nat,A: nat,B: nat] :
% 2.39/2.80 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 2.39/2.80 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ B @ C ) )
% 2.39/2.80 = ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) @ ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 2.39/2.80 thf(fact_4208_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 2.39/2.80 ! [C: int,A: int,B: int] :
% 2.39/2.80 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 2.39/2.80 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 2.39/2.80 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 2.39/2.80 thf(fact_4209_even__two__times__div__two,axiom,
% 2.39/2.80 ! [A: code_integer] :
% 2.39/2.80 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 2.39/2.80 = A ) ) ).
% 2.39/2.80
% 2.39/2.80 % even_two_times_div_two
% 2.39/2.80 thf(fact_4210_even__two__times__div__two,axiom,
% 2.39/2.80 ! [A: nat] :
% 2.39/2.80 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 2.39/2.80 = A ) ) ).
% 2.39/2.80
% 2.39/2.80 % even_two_times_div_two
% 2.39/2.80 thf(fact_4211_even__two__times__div__two,axiom,
% 2.39/2.80 ! [A: int] :
% 2.39/2.80 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 2.39/2.80 = A ) ) ).
% 2.39/2.80
% 2.39/2.80 % even_two_times_div_two
% 2.39/2.80 thf(fact_4212_even__two__times__div__two,axiom,
% 2.39/2.80 ! [A: code_natural] :
% 2.39/2.80 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) )
% 2.39/2.80 = A ) ) ).
% 2.39/2.80
% 2.39/2.80 % even_two_times_div_two
% 2.39/2.80 thf(fact_4213_Suc__times__mod__eq,axiom,
% 2.39/2.80 ! [M2: nat,N: nat] :
% 2.39/2.80 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M2 )
% 2.39/2.80 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M2 @ N ) ) @ M2 )
% 2.39/2.80 = one_one_nat ) ) ).
% 2.39/2.80
% 2.39/2.80 % Suc_times_mod_eq
% 2.39/2.80 thf(fact_4214_divmod__digit__0_I2_J,axiom,
% 2.39/2.80 ! [B: code_integer,A: code_integer] :
% 2.39/2.80 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 2.39/2.80 => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 2.39/2.80 => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) )
% 2.39/2.80 = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % divmod_digit_0(2)
% 2.39/2.80 thf(fact_4215_divmod__digit__0_I2_J,axiom,
% 2.39/2.80 ! [B: nat,A: nat] :
% 2.39/2.80 ( ( ord_less_nat @ zero_zero_nat @ B )
% 2.39/2.80 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 2.39/2.80 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) )
% 2.39/2.80 = ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % divmod_digit_0(2)
% 2.39/2.80 thf(fact_4216_divmod__digit__0_I2_J,axiom,
% 2.39/2.80 ! [B: int,A: int] :
% 2.39/2.80 ( ( ord_less_int @ zero_zero_int @ B )
% 2.39/2.80 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 2.39/2.80 => ( ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) )
% 2.39/2.80 = ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % divmod_digit_0(2)
% 2.39/2.80 thf(fact_4217_oddE,axiom,
% 2.39/2.80 ! [A: nat] :
% 2.39/2.80 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ~ ! [B5: nat] :
% 2.39/2.80 ( A
% 2.39/2.80 != ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B5 ) @ one_one_nat ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % oddE
% 2.39/2.80 thf(fact_4218_oddE,axiom,
% 2.39/2.80 ! [A: int] :
% 2.39/2.80 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 2.39/2.80 => ~ ! [B5: int] :
% 2.39/2.80 ( A
% 2.39/2.80 != ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B5 ) @ one_one_int ) ) ) ).
% 2.39/2.80
% 2.39/2.80 % oddE
% 2.39/2.80 thf(fact_4219_oddE,axiom,
% 2.39/2.80 ! [A: code_integer] :
% 2.39/2.80 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 2.39/2.81 => ~ ! [B5: code_integer] :
% 2.39/2.81 ( A
% 2.39/2.81 != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B5 ) @ one_one_Code_integer ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % oddE
% 2.39/2.81 thf(fact_4220_oddE,axiom,
% 2.39/2.81 ! [A: code_natural] :
% 2.39/2.81 ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 2.39/2.81 => ~ ! [B5: code_natural] :
% 2.39/2.81 ( A
% 2.39/2.81 != ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ B5 ) @ one_one_Code_natural ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % oddE
% 2.39/2.81 thf(fact_4221_minus__one__power__iff,axiom,
% 2.39/2.81 ! [N: nat] :
% 2.39/2.81 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 2.39/2.81 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 2.39/2.81 = one_one_int ) )
% 2.39/2.81 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 2.39/2.81 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 2.39/2.81 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % minus_one_power_iff
% 2.39/2.81 thf(fact_4222_minus__one__power__iff,axiom,
% 2.39/2.81 ! [N: nat] :
% 2.39/2.81 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 2.39/2.81 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 2.39/2.81 = one_one_rat ) )
% 2.39/2.81 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 2.39/2.81 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 2.39/2.81 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % minus_one_power_iff
% 2.39/2.81 thf(fact_4223_minus__one__power__iff,axiom,
% 2.39/2.81 ! [N: nat] :
% 2.39/2.81 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 2.39/2.81 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 2.39/2.81 = one_one_Code_integer ) )
% 2.39/2.81 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 2.39/2.81 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 2.39/2.81 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % minus_one_power_iff
% 2.39/2.81 thf(fact_4224_divmod__digit__0_I1_J,axiom,
% 2.39/2.81 ! [B: code_integer,A: code_integer] :
% 2.39/2.81 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 2.39/2.81 => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 2.39/2.81 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 2.39/2.81 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % divmod_digit_0(1)
% 2.39/2.81 thf(fact_4225_divmod__digit__0_I1_J,axiom,
% 2.39/2.81 ! [B: nat,A: nat] :
% 2.39/2.81 ( ( ord_less_nat @ zero_zero_nat @ B )
% 2.39/2.81 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 2.39/2.81 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 2.39/2.81 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % divmod_digit_0(1)
% 2.39/2.81 thf(fact_4226_divmod__digit__0_I1_J,axiom,
% 2.39/2.81 ! [B: int,A: int] :
% 2.39/2.81 ( ( ord_less_int @ zero_zero_int @ B )
% 2.39/2.81 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 2.39/2.81 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 2.39/2.81 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % divmod_digit_0(1)
% 2.39/2.81 thf(fact_4227_mult__exp__mod__exp__eq,axiom,
% 2.39/2.81 ! [M2: nat,N: nat,A: code_integer] :
% 2.39/2.81 ( ( ord_less_eq_nat @ M2 @ N )
% 2.39/2.81 => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 2.39/2.81 = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % mult_exp_mod_exp_eq
% 2.39/2.81 thf(fact_4228_mult__exp__mod__exp__eq,axiom,
% 2.39/2.81 ! [M2: nat,N: nat,A: nat] :
% 2.39/2.81 ( ( ord_less_eq_nat @ M2 @ N )
% 2.39/2.81 => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 2.39/2.81 = ( times_times_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % mult_exp_mod_exp_eq
% 2.39/2.81 thf(fact_4229_mult__exp__mod__exp__eq,axiom,
% 2.39/2.81 ! [M2: nat,N: nat,A: int] :
% 2.39/2.81 ( ( ord_less_eq_nat @ M2 @ N )
% 2.39/2.81 => ( ( modulo_modulo_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 2.39/2.81 = ( times_times_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % mult_exp_mod_exp_eq
% 2.39/2.81 thf(fact_4230_mult__exp__mod__exp__eq,axiom,
% 2.39/2.81 ! [M2: nat,N: nat,A: code_natural] :
% 2.39/2.81 ( ( ord_less_eq_nat @ M2 @ N )
% 2.39/2.81 => ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 2.39/2.81 = ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M2 ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % mult_exp_mod_exp_eq
% 2.39/2.81 thf(fact_4231_mod__double__modulus,axiom,
% 2.39/2.81 ! [M2: code_integer,X: code_integer] :
% 2.39/2.81 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ M2 )
% 2.39/2.81 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 2.39/2.81 => ( ( ( modulo364778990260209775nteger @ X @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) )
% 2.39/2.81 = ( modulo364778990260209775nteger @ X @ M2 ) )
% 2.39/2.81 | ( ( modulo364778990260209775nteger @ X @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) )
% 2.39/2.81 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ X @ M2 ) @ M2 ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % mod_double_modulus
% 2.39/2.81 thf(fact_4232_mod__double__modulus,axiom,
% 2.39/2.81 ! [M2: nat,X: nat] :
% 2.39/2.81 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 2.39/2.81 => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 2.39/2.81 => ( ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 2.39/2.81 = ( modulo_modulo_nat @ X @ M2 ) )
% 2.39/2.81 | ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 2.39/2.81 = ( plus_plus_nat @ ( modulo_modulo_nat @ X @ M2 ) @ M2 ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % mod_double_modulus
% 2.39/2.81 thf(fact_4233_mod__double__modulus,axiom,
% 2.39/2.81 ! [M2: int,X: int] :
% 2.39/2.81 ( ( ord_less_int @ zero_zero_int @ M2 )
% 2.39/2.81 => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 2.39/2.81 => ( ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) )
% 2.39/2.81 = ( modulo_modulo_int @ X @ M2 ) )
% 2.39/2.81 | ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) )
% 2.39/2.81 = ( plus_plus_int @ ( modulo_modulo_int @ X @ M2 ) @ M2 ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % mod_double_modulus
% 2.39/2.81 thf(fact_4234_divmod__digit__1_I2_J,axiom,
% 2.39/2.81 ! [A: code_integer,B: code_integer] :
% 2.39/2.81 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.81 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 2.39/2.81 => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 2.39/2.81 => ( ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 2.39/2.81 = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % divmod_digit_1(2)
% 2.39/2.81 thf(fact_4235_divmod__digit__1_I2_J,axiom,
% 2.39/2.81 ! [A: nat,B: nat] :
% 2.39/2.81 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 2.39/2.81 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 2.39/2.81 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 2.39/2.81 => ( ( minus_minus_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 2.39/2.81 = ( modulo_modulo_nat @ A @ B ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % divmod_digit_1(2)
% 2.39/2.81 thf(fact_4236_divmod__digit__1_I2_J,axiom,
% 2.39/2.81 ! [A: int,B: int] :
% 2.39/2.81 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 2.39/2.81 => ( ( ord_less_int @ zero_zero_int @ B )
% 2.39/2.81 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 2.39/2.81 => ( ( minus_minus_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 2.39/2.81 = ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % divmod_digit_1(2)
% 2.39/2.81 thf(fact_4237_even__mask__div__iff_H,axiom,
% 2.39/2.81 ! [M2: nat,N: nat] :
% 2.39/2.81 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 2.39/2.81 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 2.39/2.81
% 2.39/2.81 % even_mask_div_iff'
% 2.39/2.81 thf(fact_4238_even__mask__div__iff_H,axiom,
% 2.39/2.81 ! [M2: nat,N: nat] :
% 2.39/2.81 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 2.39/2.81 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 2.39/2.81
% 2.39/2.81 % even_mask_div_iff'
% 2.39/2.81 thf(fact_4239_even__mask__div__iff_H,axiom,
% 2.39/2.81 ! [M2: nat,N: nat] :
% 2.39/2.81 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 2.39/2.81 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 2.39/2.81
% 2.39/2.81 % even_mask_div_iff'
% 2.39/2.81 thf(fact_4240_even__mask__div__iff_H,axiom,
% 2.39/2.81 ! [M2: nat,N: nat] :
% 2.39/2.81 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ ( minus_7197305767214868737atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M2 ) @ one_one_Code_natural ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) ) )
% 2.39/2.81 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 2.39/2.81
% 2.39/2.81 % even_mask_div_iff'
% 2.39/2.81 thf(fact_4241_even__mask__div__iff,axiom,
% 2.39/2.81 ! [M2: nat,N: nat] :
% 2.39/2.81 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 2.39/2.81 = ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 2.39/2.81 = zero_z3403309356797280102nteger )
% 2.39/2.81 | ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % even_mask_div_iff
% 2.39/2.81 thf(fact_4242_even__mask__div__iff,axiom,
% 2.39/2.81 ! [M2: nat,N: nat] :
% 2.39/2.81 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 2.39/2.81 = ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 2.39/2.81 = zero_zero_nat )
% 2.39/2.81 | ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % even_mask_div_iff
% 2.39/2.81 thf(fact_4243_even__mask__div__iff,axiom,
% 2.39/2.81 ! [M2: nat,N: nat] :
% 2.39/2.81 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 2.39/2.81 = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 2.39/2.81 = zero_zero_int )
% 2.39/2.81 | ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % even_mask_div_iff
% 2.39/2.81 thf(fact_4244_even__mask__div__iff,axiom,
% 2.39/2.81 ! [M2: nat,N: nat] :
% 2.39/2.81 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ ( minus_7197305767214868737atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M2 ) @ one_one_Code_natural ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) ) )
% 2.39/2.81 = ( ( ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N )
% 2.39/2.81 = zero_z2226904508553997617atural )
% 2.39/2.81 | ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % even_mask_div_iff
% 2.39/2.81 thf(fact_4245_zle__add1__eq__le,axiom,
% 2.39/2.81 ! [W: int,Z: int] :
% 2.39/2.81 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 2.39/2.81 = ( ord_less_eq_int @ W @ Z ) ) ).
% 2.39/2.81
% 2.39/2.81 % zle_add1_eq_le
% 2.39/2.81 thf(fact_4246_verit__le__mono__div,axiom,
% 2.39/2.81 ! [A3: nat,B3: nat,N: nat] :
% 2.39/2.81 ( ( ord_less_nat @ A3 @ B3 )
% 2.39/2.81 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.39/2.81 => ( ord_less_eq_nat
% 2.39/2.81 @ ( plus_plus_nat @ ( divide_divide_nat @ A3 @ N )
% 2.39/2.81 @ ( if_nat
% 2.39/2.81 @ ( ( modulo_modulo_nat @ B3 @ N )
% 2.39/2.81 = zero_zero_nat )
% 2.39/2.81 @ one_one_nat
% 2.39/2.81 @ zero_zero_nat ) )
% 2.39/2.81 @ ( divide_divide_nat @ B3 @ N ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % verit_le_mono_div
% 2.39/2.81 thf(fact_4247_verit__le__mono__div__int,axiom,
% 2.39/2.81 ! [A3: int,B3: int,N: int] :
% 2.39/2.81 ( ( ord_less_int @ A3 @ B3 )
% 2.39/2.81 => ( ( ord_less_int @ zero_zero_int @ N )
% 2.39/2.81 => ( ord_less_eq_int
% 2.39/2.81 @ ( plus_plus_int @ ( divide_divide_int @ A3 @ N )
% 2.39/2.81 @ ( if_int
% 2.39/2.81 @ ( ( modulo_modulo_int @ B3 @ N )
% 2.39/2.81 = zero_zero_int )
% 2.39/2.81 @ one_one_int
% 2.39/2.81 @ zero_zero_int ) )
% 2.39/2.81 @ ( divide_divide_int @ B3 @ N ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % verit_le_mono_div_int
% 2.39/2.81 thf(fact_4248_zle__diff1__eq,axiom,
% 2.39/2.81 ! [W: int,Z: int] :
% 2.39/2.81 ( ( ord_less_eq_int @ W @ ( minus_minus_int @ Z @ one_one_int ) )
% 2.39/2.81 = ( ord_less_int @ W @ Z ) ) ).
% 2.39/2.81
% 2.39/2.81 % zle_diff1_eq
% 2.39/2.81 thf(fact_4249_one__div__minus__numeral,axiom,
% 2.39/2.81 ! [N: num] :
% 2.39/2.81 ( ( divide_divide_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 2.39/2.81 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % one_div_minus_numeral
% 2.39/2.81 thf(fact_4250_minus__one__div__numeral,axiom,
% 2.39/2.81 ! [N: num] :
% 2.39/2.81 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 2.39/2.81 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % minus_one_div_numeral
% 2.39/2.81 thf(fact_4251_one__mod__minus__numeral,axiom,
% 2.39/2.81 ! [N: num] :
% 2.39/2.81 ( ( modulo_modulo_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 2.39/2.81 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % one_mod_minus_numeral
% 2.39/2.81 thf(fact_4252_minus__one__mod__numeral,axiom,
% 2.39/2.81 ! [N: num] :
% 2.39/2.81 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 2.39/2.81 = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % minus_one_mod_numeral
% 2.39/2.81 thf(fact_4253_int__less__induct,axiom,
% 2.39/2.81 ! [I2: int,K: int,P2: int > $o] :
% 2.39/2.81 ( ( ord_less_int @ I2 @ K )
% 2.39/2.81 => ( ( P2 @ ( minus_minus_int @ K @ one_one_int ) )
% 2.39/2.81 => ( ! [I3: int] :
% 2.39/2.81 ( ( ord_less_int @ I3 @ K )
% 2.39/2.81 => ( ( P2 @ I3 )
% 2.39/2.81 => ( P2 @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 2.39/2.81 => ( P2 @ I2 ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % int_less_induct
% 2.39/2.81 thf(fact_4254_int__le__induct,axiom,
% 2.39/2.81 ! [I2: int,K: int,P2: int > $o] :
% 2.39/2.81 ( ( ord_less_eq_int @ I2 @ K )
% 2.39/2.81 => ( ( P2 @ K )
% 2.39/2.81 => ( ! [I3: int] :
% 2.39/2.81 ( ( ord_less_eq_int @ I3 @ K )
% 2.39/2.81 => ( ( P2 @ I3 )
% 2.39/2.81 => ( P2 @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 2.39/2.81 => ( P2 @ I2 ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % int_le_induct
% 2.39/2.81 thf(fact_4255_zless__add1__eq,axiom,
% 2.39/2.81 ! [W: int,Z: int] :
% 2.39/2.81 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 2.39/2.81 = ( ( ord_less_int @ W @ Z )
% 2.39/2.81 | ( W = Z ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % zless_add1_eq
% 2.39/2.81 thf(fact_4256_int__gr__induct,axiom,
% 2.39/2.81 ! [K: int,I2: int,P2: int > $o] :
% 2.39/2.81 ( ( ord_less_int @ K @ I2 )
% 2.39/2.81 => ( ( P2 @ ( plus_plus_int @ K @ one_one_int ) )
% 2.39/2.81 => ( ! [I3: int] :
% 2.39/2.81 ( ( ord_less_int @ K @ I3 )
% 2.39/2.81 => ( ( P2 @ I3 )
% 2.39/2.81 => ( P2 @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 2.39/2.81 => ( P2 @ I2 ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % int_gr_induct
% 2.39/2.81 thf(fact_4257_int__one__le__iff__zero__less,axiom,
% 2.39/2.81 ! [Z: int] :
% 2.39/2.81 ( ( ord_less_eq_int @ one_one_int @ Z )
% 2.39/2.81 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 2.39/2.81
% 2.39/2.81 % int_one_le_iff_zero_less
% 2.39/2.81 thf(fact_4258_pos__zmult__eq__1__iff,axiom,
% 2.39/2.81 ! [M2: int,N: int] :
% 2.39/2.81 ( ( ord_less_int @ zero_zero_int @ M2 )
% 2.39/2.81 => ( ( ( times_times_int @ M2 @ N )
% 2.39/2.81 = one_one_int )
% 2.39/2.81 = ( ( M2 = one_one_int )
% 2.39/2.81 & ( N = one_one_int ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % pos_zmult_eq_1_iff
% 2.39/2.81 thf(fact_4259_zsgn__def,axiom,
% 2.39/2.81 ( sgn_sgn_int
% 2.39/2.81 = ( ^ [I4: int] : ( if_int @ ( I4 = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ I4 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % zsgn_def
% 2.39/2.81 thf(fact_4260_odd__nonzero,axiom,
% 2.39/2.81 ! [Z: int] :
% 2.39/2.81 ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z )
% 2.39/2.81 != zero_zero_int ) ).
% 2.39/2.81
% 2.39/2.81 % odd_nonzero
% 2.39/2.81 thf(fact_4261_odd__less__0__iff,axiom,
% 2.39/2.81 ! [Z: int] :
% 2.39/2.81 ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
% 2.39/2.81 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 2.39/2.81
% 2.39/2.81 % odd_less_0_iff
% 2.39/2.81 thf(fact_4262_int__ge__induct,axiom,
% 2.39/2.81 ! [K: int,I2: int,P2: int > $o] :
% 2.39/2.81 ( ( ord_less_eq_int @ K @ I2 )
% 2.39/2.81 => ( ( P2 @ K )
% 2.39/2.81 => ( ! [I3: int] :
% 2.39/2.81 ( ( ord_less_eq_int @ K @ I3 )
% 2.39/2.81 => ( ( P2 @ I3 )
% 2.39/2.81 => ( P2 @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 2.39/2.81 => ( P2 @ I2 ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % int_ge_induct
% 2.39/2.81 thf(fact_4263_add1__zle__eq,axiom,
% 2.39/2.81 ! [W: int,Z: int] :
% 2.39/2.81 ( ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z )
% 2.39/2.81 = ( ord_less_int @ W @ Z ) ) ).
% 2.39/2.81
% 2.39/2.81 % add1_zle_eq
% 2.39/2.81 thf(fact_4264_zless__imp__add1__zle,axiom,
% 2.39/2.81 ! [W: int,Z: int] :
% 2.39/2.81 ( ( ord_less_int @ W @ Z )
% 2.39/2.81 => ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ) ).
% 2.39/2.81
% 2.39/2.81 % zless_imp_add1_zle
% 2.39/2.81 thf(fact_4265_int__induct,axiom,
% 2.39/2.81 ! [P2: int > $o,K: int,I2: int] :
% 2.39/2.81 ( ( P2 @ K )
% 2.39/2.81 => ( ! [I3: int] :
% 2.39/2.81 ( ( ord_less_eq_int @ K @ I3 )
% 2.39/2.81 => ( ( P2 @ I3 )
% 2.39/2.81 => ( P2 @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 2.39/2.81 => ( ! [I3: int] :
% 2.39/2.81 ( ( ord_less_eq_int @ I3 @ K )
% 2.39/2.81 => ( ( P2 @ I3 )
% 2.39/2.81 => ( P2 @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 2.39/2.81 => ( P2 @ I2 ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % int_induct
% 2.39/2.81 thf(fact_4266_pos__zmult__eq__1__iff__lemma,axiom,
% 2.39/2.81 ! [M2: int,N: int] :
% 2.39/2.81 ( ( ( times_times_int @ M2 @ N )
% 2.39/2.81 = one_one_int )
% 2.39/2.81 => ( ( M2 = one_one_int )
% 2.39/2.81 | ( M2
% 2.39/2.81 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % pos_zmult_eq_1_iff_lemma
% 2.39/2.81 thf(fact_4267_zmult__eq__1__iff,axiom,
% 2.39/2.81 ! [M2: int,N: int] :
% 2.39/2.81 ( ( ( times_times_int @ M2 @ N )
% 2.39/2.81 = one_one_int )
% 2.39/2.81 = ( ( ( M2 = one_one_int )
% 2.39/2.81 & ( N = one_one_int ) )
% 2.39/2.81 | ( ( M2
% 2.39/2.81 = ( uminus_uminus_int @ one_one_int ) )
% 2.39/2.81 & ( N
% 2.39/2.81 = ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % zmult_eq_1_iff
% 2.39/2.81 thf(fact_4268_le__imp__0__less,axiom,
% 2.39/2.81 ! [Z: int] :
% 2.39/2.81 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 2.39/2.81 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % le_imp_0_less
% 2.39/2.81 thf(fact_4269_flip__bit__Suc,axiom,
% 2.39/2.81 ! [N: nat,A: code_integer] :
% 2.39/2.81 ( ( bit_se1345352211410354436nteger @ ( suc @ N ) @ A )
% 2.39/2.81 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % flip_bit_Suc
% 2.39/2.81 thf(fact_4270_flip__bit__Suc,axiom,
% 2.39/2.81 ! [N: nat,A: code_natural] :
% 2.39/2.81 ( ( bit_se168947363167071951atural @ ( suc @ N ) @ A )
% 2.39/2.81 = ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se168947363167071951atural @ N @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % flip_bit_Suc
% 2.39/2.81 thf(fact_4271_flip__bit__Suc,axiom,
% 2.39/2.81 ! [N: nat,A: nat] :
% 2.39/2.81 ( ( bit_se2161824704523386999it_nat @ ( suc @ N ) @ A )
% 2.39/2.81 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % flip_bit_Suc
% 2.39/2.81 thf(fact_4272_flip__bit__Suc,axiom,
% 2.39/2.81 ! [N: nat,A: int] :
% 2.39/2.81 ( ( bit_se2159334234014336723it_int @ ( suc @ N ) @ A )
% 2.39/2.81 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % flip_bit_Suc
% 2.39/2.81 thf(fact_4273_signed__take__bit__rec,axiom,
% 2.39/2.81 ( bit_ri6519982836138164636nteger
% 2.39/2.81 = ( ^ [N3: nat,A2: code_integer] : ( if_Code_integer @ ( N3 = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ ( minus_minus_nat @ N3 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % signed_take_bit_rec
% 2.39/2.81 thf(fact_4274_signed__take__bit__rec,axiom,
% 2.39/2.81 ( bit_ri631733984087533419it_int
% 2.39/2.81 = ( ^ [N3: nat,A2: int] : ( if_int @ ( N3 = zero_zero_nat ) @ ( uminus_uminus_int @ ( modulo_modulo_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( plus_plus_int @ ( modulo_modulo_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ ( minus_minus_nat @ N3 @ one_one_nat ) @ ( divide_divide_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % signed_take_bit_rec
% 2.39/2.81 thf(fact_4275_neg__eucl__rel__int__mult__2,axiom,
% 2.39/2.81 ! [B: int,A: int,Q4: int,R2: int] :
% 2.39/2.81 ( ( ord_less_eq_int @ B @ zero_zero_int )
% 2.39/2.81 => ( ( eucl_rel_int @ ( plus_plus_int @ A @ one_one_int ) @ B @ ( product_Pair_int_int @ Q4 @ R2 ) )
% 2.39/2.81 => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q4 @ ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R2 ) @ one_one_int ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % neg_eucl_rel_int_mult_2
% 2.39/2.81 thf(fact_4276_pos__eucl__rel__int__mult__2,axiom,
% 2.39/2.81 ! [B: int,A: int,Q4: int,R2: int] :
% 2.39/2.81 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 2.39/2.81 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q4 @ R2 ) )
% 2.39/2.81 => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q4 @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R2 ) ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % pos_eucl_rel_int_mult_2
% 2.39/2.81 thf(fact_4277_signed__take__bit__Suc,axiom,
% 2.39/2.81 ! [N: nat,A: code_integer] :
% 2.39/2.81 ( ( bit_ri6519982836138164636nteger @ ( suc @ N ) @ A )
% 2.39/2.81 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % signed_take_bit_Suc
% 2.39/2.81 thf(fact_4278_signed__take__bit__Suc,axiom,
% 2.39/2.81 ! [N: nat,A: int] :
% 2.39/2.81 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ A )
% 2.39/2.81 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % signed_take_bit_Suc
% 2.39/2.81 thf(fact_4279_signed__take__bit__of__minus__1,axiom,
% 2.39/2.81 ! [N: nat] :
% 2.39/2.81 ( ( bit_ri6519982836138164636nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 2.39/2.81 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 2.39/2.81
% 2.39/2.81 % signed_take_bit_of_minus_1
% 2.39/2.81 thf(fact_4280_signed__take__bit__of__minus__1,axiom,
% 2.39/2.81 ! [N: nat] :
% 2.39/2.81 ( ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 2.39/2.81 = ( uminus_uminus_int @ one_one_int ) ) ).
% 2.39/2.81
% 2.39/2.81 % signed_take_bit_of_minus_1
% 2.39/2.81 thf(fact_4281_signed__take__bit__Suc__1,axiom,
% 2.39/2.81 ! [N: nat] :
% 2.39/2.81 ( ( bit_ri6519982836138164636nteger @ ( suc @ N ) @ one_one_Code_integer )
% 2.39/2.81 = one_one_Code_integer ) ).
% 2.39/2.81
% 2.39/2.81 % signed_take_bit_Suc_1
% 2.39/2.81 thf(fact_4282_signed__take__bit__Suc__1,axiom,
% 2.39/2.81 ! [N: nat] :
% 2.39/2.81 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ one_one_int )
% 2.39/2.81 = one_one_int ) ).
% 2.39/2.81
% 2.39/2.81 % signed_take_bit_Suc_1
% 2.39/2.81 thf(fact_4283_signed__take__bit__numeral__of__1,axiom,
% 2.39/2.81 ! [K: num] :
% 2.39/2.81 ( ( bit_ri6519982836138164636nteger @ ( numeral_numeral_nat @ K ) @ one_one_Code_integer )
% 2.39/2.81 = one_one_Code_integer ) ).
% 2.39/2.81
% 2.39/2.81 % signed_take_bit_numeral_of_1
% 2.39/2.81 thf(fact_4284_signed__take__bit__numeral__of__1,axiom,
% 2.39/2.81 ! [K: num] :
% 2.39/2.81 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ K ) @ one_one_int )
% 2.39/2.81 = one_one_int ) ).
% 2.39/2.81
% 2.39/2.81 % signed_take_bit_numeral_of_1
% 2.39/2.81 thf(fact_4285_zminus1__lemma,axiom,
% 2.39/2.81 ! [A: int,B: int,Q4: int,R2: int] :
% 2.39/2.81 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q4 @ R2 ) )
% 2.39/2.81 => ( ( B != zero_zero_int )
% 2.39/2.81 => ( eucl_rel_int @ ( uminus_uminus_int @ A ) @ B @ ( product_Pair_int_int @ ( if_int @ ( R2 = zero_zero_int ) @ ( uminus_uminus_int @ Q4 ) @ ( minus_minus_int @ ( uminus_uminus_int @ Q4 ) @ one_one_int ) ) @ ( if_int @ ( R2 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ B @ R2 ) ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % zminus1_lemma
% 2.39/2.81 thf(fact_4286_signed__take__bit__Suc__minus__bit1,axiom,
% 2.39/2.81 ! [N: nat,K: num] :
% 2.39/2.81 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 2.39/2.81 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 2.39/2.81
% 2.39/2.81 % signed_take_bit_Suc_minus_bit1
% 2.39/2.81 thf(fact_4287_divmod__BitM__2__eq,axiom,
% 2.39/2.81 ! [M2: num] :
% 2.39/2.81 ( ( unique5052692396658037445od_int @ ( bitM @ M2 ) @ ( bit0 @ one ) )
% 2.39/2.81 = ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ one_one_int ) @ one_one_int ) ) ).
% 2.39/2.81
% 2.39/2.81 % divmod_BitM_2_eq
% 2.39/2.81 thf(fact_4288_flip__bit__0,axiom,
% 2.39/2.81 ! [A: code_integer] :
% 2.39/2.81 ( ( bit_se1345352211410354436nteger @ zero_zero_nat @ A )
% 2.39/2.81 = ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % flip_bit_0
% 2.39/2.81 thf(fact_4289_flip__bit__0,axiom,
% 2.39/2.81 ! [A: code_natural] :
% 2.39/2.81 ( ( bit_se168947363167071951atural @ zero_zero_nat @ A )
% 2.39/2.81 = ( plus_p4538020629002901425atural @ ( zero_n8403883297036319079atural @ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % flip_bit_0
% 2.39/2.81 thf(fact_4290_flip__bit__0,axiom,
% 2.39/2.81 ! [A: nat] :
% 2.39/2.81 ( ( bit_se2161824704523386999it_nat @ zero_zero_nat @ A )
% 2.39/2.81 = ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % flip_bit_0
% 2.39/2.81 thf(fact_4291_flip__bit__0,axiom,
% 2.39/2.81 ! [A: int] :
% 2.39/2.81 ( ( bit_se2159334234014336723it_int @ zero_zero_nat @ A )
% 2.39/2.81 = ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % flip_bit_0
% 2.39/2.81 thf(fact_4292_take__bit__rec,axiom,
% 2.39/2.81 ( bit_se1745604003318907178nteger
% 2.39/2.81 = ( ^ [N3: nat,A2: code_integer] : ( if_Code_integer @ ( N3 = zero_zero_nat ) @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ ( minus_minus_nat @ N3 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_rec
% 2.39/2.81 thf(fact_4293_take__bit__rec,axiom,
% 2.39/2.81 ( bit_se2925701944663578781it_nat
% 2.39/2.81 = ( ^ [N3: nat,A2: nat] : ( if_nat @ ( N3 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( minus_minus_nat @ N3 @ one_one_nat ) @ ( divide_divide_nat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_rec
% 2.39/2.81 thf(fact_4294_take__bit__rec,axiom,
% 2.39/2.81 ( bit_se569199155075624693atural
% 2.39/2.81 = ( ^ [N3: nat,A2: code_natural] : ( if_Code_natural @ ( N3 = zero_zero_nat ) @ zero_z2226904508553997617atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( bit_se569199155075624693atural @ ( minus_minus_nat @ N3 @ one_one_nat ) @ ( divide5121882707175180666atural @ A2 @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( modulo8411746178871703098atural @ A2 @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_rec
% 2.39/2.81 thf(fact_4295_take__bit__rec,axiom,
% 2.39/2.81 ( bit_se2923211474154528505it_int
% 2.39/2.81 = ( ^ [N3: nat,A2: int] : ( if_int @ ( N3 = zero_zero_nat ) @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ N3 @ one_one_nat ) @ ( divide_divide_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_rec
% 2.39/2.81 thf(fact_4296_and__int__unfold,axiom,
% 2.39/2.81 ( bit_se725231765392027082nd_int
% 2.39/2.81 = ( ^ [K4: int,L3: int] :
% 2.39/2.81 ( if_int
% 2.39/2.81 @ ( ( K4 = zero_zero_int )
% 2.39/2.81 | ( L3 = zero_zero_int ) )
% 2.39/2.81 @ zero_zero_int
% 2.39/2.81 @ ( if_int
% 2.39/2.81 @ ( K4
% 2.39/2.81 = ( uminus_uminus_int @ one_one_int ) )
% 2.39/2.81 @ L3
% 2.39/2.81 @ ( if_int
% 2.39/2.81 @ ( L3
% 2.39/2.81 = ( uminus_uminus_int @ one_one_int ) )
% 2.39/2.81 @ K4
% 2.39/2.81 @ ( plus_plus_int @ ( times_times_int @ ( modulo_modulo_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % and_int_unfold
% 2.39/2.81 thf(fact_4297_one__mod__2__pow__eq,axiom,
% 2.39/2.81 ! [N: nat] :
% 2.39/2.81 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 2.39/2.81 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % one_mod_2_pow_eq
% 2.39/2.81 thf(fact_4298_one__mod__2__pow__eq,axiom,
% 2.39/2.81 ! [N: nat] :
% 2.39/2.81 ( ( modulo_modulo_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 2.39/2.81 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % one_mod_2_pow_eq
% 2.39/2.81 thf(fact_4299_one__mod__2__pow__eq,axiom,
% 2.39/2.81 ! [N: nat] :
% 2.39/2.81 ( ( modulo8411746178871703098atural @ one_one_Code_natural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 2.39/2.81 = ( zero_n8403883297036319079atural @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % one_mod_2_pow_eq
% 2.39/2.81 thf(fact_4300_one__mod__2__pow__eq,axiom,
% 2.39/2.81 ! [N: nat] :
% 2.39/2.81 ( ( modulo_modulo_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 2.39/2.81 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % one_mod_2_pow_eq
% 2.39/2.81 thf(fact_4301_upto__aux__rec,axiom,
% 2.39/2.81 ( upto_aux
% 2.39/2.81 = ( ^ [I4: int,J2: int,Js: list_int] : ( if_list_int @ ( ord_less_int @ J2 @ I4 ) @ Js @ ( upto_aux @ I4 @ ( minus_minus_int @ J2 @ one_one_int ) @ ( cons_int @ J2 @ Js ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % upto_aux_rec
% 2.39/2.81 thf(fact_4302_push__bit__numeral__minus__1,axiom,
% 2.39/2.81 ! [N: num] :
% 2.39/2.81 ( ( bit_se7788150548672797655nteger @ ( numeral_numeral_nat @ N ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 2.39/2.81 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ N ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % push_bit_numeral_minus_1
% 2.39/2.81 thf(fact_4303_push__bit__numeral__minus__1,axiom,
% 2.39/2.81 ! [N: num] :
% 2.39/2.81 ( ( bit_se545348938243370406it_int @ ( numeral_numeral_nat @ N ) @ ( uminus_uminus_int @ one_one_int ) )
% 2.39/2.81 = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ N ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % push_bit_numeral_minus_1
% 2.39/2.81 thf(fact_4304_of__bool__eq_I2_J,axiom,
% 2.39/2.81 ( ( zero_n356916108424825756nteger @ $true )
% 2.39/2.81 = one_one_Code_integer ) ).
% 2.39/2.81
% 2.39/2.81 % of_bool_eq(2)
% 2.39/2.81 thf(fact_4305_of__bool__eq_I2_J,axiom,
% 2.39/2.81 ( ( zero_n2052037380579107095ol_rat @ $true )
% 2.39/2.81 = one_one_rat ) ).
% 2.39/2.81
% 2.39/2.81 % of_bool_eq(2)
% 2.39/2.81 thf(fact_4306_of__bool__eq_I2_J,axiom,
% 2.39/2.81 ( ( zero_n2687167440665602831ol_nat @ $true )
% 2.39/2.81 = one_one_nat ) ).
% 2.39/2.81
% 2.39/2.81 % of_bool_eq(2)
% 2.39/2.81 thf(fact_4307_of__bool__eq_I2_J,axiom,
% 2.39/2.81 ( ( zero_n2684676970156552555ol_int @ $true )
% 2.39/2.81 = one_one_int ) ).
% 2.39/2.81
% 2.39/2.81 % of_bool_eq(2)
% 2.39/2.81 thf(fact_4308_of__bool__eq__1__iff,axiom,
% 2.39/2.81 ! [P2: $o] :
% 2.39/2.81 ( ( ( zero_n356916108424825756nteger @ P2 )
% 2.39/2.81 = one_one_Code_integer )
% 2.39/2.81 = P2 ) ).
% 2.39/2.81
% 2.39/2.81 % of_bool_eq_1_iff
% 2.39/2.81 thf(fact_4309_of__bool__eq__1__iff,axiom,
% 2.39/2.81 ! [P2: $o] :
% 2.39/2.81 ( ( ( zero_n2052037380579107095ol_rat @ P2 )
% 2.39/2.81 = one_one_rat )
% 2.39/2.81 = P2 ) ).
% 2.39/2.81
% 2.39/2.81 % of_bool_eq_1_iff
% 2.39/2.81 thf(fact_4310_of__bool__eq__1__iff,axiom,
% 2.39/2.81 ! [P2: $o] :
% 2.39/2.81 ( ( ( zero_n2687167440665602831ol_nat @ P2 )
% 2.39/2.81 = one_one_nat )
% 2.39/2.81 = P2 ) ).
% 2.39/2.81
% 2.39/2.81 % of_bool_eq_1_iff
% 2.39/2.81 thf(fact_4311_of__bool__eq__1__iff,axiom,
% 2.39/2.81 ! [P2: $o] :
% 2.39/2.81 ( ( ( zero_n2684676970156552555ol_int @ P2 )
% 2.39/2.81 = one_one_int )
% 2.39/2.81 = P2 ) ).
% 2.39/2.81
% 2.39/2.81 % of_bool_eq_1_iff
% 2.39/2.81 thf(fact_4312_take__bit__Suc__1,axiom,
% 2.39/2.81 ! [N: nat] :
% 2.39/2.81 ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ one_one_Code_integer )
% 2.39/2.81 = one_one_Code_integer ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_Suc_1
% 2.39/2.81 thf(fact_4313_take__bit__Suc__1,axiom,
% 2.39/2.81 ! [N: nat] :
% 2.39/2.81 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ one_one_nat )
% 2.39/2.81 = one_one_nat ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_Suc_1
% 2.39/2.81 thf(fact_4314_take__bit__Suc__1,axiom,
% 2.39/2.81 ! [N: nat] :
% 2.39/2.81 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ one_one_int )
% 2.39/2.81 = one_one_int ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_Suc_1
% 2.39/2.81 thf(fact_4315_of__bool__less__one__iff,axiom,
% 2.39/2.81 ! [P2: $o] :
% 2.39/2.81 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P2 ) @ one_one_Code_integer )
% 2.39/2.81 = ~ P2 ) ).
% 2.39/2.81
% 2.39/2.81 % of_bool_less_one_iff
% 2.39/2.81 thf(fact_4316_of__bool__less__one__iff,axiom,
% 2.39/2.81 ! [P2: $o] :
% 2.39/2.81 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P2 ) @ one_one_rat )
% 2.39/2.81 = ~ P2 ) ).
% 2.39/2.81
% 2.39/2.81 % of_bool_less_one_iff
% 2.39/2.81 thf(fact_4317_of__bool__less__one__iff,axiom,
% 2.39/2.81 ! [P2: $o] :
% 2.39/2.81 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P2 ) @ one_one_nat )
% 2.39/2.81 = ~ P2 ) ).
% 2.39/2.81
% 2.39/2.81 % of_bool_less_one_iff
% 2.39/2.81 thf(fact_4318_of__bool__less__one__iff,axiom,
% 2.39/2.81 ! [P2: $o] :
% 2.39/2.81 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P2 ) @ one_one_int )
% 2.39/2.81 = ~ P2 ) ).
% 2.39/2.81
% 2.39/2.81 % of_bool_less_one_iff
% 2.39/2.81 thf(fact_4319_and_Oleft__neutral,axiom,
% 2.39/2.81 ! [A: code_integer] :
% 2.39/2.81 ( ( bit_se3949692690581998587nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ A )
% 2.39/2.81 = A ) ).
% 2.39/2.81
% 2.39/2.81 % and.left_neutral
% 2.39/2.81 thf(fact_4320_and_Oleft__neutral,axiom,
% 2.39/2.81 ! [A: int] :
% 2.39/2.81 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ one_one_int ) @ A )
% 2.39/2.81 = A ) ).
% 2.39/2.81
% 2.39/2.81 % and.left_neutral
% 2.39/2.81 thf(fact_4321_and_Oright__neutral,axiom,
% 2.39/2.81 ! [A: code_integer] :
% 2.39/2.81 ( ( bit_se3949692690581998587nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 2.39/2.81 = A ) ).
% 2.39/2.81
% 2.39/2.81 % and.right_neutral
% 2.39/2.81 thf(fact_4322_and_Oright__neutral,axiom,
% 2.39/2.81 ! [A: int] :
% 2.39/2.81 ( ( bit_se725231765392027082nd_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 2.39/2.81 = A ) ).
% 2.39/2.81
% 2.39/2.81 % and.right_neutral
% 2.39/2.81 thf(fact_4323_bit_Oconj__one__right,axiom,
% 2.39/2.81 ! [X: code_integer] :
% 2.39/2.81 ( ( bit_se3949692690581998587nteger @ X @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 2.39/2.81 = X ) ).
% 2.39/2.81
% 2.39/2.81 % bit.conj_one_right
% 2.39/2.81 thf(fact_4324_bit_Oconj__one__right,axiom,
% 2.39/2.81 ! [X: int] :
% 2.39/2.81 ( ( bit_se725231765392027082nd_int @ X @ ( uminus_uminus_int @ one_one_int ) )
% 2.39/2.81 = X ) ).
% 2.39/2.81
% 2.39/2.81 % bit.conj_one_right
% 2.39/2.81 thf(fact_4325_of__bool__not__iff,axiom,
% 2.39/2.81 ! [P2: $o] :
% 2.39/2.81 ( ( zero_n2052037380579107095ol_rat @ ~ P2 )
% 2.39/2.81 = ( minus_minus_rat @ one_one_rat @ ( zero_n2052037380579107095ol_rat @ P2 ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % of_bool_not_iff
% 2.39/2.81 thf(fact_4326_of__bool__not__iff,axiom,
% 2.39/2.81 ! [P2: $o] :
% 2.39/2.81 ( ( zero_n356916108424825756nteger @ ~ P2 )
% 2.39/2.81 = ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( zero_n356916108424825756nteger @ P2 ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % of_bool_not_iff
% 2.39/2.81 thf(fact_4327_of__bool__not__iff,axiom,
% 2.39/2.81 ! [P2: $o] :
% 2.39/2.81 ( ( zero_n2684676970156552555ol_int @ ~ P2 )
% 2.39/2.81 = ( minus_minus_int @ one_one_int @ ( zero_n2684676970156552555ol_int @ P2 ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % of_bool_not_iff
% 2.39/2.81 thf(fact_4328_take__bit__numeral__1,axiom,
% 2.39/2.81 ! [L: num] :
% 2.39/2.81 ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ L ) @ one_one_Code_integer )
% 2.39/2.81 = one_one_Code_integer ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_numeral_1
% 2.39/2.81 thf(fact_4329_take__bit__numeral__1,axiom,
% 2.39/2.81 ! [L: num] :
% 2.39/2.81 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ one_one_nat )
% 2.39/2.81 = one_one_nat ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_numeral_1
% 2.39/2.81 thf(fact_4330_take__bit__numeral__1,axiom,
% 2.39/2.81 ! [L: num] :
% 2.39/2.81 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ one_one_int )
% 2.39/2.81 = one_one_int ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_numeral_1
% 2.39/2.81 thf(fact_4331_take__bit__of__1__eq__0__iff,axiom,
% 2.39/2.81 ! [N: nat] :
% 2.39/2.81 ( ( ( bit_se2925701944663578781it_nat @ N @ one_one_nat )
% 2.39/2.81 = zero_zero_nat )
% 2.39/2.81 = ( N = zero_zero_nat ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_of_1_eq_0_iff
% 2.39/2.81 thf(fact_4332_take__bit__of__1__eq__0__iff,axiom,
% 2.39/2.81 ! [N: nat] :
% 2.39/2.81 ( ( ( bit_se1745604003318907178nteger @ N @ one_one_Code_integer )
% 2.39/2.81 = zero_z3403309356797280102nteger )
% 2.39/2.81 = ( N = zero_zero_nat ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_of_1_eq_0_iff
% 2.39/2.81 thf(fact_4333_take__bit__of__1__eq__0__iff,axiom,
% 2.39/2.81 ! [N: nat] :
% 2.39/2.81 ( ( ( bit_se569199155075624693atural @ N @ one_one_Code_natural )
% 2.39/2.81 = zero_z2226904508553997617atural )
% 2.39/2.81 = ( N = zero_zero_nat ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_of_1_eq_0_iff
% 2.39/2.81 thf(fact_4334_take__bit__of__1__eq__0__iff,axiom,
% 2.39/2.81 ! [N: nat] :
% 2.39/2.81 ( ( ( bit_se2923211474154528505it_int @ N @ one_one_int )
% 2.39/2.81 = zero_zero_int )
% 2.39/2.81 = ( N = zero_zero_nat ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_of_1_eq_0_iff
% 2.39/2.81 thf(fact_4335_and__numerals_I8_J,axiom,
% 2.39/2.81 ! [X: num] :
% 2.39/2.81 ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ one_one_Code_integer )
% 2.39/2.81 = one_one_Code_integer ) ).
% 2.39/2.81
% 2.39/2.81 % and_numerals(8)
% 2.39/2.81 thf(fact_4336_and__numerals_I8_J,axiom,
% 2.39/2.81 ! [X: num] :
% 2.39/2.81 ( ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ ( bit1 @ X ) ) @ one_one_Code_natural )
% 2.39/2.81 = one_one_Code_natural ) ).
% 2.39/2.81
% 2.39/2.81 % and_numerals(8)
% 2.39/2.81 thf(fact_4337_and__numerals_I8_J,axiom,
% 2.39/2.81 ! [X: num] :
% 2.39/2.81 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ one_one_int )
% 2.39/2.81 = one_one_int ) ).
% 2.39/2.81
% 2.39/2.81 % and_numerals(8)
% 2.39/2.81 thf(fact_4338_and__numerals_I8_J,axiom,
% 2.39/2.81 ! [X: num] :
% 2.39/2.81 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ one_one_nat )
% 2.39/2.81 = one_one_nat ) ).
% 2.39/2.81
% 2.39/2.81 % and_numerals(8)
% 2.39/2.81 thf(fact_4339_and__numerals_I2_J,axiom,
% 2.39/2.81 ! [Y: num] :
% 2.39/2.81 ( ( bit_se3949692690581998587nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 2.39/2.81 = one_one_Code_integer ) ).
% 2.39/2.81
% 2.39/2.81 % and_numerals(2)
% 2.39/2.81 thf(fact_4340_and__numerals_I2_J,axiom,
% 2.39/2.81 ! [Y: num] :
% 2.39/2.81 ( ( bit_se2773287842338716102atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit1 @ Y ) ) )
% 2.39/2.81 = one_one_Code_natural ) ).
% 2.39/2.81
% 2.39/2.81 % and_numerals(2)
% 2.39/2.81 thf(fact_4341_and__numerals_I2_J,axiom,
% 2.39/2.81 ! [Y: num] :
% 2.39/2.81 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 2.39/2.81 = one_one_int ) ).
% 2.39/2.81
% 2.39/2.81 % and_numerals(2)
% 2.39/2.81 thf(fact_4342_and__numerals_I2_J,axiom,
% 2.39/2.81 ! [Y: num] :
% 2.39/2.81 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 2.39/2.81 = one_one_nat ) ).
% 2.39/2.81
% 2.39/2.81 % and_numerals(2)
% 2.39/2.81 thf(fact_4343_sgn__mult__self__eq,axiom,
% 2.39/2.81 ! [A: rat] :
% 2.39/2.81 ( ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( sgn_sgn_rat @ A ) )
% 2.39/2.81 = ( zero_n2052037380579107095ol_rat @ ( A != zero_zero_rat ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % sgn_mult_self_eq
% 2.39/2.81 thf(fact_4344_sgn__mult__self__eq,axiom,
% 2.39/2.81 ! [A: code_integer] :
% 2.39/2.81 ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ A ) )
% 2.39/2.81 = ( zero_n356916108424825756nteger @ ( A != zero_z3403309356797280102nteger ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % sgn_mult_self_eq
% 2.39/2.81 thf(fact_4345_sgn__mult__self__eq,axiom,
% 2.39/2.81 ! [A: int] :
% 2.39/2.81 ( ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ A ) )
% 2.39/2.81 = ( zero_n2684676970156552555ol_int @ ( A != zero_zero_int ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % sgn_mult_self_eq
% 2.39/2.81 thf(fact_4346_and__numerals_I1_J,axiom,
% 2.39/2.81 ! [Y: num] :
% 2.39/2.81 ( ( bit_se3949692690581998587nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 2.39/2.81 = zero_z3403309356797280102nteger ) ).
% 2.39/2.81
% 2.39/2.81 % and_numerals(1)
% 2.39/2.81 thf(fact_4347_and__numerals_I1_J,axiom,
% 2.39/2.81 ! [Y: num] :
% 2.39/2.81 ( ( bit_se2773287842338716102atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ Y ) ) )
% 2.39/2.81 = zero_z2226904508553997617atural ) ).
% 2.39/2.81
% 2.39/2.81 % and_numerals(1)
% 2.39/2.81 thf(fact_4348_and__numerals_I1_J,axiom,
% 2.39/2.81 ! [Y: num] :
% 2.39/2.81 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 2.39/2.81 = zero_zero_int ) ).
% 2.39/2.81
% 2.39/2.81 % and_numerals(1)
% 2.39/2.81 thf(fact_4349_and__numerals_I1_J,axiom,
% 2.39/2.81 ! [Y: num] :
% 2.39/2.81 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 2.39/2.81 = zero_zero_nat ) ).
% 2.39/2.81
% 2.39/2.81 % and_numerals(1)
% 2.39/2.81 thf(fact_4350_and__numerals_I5_J,axiom,
% 2.39/2.81 ! [X: num] :
% 2.39/2.81 ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X ) ) @ one_one_Code_integer )
% 2.39/2.81 = zero_z3403309356797280102nteger ) ).
% 2.39/2.81
% 2.39/2.81 % and_numerals(5)
% 2.39/2.81 thf(fact_4351_and__numerals_I5_J,axiom,
% 2.39/2.81 ! [X: num] :
% 2.39/2.81 ( ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ ( bit0 @ X ) ) @ one_one_Code_natural )
% 2.39/2.81 = zero_z2226904508553997617atural ) ).
% 2.39/2.81
% 2.39/2.81 % and_numerals(5)
% 2.39/2.81 thf(fact_4352_and__numerals_I5_J,axiom,
% 2.39/2.81 ! [X: num] :
% 2.39/2.81 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ one_one_int )
% 2.39/2.81 = zero_zero_int ) ).
% 2.39/2.81
% 2.39/2.81 % and_numerals(5)
% 2.39/2.81 thf(fact_4353_and__numerals_I5_J,axiom,
% 2.39/2.81 ! [X: num] :
% 2.39/2.81 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ one_one_nat )
% 2.39/2.81 = zero_zero_nat ) ).
% 2.39/2.81
% 2.39/2.81 % and_numerals(5)
% 2.39/2.81 thf(fact_4354_and__numerals_I3_J,axiom,
% 2.39/2.81 ! [X: num,Y: num] :
% 2.39/2.81 ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 2.39/2.81 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % and_numerals(3)
% 2.39/2.81 thf(fact_4355_and__numerals_I3_J,axiom,
% 2.39/2.81 ! [X: num,Y: num] :
% 2.39/2.81 ( ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ ( bit0 @ X ) ) @ ( numera5444537566228673987atural @ ( bit0 @ Y ) ) )
% 2.39/2.81 = ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % and_numerals(3)
% 2.39/2.81 thf(fact_4356_and__numerals_I3_J,axiom,
% 2.39/2.81 ! [X: num,Y: num] :
% 2.39/2.81 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 2.39/2.81 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % and_numerals(3)
% 2.39/2.81 thf(fact_4357_and__numerals_I3_J,axiom,
% 2.39/2.81 ! [X: num,Y: num] :
% 2.39/2.81 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 2.39/2.81 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % and_numerals(3)
% 2.39/2.81 thf(fact_4358_take__bit__of__1,axiom,
% 2.39/2.81 ! [N: nat] :
% 2.39/2.81 ( ( bit_se1745604003318907178nteger @ N @ one_one_Code_integer )
% 2.39/2.81 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_of_1
% 2.39/2.81 thf(fact_4359_take__bit__of__1,axiom,
% 2.39/2.81 ! [N: nat] :
% 2.39/2.81 ( ( bit_se2925701944663578781it_nat @ N @ one_one_nat )
% 2.39/2.81 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_of_1
% 2.39/2.81 thf(fact_4360_take__bit__of__1,axiom,
% 2.39/2.81 ! [N: nat] :
% 2.39/2.81 ( ( bit_se2923211474154528505it_int @ N @ one_one_int )
% 2.39/2.81 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_of_1
% 2.39/2.81 thf(fact_4361_and__minus__numerals_I6_J,axiom,
% 2.39/2.81 ! [N: num] :
% 2.39/2.81 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 2.39/2.81 = one_one_int ) ).
% 2.39/2.81
% 2.39/2.81 % and_minus_numerals(6)
% 2.39/2.81 thf(fact_4362_and__minus__numerals_I2_J,axiom,
% 2.39/2.81 ! [N: num] :
% 2.39/2.81 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 2.39/2.81 = one_one_int ) ).
% 2.39/2.81
% 2.39/2.81 % and_minus_numerals(2)
% 2.39/2.81 thf(fact_4363_dbl__inc__simps_I3_J,axiom,
% 2.39/2.81 ( ( neg_nu5851722552734809277nc_int @ one_one_int )
% 2.39/2.81 = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % dbl_inc_simps(3)
% 2.39/2.81 thf(fact_4364_dbl__inc__simps_I3_J,axiom,
% 2.39/2.81 ( ( neg_nu5219082963157363817nc_rat @ one_one_rat )
% 2.39/2.81 = ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % dbl_inc_simps(3)
% 2.39/2.81 thf(fact_4365_dbl__inc__simps_I3_J,axiom,
% 2.39/2.81 ( ( neg_nu5831290666863070958nteger @ one_one_Code_integer )
% 2.39/2.81 = ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % dbl_inc_simps(3)
% 2.39/2.81 thf(fact_4366_and__numerals_I6_J,axiom,
% 2.39/2.81 ! [X: num,Y: num] :
% 2.39/2.81 ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 2.39/2.81 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % and_numerals(6)
% 2.39/2.81 thf(fact_4367_and__numerals_I6_J,axiom,
% 2.39/2.81 ! [X: num,Y: num] :
% 2.39/2.81 ( ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ ( bit1 @ X ) ) @ ( numera5444537566228673987atural @ ( bit0 @ Y ) ) )
% 2.39/2.81 = ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % and_numerals(6)
% 2.39/2.81 thf(fact_4368_and__numerals_I6_J,axiom,
% 2.39/2.81 ! [X: num,Y: num] :
% 2.39/2.81 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 2.39/2.81 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % and_numerals(6)
% 2.39/2.81 thf(fact_4369_and__numerals_I6_J,axiom,
% 2.39/2.81 ! [X: num,Y: num] :
% 2.39/2.81 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 2.39/2.81 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % and_numerals(6)
% 2.39/2.81 thf(fact_4370_and__numerals_I4_J,axiom,
% 2.39/2.81 ! [X: num,Y: num] :
% 2.39/2.81 ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 2.39/2.81 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % and_numerals(4)
% 2.39/2.81 thf(fact_4371_and__numerals_I4_J,axiom,
% 2.39/2.81 ! [X: num,Y: num] :
% 2.39/2.81 ( ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ ( bit0 @ X ) ) @ ( numera5444537566228673987atural @ ( bit1 @ Y ) ) )
% 2.39/2.81 = ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % and_numerals(4)
% 2.39/2.81 thf(fact_4372_and__numerals_I4_J,axiom,
% 2.39/2.81 ! [X: num,Y: num] :
% 2.39/2.81 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 2.39/2.81 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % and_numerals(4)
% 2.39/2.81 thf(fact_4373_and__numerals_I4_J,axiom,
% 2.39/2.81 ! [X: num,Y: num] :
% 2.39/2.81 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 2.39/2.81 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % and_numerals(4)
% 2.39/2.81 thf(fact_4374_push__bit__Suc,axiom,
% 2.39/2.81 ! [N: nat,A: code_integer] :
% 2.39/2.81 ( ( bit_se7788150548672797655nteger @ ( suc @ N ) @ A )
% 2.39/2.81 = ( bit_se7788150548672797655nteger @ N @ ( times_3573771949741848930nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % push_bit_Suc
% 2.39/2.81 thf(fact_4375_push__bit__Suc,axiom,
% 2.39/2.81 ! [N: nat,A: code_natural] :
% 2.39/2.81 ( ( bit_se6611745700429515170atural @ ( suc @ N ) @ A )
% 2.39/2.81 = ( bit_se6611745700429515170atural @ N @ ( times_2397367101498566445atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % push_bit_Suc
% 2.39/2.81 thf(fact_4376_push__bit__Suc,axiom,
% 2.39/2.81 ! [N: nat,A: int] :
% 2.39/2.81 ( ( bit_se545348938243370406it_int @ ( suc @ N ) @ A )
% 2.39/2.81 = ( bit_se545348938243370406it_int @ N @ ( times_times_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % push_bit_Suc
% 2.39/2.81 thf(fact_4377_push__bit__Suc,axiom,
% 2.39/2.81 ! [N: nat,A: nat] :
% 2.39/2.81 ( ( bit_se547839408752420682it_nat @ ( suc @ N ) @ A )
% 2.39/2.81 = ( bit_se547839408752420682it_nat @ N @ ( times_times_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % push_bit_Suc
% 2.39/2.81 thf(fact_4378_push__bit__of__1,axiom,
% 2.39/2.81 ! [N: nat] :
% 2.39/2.81 ( ( bit_se7788150548672797655nteger @ N @ one_one_Code_integer )
% 2.39/2.81 = ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ).
% 2.39/2.81
% 2.39/2.81 % push_bit_of_1
% 2.39/2.81 thf(fact_4379_push__bit__of__1,axiom,
% 2.39/2.81 ! [N: nat] :
% 2.39/2.81 ( ( bit_se6611745700429515170atural @ N @ one_one_Code_natural )
% 2.39/2.81 = ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) ) ).
% 2.39/2.81
% 2.39/2.81 % push_bit_of_1
% 2.39/2.81 thf(fact_4380_push__bit__of__1,axiom,
% 2.39/2.81 ! [N: nat] :
% 2.39/2.81 ( ( bit_se545348938243370406it_int @ N @ one_one_int )
% 2.39/2.81 = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 2.39/2.81
% 2.39/2.81 % push_bit_of_1
% 2.39/2.81 thf(fact_4381_push__bit__of__1,axiom,
% 2.39/2.81 ! [N: nat] :
% 2.39/2.81 ( ( bit_se547839408752420682it_nat @ N @ one_one_nat )
% 2.39/2.81 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 2.39/2.81
% 2.39/2.81 % push_bit_of_1
% 2.39/2.81 thf(fact_4382_and__minus__numerals_I5_J,axiom,
% 2.39/2.81 ! [N: num] :
% 2.39/2.81 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 2.39/2.81 = zero_zero_int ) ).
% 2.39/2.81
% 2.39/2.81 % and_minus_numerals(5)
% 2.39/2.81 thf(fact_4383_and__minus__numerals_I1_J,axiom,
% 2.39/2.81 ! [N: num] :
% 2.39/2.81 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 2.39/2.81 = zero_zero_int ) ).
% 2.39/2.81
% 2.39/2.81 % and_minus_numerals(1)
% 2.39/2.81 thf(fact_4384_dbl__dec__simps_I4_J,axiom,
% 2.39/2.81 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ one_one_int ) )
% 2.39/2.81 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % dbl_dec_simps(4)
% 2.39/2.81 thf(fact_4385_dbl__dec__simps_I4_J,axiom,
% 2.39/2.81 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 2.39/2.81 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % dbl_dec_simps(4)
% 2.39/2.81 thf(fact_4386_dbl__dec__simps_I4_J,axiom,
% 2.39/2.81 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 2.39/2.81 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % dbl_dec_simps(4)
% 2.39/2.81 thf(fact_4387_and__numerals_I7_J,axiom,
% 2.39/2.81 ! [X: num,Y: num] :
% 2.39/2.81 ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 2.39/2.81 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % and_numerals(7)
% 2.39/2.81 thf(fact_4388_and__numerals_I7_J,axiom,
% 2.39/2.81 ! [X: num,Y: num] :
% 2.39/2.81 ( ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ ( bit1 @ X ) ) @ ( numera5444537566228673987atural @ ( bit1 @ Y ) ) )
% 2.39/2.81 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % and_numerals(7)
% 2.39/2.81 thf(fact_4389_and__numerals_I7_J,axiom,
% 2.39/2.81 ! [X: num,Y: num] :
% 2.39/2.81 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 2.39/2.81 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % and_numerals(7)
% 2.39/2.81 thf(fact_4390_and__numerals_I7_J,axiom,
% 2.39/2.81 ! [X: num,Y: num] :
% 2.39/2.81 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 2.39/2.81 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % and_numerals(7)
% 2.39/2.81 thf(fact_4391_one__div__2__pow__eq,axiom,
% 2.39/2.81 ! [N: nat] :
% 2.39/2.81 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 2.39/2.81 = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % one_div_2_pow_eq
% 2.39/2.81 thf(fact_4392_one__div__2__pow__eq,axiom,
% 2.39/2.81 ! [N: nat] :
% 2.39/2.81 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 2.39/2.81 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % one_div_2_pow_eq
% 2.39/2.81 thf(fact_4393_one__div__2__pow__eq,axiom,
% 2.39/2.81 ! [N: nat] :
% 2.39/2.81 ( ( divide5121882707175180666atural @ one_one_Code_natural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 2.39/2.81 = ( zero_n8403883297036319079atural @ ( N = zero_zero_nat ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % one_div_2_pow_eq
% 2.39/2.81 thf(fact_4394_one__div__2__pow__eq,axiom,
% 2.39/2.81 ! [N: nat] :
% 2.39/2.81 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 2.39/2.81 = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % one_div_2_pow_eq
% 2.39/2.81 thf(fact_4395_bits__1__div__exp,axiom,
% 2.39/2.81 ! [N: nat] :
% 2.39/2.81 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 2.39/2.81 = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % bits_1_div_exp
% 2.39/2.81 thf(fact_4396_bits__1__div__exp,axiom,
% 2.39/2.81 ! [N: nat] :
% 2.39/2.81 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 2.39/2.81 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % bits_1_div_exp
% 2.39/2.81 thf(fact_4397_bits__1__div__exp,axiom,
% 2.39/2.81 ! [N: nat] :
% 2.39/2.81 ( ( divide5121882707175180666atural @ one_one_Code_natural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 2.39/2.81 = ( zero_n8403883297036319079atural @ ( N = zero_zero_nat ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % bits_1_div_exp
% 2.39/2.81 thf(fact_4398_bits__1__div__exp,axiom,
% 2.39/2.81 ! [N: nat] :
% 2.39/2.81 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 2.39/2.81 = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % bits_1_div_exp
% 2.39/2.81 thf(fact_4399_take__bit__of__exp,axiom,
% 2.39/2.81 ! [M2: nat,N: nat] :
% 2.39/2.81 ( ( bit_se2925701944663578781it_nat @ M2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 2.39/2.81 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ N @ M2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_of_exp
% 2.39/2.81 thf(fact_4400_take__bit__of__exp,axiom,
% 2.39/2.81 ! [M2: nat,N: nat] :
% 2.39/2.81 ( ( bit_se1745604003318907178nteger @ M2 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 2.39/2.81 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ N @ M2 ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_of_exp
% 2.39/2.81 thf(fact_4401_take__bit__of__exp,axiom,
% 2.39/2.81 ! [M2: nat,N: nat] :
% 2.39/2.81 ( ( bit_se569199155075624693atural @ M2 @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 2.39/2.81 = ( times_2397367101498566445atural @ ( zero_n8403883297036319079atural @ ( ord_less_nat @ N @ M2 ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_of_exp
% 2.39/2.81 thf(fact_4402_take__bit__of__exp,axiom,
% 2.39/2.81 ! [M2: nat,N: nat] :
% 2.39/2.81 ( ( bit_se2923211474154528505it_int @ M2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 2.39/2.81 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ N @ M2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_of_exp
% 2.39/2.81 thf(fact_4403_take__bit__of__2,axiom,
% 2.39/2.81 ! [N: nat] :
% 2.39/2.81 ( ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.81 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_of_2
% 2.39/2.81 thf(fact_4404_take__bit__of__2,axiom,
% 2.39/2.81 ! [N: nat] :
% 2.39/2.81 ( ( bit_se1745604003318907178nteger @ N @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 2.39/2.81 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_of_2
% 2.39/2.81 thf(fact_4405_take__bit__of__2,axiom,
% 2.39/2.81 ! [N: nat] :
% 2.39/2.81 ( ( bit_se569199155075624693atural @ N @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 2.39/2.81 = ( times_2397367101498566445atural @ ( zero_n8403883297036319079atural @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_of_2
% 2.39/2.81 thf(fact_4406_take__bit__of__2,axiom,
% 2.39/2.81 ! [N: nat] :
% 2.39/2.81 ( ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 2.39/2.81 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_of_2
% 2.39/2.81 thf(fact_4407_zmod__numeral__Bit1,axiom,
% 2.39/2.81 ! [V2: num,W: num] :
% 2.39/2.81 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ V2 ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 2.39/2.81 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V2 ) @ ( numeral_numeral_int @ W ) ) ) @ one_one_int ) ) ).
% 2.39/2.81
% 2.39/2.81 % zmod_numeral_Bit1
% 2.39/2.81 thf(fact_4408_signed__take__bit__Suc__bit1,axiom,
% 2.39/2.81 ! [N: nat,K: num] :
% 2.39/2.81 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 2.39/2.81 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 2.39/2.81
% 2.39/2.81 % signed_take_bit_Suc_bit1
% 2.39/2.81 thf(fact_4409_of__bool__conj,axiom,
% 2.39/2.81 ! [P2: $o,Q2: $o] :
% 2.39/2.81 ( ( zero_n2687167440665602831ol_nat
% 2.39/2.81 @ ( P2
% 2.39/2.81 & Q2 ) )
% 2.39/2.81 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ P2 ) @ ( zero_n2687167440665602831ol_nat @ Q2 ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % of_bool_conj
% 2.39/2.81 thf(fact_4410_of__bool__conj,axiom,
% 2.39/2.81 ! [P2: $o,Q2: $o] :
% 2.39/2.81 ( ( zero_n356916108424825756nteger
% 2.39/2.81 @ ( P2
% 2.39/2.81 & Q2 ) )
% 2.39/2.81 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ P2 ) @ ( zero_n356916108424825756nteger @ Q2 ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % of_bool_conj
% 2.39/2.81 thf(fact_4411_of__bool__conj,axiom,
% 2.39/2.81 ! [P2: $o,Q2: $o] :
% 2.39/2.81 ( ( zero_n8403883297036319079atural
% 2.39/2.81 @ ( P2
% 2.39/2.81 & Q2 ) )
% 2.39/2.81 = ( times_2397367101498566445atural @ ( zero_n8403883297036319079atural @ P2 ) @ ( zero_n8403883297036319079atural @ Q2 ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % of_bool_conj
% 2.39/2.81 thf(fact_4412_of__bool__conj,axiom,
% 2.39/2.81 ! [P2: $o,Q2: $o] :
% 2.39/2.81 ( ( zero_n2684676970156552555ol_int
% 2.39/2.81 @ ( P2
% 2.39/2.81 & Q2 ) )
% 2.39/2.81 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ P2 ) @ ( zero_n2684676970156552555ol_int @ Q2 ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % of_bool_conj
% 2.39/2.81 thf(fact_4413_and__eq__minus__1__iff,axiom,
% 2.39/2.81 ! [A: code_integer,B: code_integer] :
% 2.39/2.81 ( ( ( bit_se3949692690581998587nteger @ A @ B )
% 2.39/2.81 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 2.39/2.81 = ( ( A
% 2.39/2.81 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 2.39/2.81 & ( B
% 2.39/2.81 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % and_eq_minus_1_iff
% 2.39/2.81 thf(fact_4414_and__eq__minus__1__iff,axiom,
% 2.39/2.81 ! [A: int,B: int] :
% 2.39/2.81 ( ( ( bit_se725231765392027082nd_int @ A @ B )
% 2.39/2.81 = ( uminus_uminus_int @ one_one_int ) )
% 2.39/2.81 = ( ( A
% 2.39/2.81 = ( uminus_uminus_int @ one_one_int ) )
% 2.39/2.81 & ( B
% 2.39/2.81 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % and_eq_minus_1_iff
% 2.39/2.81 thf(fact_4415_of__bool__less__eq__one,axiom,
% 2.39/2.81 ! [P2: $o] : ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P2 ) @ one_one_Code_integer ) ).
% 2.39/2.81
% 2.39/2.81 % of_bool_less_eq_one
% 2.39/2.81 thf(fact_4416_of__bool__less__eq__one,axiom,
% 2.39/2.81 ! [P2: $o] : ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P2 ) @ one_one_rat ) ).
% 2.39/2.81
% 2.39/2.81 % of_bool_less_eq_one
% 2.39/2.81 thf(fact_4417_of__bool__less__eq__one,axiom,
% 2.39/2.81 ! [P2: $o] : ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P2 ) @ one_one_nat ) ).
% 2.39/2.81
% 2.39/2.81 % of_bool_less_eq_one
% 2.39/2.81 thf(fact_4418_of__bool__less__eq__one,axiom,
% 2.39/2.81 ! [P2: $o] : ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P2 ) @ one_one_int ) ).
% 2.39/2.81
% 2.39/2.81 % of_bool_less_eq_one
% 2.39/2.81 thf(fact_4419_of__bool__def,axiom,
% 2.39/2.81 ( zero_n2687167440665602831ol_nat
% 2.39/2.81 = ( ^ [P6: $o] : ( if_nat @ P6 @ one_one_nat @ zero_zero_nat ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % of_bool_def
% 2.39/2.81 thf(fact_4420_of__bool__def,axiom,
% 2.39/2.81 ( zero_n2052037380579107095ol_rat
% 2.39/2.81 = ( ^ [P6: $o] : ( if_rat @ P6 @ one_one_rat @ zero_zero_rat ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % of_bool_def
% 2.39/2.81 thf(fact_4421_of__bool__def,axiom,
% 2.39/2.81 ( zero_n356916108424825756nteger
% 2.39/2.81 = ( ^ [P6: $o] : ( if_Code_integer @ P6 @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % of_bool_def
% 2.39/2.81 thf(fact_4422_of__bool__def,axiom,
% 2.39/2.81 ( zero_n8403883297036319079atural
% 2.39/2.81 = ( ^ [P6: $o] : ( if_Code_natural @ P6 @ one_one_Code_natural @ zero_z2226904508553997617atural ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % of_bool_def
% 2.39/2.81 thf(fact_4423_of__bool__def,axiom,
% 2.39/2.81 ( zero_n2684676970156552555ol_int
% 2.39/2.81 = ( ^ [P6: $o] : ( if_int @ P6 @ one_one_int @ zero_zero_int ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % of_bool_def
% 2.39/2.81 thf(fact_4424_split__of__bool,axiom,
% 2.39/2.81 ! [P2: nat > $o,P5: $o] :
% 2.39/2.81 ( ( P2 @ ( zero_n2687167440665602831ol_nat @ P5 ) )
% 2.39/2.81 = ( ( P5
% 2.39/2.81 => ( P2 @ one_one_nat ) )
% 2.39/2.81 & ( ~ P5
% 2.39/2.81 => ( P2 @ zero_zero_nat ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % split_of_bool
% 2.39/2.81 thf(fact_4425_split__of__bool,axiom,
% 2.39/2.81 ! [P2: rat > $o,P5: $o] :
% 2.39/2.81 ( ( P2 @ ( zero_n2052037380579107095ol_rat @ P5 ) )
% 2.39/2.81 = ( ( P5
% 2.39/2.81 => ( P2 @ one_one_rat ) )
% 2.39/2.81 & ( ~ P5
% 2.39/2.81 => ( P2 @ zero_zero_rat ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % split_of_bool
% 2.39/2.81 thf(fact_4426_split__of__bool,axiom,
% 2.39/2.81 ! [P2: code_integer > $o,P5: $o] :
% 2.39/2.81 ( ( P2 @ ( zero_n356916108424825756nteger @ P5 ) )
% 2.39/2.81 = ( ( P5
% 2.39/2.81 => ( P2 @ one_one_Code_integer ) )
% 2.39/2.81 & ( ~ P5
% 2.39/2.81 => ( P2 @ zero_z3403309356797280102nteger ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % split_of_bool
% 2.39/2.81 thf(fact_4427_split__of__bool,axiom,
% 2.39/2.81 ! [P2: code_natural > $o,P5: $o] :
% 2.39/2.81 ( ( P2 @ ( zero_n8403883297036319079atural @ P5 ) )
% 2.39/2.81 = ( ( P5
% 2.39/2.81 => ( P2 @ one_one_Code_natural ) )
% 2.39/2.81 & ( ~ P5
% 2.39/2.81 => ( P2 @ zero_z2226904508553997617atural ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % split_of_bool
% 2.39/2.81 thf(fact_4428_split__of__bool,axiom,
% 2.39/2.81 ! [P2: int > $o,P5: $o] :
% 2.39/2.81 ( ( P2 @ ( zero_n2684676970156552555ol_int @ P5 ) )
% 2.39/2.81 = ( ( P5
% 2.39/2.81 => ( P2 @ one_one_int ) )
% 2.39/2.81 & ( ~ P5
% 2.39/2.81 => ( P2 @ zero_zero_int ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % split_of_bool
% 2.39/2.81 thf(fact_4429_split__of__bool__asm,axiom,
% 2.39/2.81 ! [P2: nat > $o,P5: $o] :
% 2.39/2.81 ( ( P2 @ ( zero_n2687167440665602831ol_nat @ P5 ) )
% 2.39/2.81 = ( ~ ( ( P5
% 2.39/2.81 & ~ ( P2 @ one_one_nat ) )
% 2.39/2.81 | ( ~ P5
% 2.39/2.81 & ~ ( P2 @ zero_zero_nat ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % split_of_bool_asm
% 2.39/2.81 thf(fact_4430_split__of__bool__asm,axiom,
% 2.39/2.81 ! [P2: rat > $o,P5: $o] :
% 2.39/2.81 ( ( P2 @ ( zero_n2052037380579107095ol_rat @ P5 ) )
% 2.39/2.81 = ( ~ ( ( P5
% 2.39/2.81 & ~ ( P2 @ one_one_rat ) )
% 2.39/2.81 | ( ~ P5
% 2.39/2.81 & ~ ( P2 @ zero_zero_rat ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % split_of_bool_asm
% 2.39/2.81 thf(fact_4431_split__of__bool__asm,axiom,
% 2.39/2.81 ! [P2: code_integer > $o,P5: $o] :
% 2.39/2.81 ( ( P2 @ ( zero_n356916108424825756nteger @ P5 ) )
% 2.39/2.81 = ( ~ ( ( P5
% 2.39/2.81 & ~ ( P2 @ one_one_Code_integer ) )
% 2.39/2.81 | ( ~ P5
% 2.39/2.81 & ~ ( P2 @ zero_z3403309356797280102nteger ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % split_of_bool_asm
% 2.39/2.81 thf(fact_4432_split__of__bool__asm,axiom,
% 2.39/2.81 ! [P2: code_natural > $o,P5: $o] :
% 2.39/2.81 ( ( P2 @ ( zero_n8403883297036319079atural @ P5 ) )
% 2.39/2.81 = ( ~ ( ( P5
% 2.39/2.81 & ~ ( P2 @ one_one_Code_natural ) )
% 2.39/2.81 | ( ~ P5
% 2.39/2.81 & ~ ( P2 @ zero_z2226904508553997617atural ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % split_of_bool_asm
% 2.39/2.81 thf(fact_4433_split__of__bool__asm,axiom,
% 2.39/2.81 ! [P2: int > $o,P5: $o] :
% 2.39/2.81 ( ( P2 @ ( zero_n2684676970156552555ol_int @ P5 ) )
% 2.39/2.81 = ( ~ ( ( P5
% 2.39/2.81 & ~ ( P2 @ one_one_int ) )
% 2.39/2.81 | ( ~ P5
% 2.39/2.81 & ~ ( P2 @ zero_zero_int ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % split_of_bool_asm
% 2.39/2.81 thf(fact_4434_and_Ocomm__monoid__axioms,axiom,
% 2.39/2.81 comm_m1654649897431166824nteger @ bit_se3949692690581998587nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ).
% 2.39/2.81
% 2.39/2.81 % and.comm_monoid_axioms
% 2.39/2.81 thf(fact_4435_and_Ocomm__monoid__axioms,axiom,
% 2.39/2.81 comm_monoid_int @ bit_se725231765392027082nd_int @ ( uminus_uminus_int @ one_one_int ) ).
% 2.39/2.81
% 2.39/2.81 % and.comm_monoid_axioms
% 2.39/2.81 thf(fact_4436_take__bit__decr__eq,axiom,
% 2.39/2.81 ! [N: nat,K: int] :
% 2.39/2.81 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 2.39/2.81 != zero_zero_int )
% 2.39/2.81 => ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ one_one_int ) )
% 2.39/2.81 = ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ one_one_int ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_decr_eq
% 2.39/2.81 thf(fact_4437_numeral__Bit1,axiom,
% 2.39/2.81 ! [N: num] :
% 2.39/2.81 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 2.39/2.81 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 2.39/2.81
% 2.39/2.81 % numeral_Bit1
% 2.39/2.81 thf(fact_4438_numeral__Bit1,axiom,
% 2.39/2.81 ! [N: num] :
% 2.39/2.81 ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 2.39/2.81 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 2.39/2.81
% 2.39/2.81 % numeral_Bit1
% 2.39/2.81 thf(fact_4439_numeral__Bit1,axiom,
% 2.39/2.81 ! [N: num] :
% 2.39/2.81 ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 2.39/2.81 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 2.39/2.81
% 2.39/2.81 % numeral_Bit1
% 2.39/2.81 thf(fact_4440_numeral__Bit1,axiom,
% 2.39/2.81 ! [N: num] :
% 2.39/2.81 ( ( numera6620942414471956472nteger @ ( bit1 @ N ) )
% 2.39/2.81 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ N ) ) @ one_one_Code_integer ) ) ).
% 2.39/2.81
% 2.39/2.81 % numeral_Bit1
% 2.39/2.81 thf(fact_4441_numeral__Bit1,axiom,
% 2.39/2.81 ! [N: num] :
% 2.39/2.81 ( ( numera5444537566228673987atural @ ( bit1 @ N ) )
% 2.39/2.81 = ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ N ) @ ( numera5444537566228673987atural @ N ) ) @ one_one_Code_natural ) ) ).
% 2.39/2.81
% 2.39/2.81 % numeral_Bit1
% 2.39/2.81 thf(fact_4442_and_Omonoid__axioms,axiom,
% 2.39/2.81 monoid_Code_integer @ bit_se3949692690581998587nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ).
% 2.39/2.81
% 2.39/2.81 % and.monoid_axioms
% 2.39/2.81 thf(fact_4443_and_Omonoid__axioms,axiom,
% 2.39/2.81 monoid_int @ bit_se725231765392027082nd_int @ ( uminus_uminus_int @ one_one_int ) ).
% 2.39/2.81
% 2.39/2.81 % and.monoid_axioms
% 2.39/2.81 thf(fact_4444_and_Osemilattice__neutr__axioms,axiom,
% 2.39/2.81 semila6106414119144251899nteger @ bit_se3949692690581998587nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ).
% 2.39/2.81
% 2.39/2.81 % and.semilattice_neutr_axioms
% 2.39/2.81 thf(fact_4445_and_Osemilattice__neutr__axioms,axiom,
% 2.39/2.81 semila9079005292280841162tr_int @ bit_se725231765392027082nd_int @ ( uminus_uminus_int @ one_one_int ) ).
% 2.39/2.81
% 2.39/2.81 % and.semilattice_neutr_axioms
% 2.39/2.81 thf(fact_4446_take__bit__Suc__bit1,axiom,
% 2.39/2.81 ! [N: nat,K: num] :
% 2.39/2.81 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 2.39/2.81 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_Suc_bit1
% 2.39/2.81 thf(fact_4447_take__bit__Suc__bit1,axiom,
% 2.39/2.81 ! [N: nat,K: num] :
% 2.39/2.81 ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ ( numera6620942414471956472nteger @ ( bit1 @ K ) ) )
% 2.39/2.81 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N @ ( numera6620942414471956472nteger @ K ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_Suc_bit1
% 2.39/2.81 thf(fact_4448_take__bit__Suc__bit1,axiom,
% 2.39/2.81 ! [N: nat,K: num] :
% 2.39/2.81 ( ( bit_se569199155075624693atural @ ( suc @ N ) @ ( numera5444537566228673987atural @ ( bit1 @ K ) ) )
% 2.39/2.81 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( bit_se569199155075624693atural @ N @ ( numera5444537566228673987atural @ K ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ one_one_Code_natural ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_Suc_bit1
% 2.39/2.81 thf(fact_4449_take__bit__Suc__bit1,axiom,
% 2.39/2.81 ! [N: nat,K: num] :
% 2.39/2.81 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 2.39/2.81 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_Suc_bit1
% 2.39/2.81 thf(fact_4450_power3__eq__cube,axiom,
% 2.39/2.81 ! [A: assn] :
% 2.39/2.81 ( ( power_power_assn @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 2.39/2.81 = ( times_times_assn @ ( times_times_assn @ A @ A ) @ A ) ) ).
% 2.39/2.81
% 2.39/2.81 % power3_eq_cube
% 2.39/2.81 thf(fact_4451_power3__eq__cube,axiom,
% 2.39/2.81 ! [A: nat] :
% 2.39/2.81 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 2.39/2.81 = ( times_times_nat @ ( times_times_nat @ A @ A ) @ A ) ) ).
% 2.39/2.81
% 2.39/2.81 % power3_eq_cube
% 2.39/2.81 thf(fact_4452_power3__eq__cube,axiom,
% 2.39/2.81 ! [A: int] :
% 2.39/2.81 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 2.39/2.81 = ( times_times_int @ ( times_times_int @ A @ A ) @ A ) ) ).
% 2.39/2.81
% 2.39/2.81 % power3_eq_cube
% 2.39/2.81 thf(fact_4453_power3__eq__cube,axiom,
% 2.39/2.81 ! [A: code_integer] :
% 2.39/2.81 ( ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 2.39/2.81 = ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ A @ A ) @ A ) ) ).
% 2.39/2.81
% 2.39/2.81 % power3_eq_cube
% 2.39/2.81 thf(fact_4454_power3__eq__cube,axiom,
% 2.39/2.81 ! [A: code_natural] :
% 2.39/2.81 ( ( power_7079662738309270450atural @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 2.39/2.81 = ( times_2397367101498566445atural @ ( times_2397367101498566445atural @ A @ A ) @ A ) ) ).
% 2.39/2.81
% 2.39/2.81 % power3_eq_cube
% 2.39/2.81 thf(fact_4455_push__bit__double,axiom,
% 2.39/2.81 ! [N: nat,A: code_integer] :
% 2.39/2.81 ( ( bit_se7788150548672797655nteger @ N @ ( times_3573771949741848930nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 2.39/2.81 = ( times_3573771949741848930nteger @ ( bit_se7788150548672797655nteger @ N @ A ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % push_bit_double
% 2.39/2.81 thf(fact_4456_push__bit__double,axiom,
% 2.39/2.81 ! [N: nat,A: code_natural] :
% 2.39/2.81 ( ( bit_se6611745700429515170atural @ N @ ( times_2397367101498566445atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) )
% 2.39/2.81 = ( times_2397367101498566445atural @ ( bit_se6611745700429515170atural @ N @ A ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % push_bit_double
% 2.39/2.81 thf(fact_4457_push__bit__double,axiom,
% 2.39/2.81 ! [N: nat,A: int] :
% 2.39/2.81 ( ( bit_se545348938243370406it_int @ N @ ( times_times_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 2.39/2.81 = ( times_times_int @ ( bit_se545348938243370406it_int @ N @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % push_bit_double
% 2.39/2.81 thf(fact_4458_push__bit__double,axiom,
% 2.39/2.81 ! [N: nat,A: nat] :
% 2.39/2.81 ( ( bit_se547839408752420682it_nat @ N @ ( times_times_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 2.39/2.81 = ( times_times_nat @ ( bit_se547839408752420682it_nat @ N @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % push_bit_double
% 2.39/2.81 thf(fact_4459_take__bit__Suc__minus__bit1,axiom,
% 2.39/2.81 ! [N: nat,K: num] :
% 2.39/2.81 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 2.39/2.81 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_Suc_minus_bit1
% 2.39/2.81 thf(fact_4460_take__bit__Suc__bit0,axiom,
% 2.39/2.81 ! [N: nat,K: num] :
% 2.39/2.81 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 2.39/2.81 = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_Suc_bit0
% 2.39/2.81 thf(fact_4461_take__bit__Suc__bit0,axiom,
% 2.39/2.81 ! [N: nat,K: num] :
% 2.39/2.81 ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ ( numera6620942414471956472nteger @ ( bit0 @ K ) ) )
% 2.39/2.81 = ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N @ ( numera6620942414471956472nteger @ K ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_Suc_bit0
% 2.39/2.81 thf(fact_4462_take__bit__Suc__bit0,axiom,
% 2.39/2.81 ! [N: nat,K: num] :
% 2.39/2.81 ( ( bit_se569199155075624693atural @ ( suc @ N ) @ ( numera5444537566228673987atural @ ( bit0 @ K ) ) )
% 2.39/2.81 = ( times_2397367101498566445atural @ ( bit_se569199155075624693atural @ N @ ( numera5444537566228673987atural @ K ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_Suc_bit0
% 2.39/2.81 thf(fact_4463_take__bit__Suc__bit0,axiom,
% 2.39/2.81 ! [N: nat,K: num] :
% 2.39/2.81 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 2.39/2.81 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_Suc_bit0
% 2.39/2.81 thf(fact_4464_and__one__eq,axiom,
% 2.39/2.81 ! [A: code_integer] :
% 2.39/2.81 ( ( bit_se3949692690581998587nteger @ A @ one_one_Code_integer )
% 2.39/2.81 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % and_one_eq
% 2.39/2.81 thf(fact_4465_and__one__eq,axiom,
% 2.39/2.81 ! [A: code_natural] :
% 2.39/2.81 ( ( bit_se2773287842338716102atural @ A @ one_one_Code_natural )
% 2.39/2.81 = ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % and_one_eq
% 2.39/2.81 thf(fact_4466_and__one__eq,axiom,
% 2.39/2.81 ! [A: int] :
% 2.39/2.81 ( ( bit_se725231765392027082nd_int @ A @ one_one_int )
% 2.39/2.81 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % and_one_eq
% 2.39/2.81 thf(fact_4467_and__one__eq,axiom,
% 2.39/2.81 ! [A: nat] :
% 2.39/2.81 ( ( bit_se727722235901077358nd_nat @ A @ one_one_nat )
% 2.39/2.81 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % and_one_eq
% 2.39/2.81 thf(fact_4468_one__and__eq,axiom,
% 2.39/2.81 ! [A: code_integer] :
% 2.39/2.81 ( ( bit_se3949692690581998587nteger @ one_one_Code_integer @ A )
% 2.39/2.81 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % one_and_eq
% 2.39/2.81 thf(fact_4469_one__and__eq,axiom,
% 2.39/2.81 ! [A: code_natural] :
% 2.39/2.81 ( ( bit_se2773287842338716102atural @ one_one_Code_natural @ A )
% 2.39/2.81 = ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % one_and_eq
% 2.39/2.81 thf(fact_4470_one__and__eq,axiom,
% 2.39/2.81 ! [A: int] :
% 2.39/2.81 ( ( bit_se725231765392027082nd_int @ one_one_int @ A )
% 2.39/2.81 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % one_and_eq
% 2.39/2.81 thf(fact_4471_one__and__eq,axiom,
% 2.39/2.81 ! [A: nat] :
% 2.39/2.81 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ A )
% 2.39/2.81 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % one_and_eq
% 2.39/2.81 thf(fact_4472_numeral__BitM,axiom,
% 2.39/2.81 ! [N: num] :
% 2.39/2.81 ( ( numeral_numeral_int @ ( bitM @ N ) )
% 2.39/2.81 = ( minus_minus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ one_one_int ) ) ).
% 2.39/2.81
% 2.39/2.81 % numeral_BitM
% 2.39/2.81 thf(fact_4473_numeral__BitM,axiom,
% 2.39/2.81 ! [N: num] :
% 2.39/2.81 ( ( numeral_numeral_rat @ ( bitM @ N ) )
% 2.39/2.81 = ( minus_minus_rat @ ( numeral_numeral_rat @ ( bit0 @ N ) ) @ one_one_rat ) ) ).
% 2.39/2.81
% 2.39/2.81 % numeral_BitM
% 2.39/2.81 thf(fact_4474_numeral__BitM,axiom,
% 2.39/2.81 ! [N: num] :
% 2.39/2.81 ( ( numera6620942414471956472nteger @ ( bitM @ N ) )
% 2.39/2.81 = ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ one_one_Code_integer ) ) ).
% 2.39/2.81
% 2.39/2.81 % numeral_BitM
% 2.39/2.81 thf(fact_4475_push__bit__eq__mult,axiom,
% 2.39/2.81 ( bit_se7788150548672797655nteger
% 2.39/2.81 = ( ^ [N3: nat,A2: code_integer] : ( times_3573771949741848930nteger @ A2 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % push_bit_eq_mult
% 2.39/2.81 thf(fact_4476_push__bit__eq__mult,axiom,
% 2.39/2.81 ( bit_se6611745700429515170atural
% 2.39/2.81 = ( ^ [N3: nat,A2: code_natural] : ( times_2397367101498566445atural @ A2 @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % push_bit_eq_mult
% 2.39/2.81 thf(fact_4477_push__bit__eq__mult,axiom,
% 2.39/2.81 ( bit_se545348938243370406it_int
% 2.39/2.81 = ( ^ [N3: nat,A2: int] : ( times_times_int @ A2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % push_bit_eq_mult
% 2.39/2.81 thf(fact_4478_push__bit__eq__mult,axiom,
% 2.39/2.81 ( bit_se547839408752420682it_nat
% 2.39/2.81 = ( ^ [N3: nat,A2: nat] : ( times_times_nat @ A2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % push_bit_eq_mult
% 2.39/2.81 thf(fact_4479_bits__induct,axiom,
% 2.39/2.81 ! [P2: code_integer > $o,A: code_integer] :
% 2.39/2.81 ( ! [A6: code_integer] :
% 2.39/2.81 ( ( ( divide6298287555418463151nteger @ A6 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 2.39/2.81 = A6 )
% 2.39/2.81 => ( P2 @ A6 ) )
% 2.39/2.81 => ( ! [A6: code_integer,B5: $o] :
% 2.39/2.81 ( ( P2 @ A6 )
% 2.39/2.81 => ( ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B5 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A6 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 2.39/2.81 = A6 )
% 2.39/2.81 => ( P2 @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B5 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A6 ) ) ) ) )
% 2.39/2.81 => ( P2 @ A ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % bits_induct
% 2.39/2.81 thf(fact_4480_bits__induct,axiom,
% 2.39/2.81 ! [P2: nat > $o,A: nat] :
% 2.39/2.81 ( ! [A6: nat] :
% 2.39/2.81 ( ( ( divide_divide_nat @ A6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.81 = A6 )
% 2.39/2.81 => ( P2 @ A6 ) )
% 2.39/2.81 => ( ! [A6: nat,B5: $o] :
% 2.39/2.81 ( ( P2 @ A6 )
% 2.39/2.81 => ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B5 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A6 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.81 = A6 )
% 2.39/2.81 => ( P2 @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B5 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A6 ) ) ) ) )
% 2.39/2.81 => ( P2 @ A ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % bits_induct
% 2.39/2.81 thf(fact_4481_bits__induct,axiom,
% 2.39/2.81 ! [P2: code_natural > $o,A: code_natural] :
% 2.39/2.81 ( ! [A6: code_natural] :
% 2.39/2.81 ( ( ( divide5121882707175180666atural @ A6 @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 2.39/2.81 = A6 )
% 2.39/2.81 => ( P2 @ A6 ) )
% 2.39/2.81 => ( ! [A6: code_natural,B5: $o] :
% 2.39/2.81 ( ( P2 @ A6 )
% 2.39/2.81 => ( ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ ( zero_n8403883297036319079atural @ B5 ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A6 ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 2.39/2.81 = A6 )
% 2.39/2.81 => ( P2 @ ( plus_p4538020629002901425atural @ ( zero_n8403883297036319079atural @ B5 ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A6 ) ) ) ) )
% 2.39/2.81 => ( P2 @ A ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % bits_induct
% 2.39/2.81 thf(fact_4482_bits__induct,axiom,
% 2.39/2.81 ! [P2: int > $o,A: int] :
% 2.39/2.81 ( ! [A6: int] :
% 2.39/2.81 ( ( ( divide_divide_int @ A6 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 2.39/2.81 = A6 )
% 2.39/2.81 => ( P2 @ A6 ) )
% 2.39/2.81 => ( ! [A6: int,B5: $o] :
% 2.39/2.81 ( ( P2 @ A6 )
% 2.39/2.81 => ( ( ( divide_divide_int @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B5 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A6 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 2.39/2.81 = A6 )
% 2.39/2.81 => ( P2 @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B5 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A6 ) ) ) ) )
% 2.39/2.81 => ( P2 @ A ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % bits_induct
% 2.39/2.81 thf(fact_4483_push__bit__minus__one,axiom,
% 2.39/2.81 ! [N: nat] :
% 2.39/2.81 ( ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 2.39/2.81 = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % push_bit_minus_one
% 2.39/2.81 thf(fact_4484_exp__mod__exp,axiom,
% 2.39/2.81 ! [M2: nat,N: nat] :
% 2.39/2.81 ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 2.39/2.81 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ M2 @ N ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % exp_mod_exp
% 2.39/2.81 thf(fact_4485_exp__mod__exp,axiom,
% 2.39/2.81 ! [M2: nat,N: nat] :
% 2.39/2.81 ( ( modulo_modulo_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 2.39/2.81 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ M2 @ N ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % exp_mod_exp
% 2.39/2.81 thf(fact_4486_exp__mod__exp,axiom,
% 2.39/2.81 ! [M2: nat,N: nat] :
% 2.39/2.81 ( ( modulo8411746178871703098atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M2 ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 2.39/2.81 = ( times_2397367101498566445atural @ ( zero_n8403883297036319079atural @ ( ord_less_nat @ M2 @ N ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % exp_mod_exp
% 2.39/2.81 thf(fact_4487_exp__mod__exp,axiom,
% 2.39/2.81 ! [M2: nat,N: nat] :
% 2.39/2.81 ( ( modulo_modulo_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 2.39/2.81 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ M2 @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % exp_mod_exp
% 2.39/2.81 thf(fact_4488_take__bit__incr__eq,axiom,
% 2.39/2.81 ! [N: nat,K: int] :
% 2.39/2.81 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 2.39/2.81 != ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 2.39/2.81 => ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 2.39/2.81 = ( plus_plus_int @ one_one_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_incr_eq
% 2.39/2.81 thf(fact_4489_take__bit__Suc__minus__1__eq,axiom,
% 2.39/2.81 ! [N: nat] :
% 2.39/2.81 ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 2.39/2.81 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ one_one_Code_integer ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_Suc_minus_1_eq
% 2.39/2.81 thf(fact_4490_take__bit__Suc__minus__1__eq,axiom,
% 2.39/2.81 ! [N: nat] :
% 2.39/2.81 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ one_one_int ) )
% 2.39/2.81 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ one_one_int ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_Suc_minus_1_eq
% 2.39/2.81 thf(fact_4491_take__bit__Suc,axiom,
% 2.39/2.81 ! [N: nat,A: code_integer] :
% 2.39/2.81 ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ A )
% 2.39/2.81 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_Suc
% 2.39/2.81 thf(fact_4492_take__bit__Suc,axiom,
% 2.39/2.81 ! [N: nat,A: nat] :
% 2.39/2.81 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ A )
% 2.39/2.81 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_Suc
% 2.39/2.81 thf(fact_4493_take__bit__Suc,axiom,
% 2.39/2.81 ! [N: nat,A: code_natural] :
% 2.39/2.81 ( ( bit_se569199155075624693atural @ ( suc @ N ) @ A )
% 2.39/2.81 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( bit_se569199155075624693atural @ N @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_Suc
% 2.39/2.81 thf(fact_4494_take__bit__Suc,axiom,
% 2.39/2.81 ! [N: nat,A: int] :
% 2.39/2.81 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A )
% 2.39/2.81 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_Suc
% 2.39/2.81 thf(fact_4495_take__bit__numeral__minus__1__eq,axiom,
% 2.39/2.81 ! [K: num] :
% 2.39/2.81 ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ K ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 2.39/2.81 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_Code_integer ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_numeral_minus_1_eq
% 2.39/2.81 thf(fact_4496_take__bit__numeral__minus__1__eq,axiom,
% 2.39/2.81 ! [K: num] :
% 2.39/2.81 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ K ) @ ( uminus_uminus_int @ one_one_int ) )
% 2.39/2.81 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_int ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_numeral_minus_1_eq
% 2.39/2.81 thf(fact_4497_stable__imp__take__bit__eq,axiom,
% 2.39/2.81 ! [A: code_integer,N: nat] :
% 2.39/2.81 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 2.39/2.81 = A )
% 2.39/2.81 => ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 2.39/2.81 => ( ( bit_se1745604003318907178nteger @ N @ A )
% 2.39/2.81 = zero_z3403309356797280102nteger ) )
% 2.39/2.81 & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 2.39/2.81 => ( ( bit_se1745604003318907178nteger @ N @ A )
% 2.39/2.81 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % stable_imp_take_bit_eq
% 2.39/2.81 thf(fact_4498_stable__imp__take__bit__eq,axiom,
% 2.39/2.81 ! [A: nat,N: nat] :
% 2.39/2.81 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.39/2.81 = A )
% 2.39/2.81 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 2.39/2.81 => ( ( bit_se2925701944663578781it_nat @ N @ A )
% 2.39/2.81 = zero_zero_nat ) )
% 2.39/2.81 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 2.39/2.81 => ( ( bit_se2925701944663578781it_nat @ N @ A )
% 2.39/2.81 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % stable_imp_take_bit_eq
% 2.39/2.81 thf(fact_4499_stable__imp__take__bit__eq,axiom,
% 2.39/2.81 ! [A: code_natural,N: nat] :
% 2.39/2.81 ( ( ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 2.39/2.81 = A )
% 2.39/2.81 => ( ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 2.39/2.81 => ( ( bit_se569199155075624693atural @ N @ A )
% 2.39/2.81 = zero_z2226904508553997617atural ) )
% 2.39/2.81 & ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 2.39/2.81 => ( ( bit_se569199155075624693atural @ N @ A )
% 2.39/2.81 = ( minus_7197305767214868737atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) @ one_one_Code_natural ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % stable_imp_take_bit_eq
% 2.39/2.81 thf(fact_4500_stable__imp__take__bit__eq,axiom,
% 2.39/2.81 ! [A: int,N: nat] :
% 2.39/2.81 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 2.39/2.81 = A )
% 2.39/2.81 => ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 2.39/2.81 => ( ( bit_se2923211474154528505it_int @ N @ A )
% 2.39/2.81 = zero_zero_int ) )
% 2.39/2.81 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 2.39/2.81 => ( ( bit_se2923211474154528505it_int @ N @ A )
% 2.39/2.81 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % stable_imp_take_bit_eq
% 2.39/2.81 thf(fact_4501_exp__div__exp__eq,axiom,
% 2.39/2.81 ! [M2: nat,N: nat] :
% 2.39/2.81 ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 2.39/2.81 = ( times_3573771949741848930nteger
% 2.39/2.81 @ ( zero_n356916108424825756nteger
% 2.39/2.81 @ ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 )
% 2.39/2.81 != zero_z3403309356797280102nteger )
% 2.39/2.81 & ( ord_less_eq_nat @ N @ M2 ) ) )
% 2.39/2.81 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M2 @ N ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % exp_div_exp_eq
% 2.39/2.81 thf(fact_4502_exp__div__exp__eq,axiom,
% 2.39/2.81 ! [M2: nat,N: nat] :
% 2.39/2.81 ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 2.39/2.81 = ( times_times_nat
% 2.39/2.81 @ ( zero_n2687167440665602831ol_nat
% 2.39/2.81 @ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 )
% 2.39/2.81 != zero_zero_nat )
% 2.39/2.81 & ( ord_less_eq_nat @ N @ M2 ) ) )
% 2.39/2.81 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M2 @ N ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % exp_div_exp_eq
% 2.39/2.81 thf(fact_4503_exp__div__exp__eq,axiom,
% 2.39/2.81 ! [M2: nat,N: nat] :
% 2.39/2.81 ( ( divide5121882707175180666atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M2 ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 2.39/2.81 = ( times_2397367101498566445atural
% 2.39/2.81 @ ( zero_n8403883297036319079atural
% 2.39/2.81 @ ( ( ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M2 )
% 2.39/2.81 != zero_z2226904508553997617atural )
% 2.39/2.81 & ( ord_less_eq_nat @ N @ M2 ) ) )
% 2.39/2.81 @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M2 @ N ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % exp_div_exp_eq
% 2.39/2.81 thf(fact_4504_exp__div__exp__eq,axiom,
% 2.39/2.81 ! [M2: nat,N: nat] :
% 2.39/2.81 ( ( divide_divide_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 2.39/2.81 = ( times_times_int
% 2.39/2.81 @ ( zero_n2684676970156552555ol_int
% 2.39/2.81 @ ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 )
% 2.39/2.81 != zero_zero_int )
% 2.39/2.81 & ( ord_less_eq_nat @ N @ M2 ) ) )
% 2.39/2.81 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M2 @ N ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % exp_div_exp_eq
% 2.39/2.81 thf(fact_4505_signed__take__bit__numeral__minus__bit1,axiom,
% 2.39/2.81 ! [L: num,K: num] :
% 2.39/2.81 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 2.39/2.81 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 2.39/2.81
% 2.39/2.81 % signed_take_bit_numeral_minus_bit1
% 2.39/2.81 thf(fact_4506_signed__take__bit__numeral__bit1,axiom,
% 2.39/2.81 ! [L: num,K: num] :
% 2.39/2.81 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 2.39/2.81 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 2.39/2.81
% 2.39/2.81 % signed_take_bit_numeral_bit1
% 2.39/2.81 thf(fact_4507_take__bit__numeral__minus__bit1,axiom,
% 2.39/2.81 ! [L: num,K: num] :
% 2.39/2.81 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 2.39/2.81 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_numeral_minus_bit1
% 2.39/2.81 thf(fact_4508_and__int_Osimps,axiom,
% 2.39/2.81 ( bit_se725231765392027082nd_int
% 2.39/2.81 = ( ^ [K4: int,L3: int] :
% 2.39/2.81 ( if_int
% 2.39/2.81 @ ( ( member_int2 @ K4 @ ( insert_int2 @ zero_zero_int @ ( insert_int2 @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 2.39/2.81 & ( member_int2 @ L3 @ ( insert_int2 @ zero_zero_int @ ( insert_int2 @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 2.39/2.81 @ ( uminus_uminus_int
% 2.39/2.81 @ ( zero_n2684676970156552555ol_int
% 2.39/2.81 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K4 )
% 2.39/2.81 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L3 ) ) ) )
% 2.39/2.81 @ ( plus_plus_int
% 2.39/2.81 @ ( zero_n2684676970156552555ol_int
% 2.39/2.81 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K4 )
% 2.39/2.81 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L3 ) ) )
% 2.39/2.81 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % and_int.simps
% 2.39/2.81 thf(fact_4509_and__int_Oelims,axiom,
% 2.39/2.81 ! [X: int,Xa: int,Y: int] :
% 2.39/2.81 ( ( ( bit_se725231765392027082nd_int @ X @ Xa )
% 2.39/2.81 = Y )
% 2.39/2.81 => ( ( ( ( member_int2 @ X @ ( insert_int2 @ zero_zero_int @ ( insert_int2 @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 2.39/2.81 & ( member_int2 @ Xa @ ( insert_int2 @ zero_zero_int @ ( insert_int2 @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 2.39/2.81 => ( Y
% 2.39/2.81 = ( uminus_uminus_int
% 2.39/2.81 @ ( zero_n2684676970156552555ol_int
% 2.39/2.81 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 2.39/2.81 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ) )
% 2.39/2.81 & ( ~ ( ( member_int2 @ X @ ( insert_int2 @ zero_zero_int @ ( insert_int2 @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 2.39/2.81 & ( member_int2 @ Xa @ ( insert_int2 @ zero_zero_int @ ( insert_int2 @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 2.39/2.81 => ( Y
% 2.39/2.81 = ( plus_plus_int
% 2.39/2.81 @ ( zero_n2684676970156552555ol_int
% 2.39/2.81 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 2.39/2.81 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) )
% 2.39/2.81 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % and_int.elims
% 2.39/2.81 thf(fact_4510_take__bit__numeral__bit1,axiom,
% 2.39/2.81 ! [L: num,K: num] :
% 2.39/2.81 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 2.39/2.81 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_numeral_bit1
% 2.39/2.81 thf(fact_4511_take__bit__numeral__bit1,axiom,
% 2.39/2.81 ! [L: num,K: num] :
% 2.39/2.81 ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ L ) @ ( numera6620942414471956472nteger @ ( bit1 @ K ) ) )
% 2.39/2.81 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ ( pred_numeral @ L ) @ ( numera6620942414471956472nteger @ K ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_numeral_bit1
% 2.39/2.81 thf(fact_4512_take__bit__numeral__bit1,axiom,
% 2.39/2.81 ! [L: num,K: num] :
% 2.39/2.81 ( ( bit_se569199155075624693atural @ ( numeral_numeral_nat @ L ) @ ( numera5444537566228673987atural @ ( bit1 @ K ) ) )
% 2.39/2.81 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( bit_se569199155075624693atural @ ( pred_numeral @ L ) @ ( numera5444537566228673987atural @ K ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ one_one_Code_natural ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_numeral_bit1
% 2.39/2.81 thf(fact_4513_take__bit__numeral__bit1,axiom,
% 2.39/2.81 ! [L: num,K: num] :
% 2.39/2.81 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 2.39/2.81 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_numeral_bit1
% 2.39/2.81 thf(fact_4514_upto__rec__numeral_I4_J,axiom,
% 2.39/2.81 ! [M2: num,N: num] :
% 2.39/2.81 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 2.39/2.81 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 2.39/2.81 = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 2.39/2.81 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 2.39/2.81 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 2.39/2.81 = nil_int ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % upto_rec_numeral(4)
% 2.39/2.81 thf(fact_4515_upto__rec__numeral_I3_J,axiom,
% 2.39/2.81 ! [M2: num,N: num] :
% 2.39/2.81 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) )
% 2.39/2.81 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) )
% 2.39/2.81 = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 2.39/2.81 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) )
% 2.39/2.81 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) )
% 2.39/2.81 = nil_int ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % upto_rec_numeral(3)
% 2.39/2.81 thf(fact_4516_Int__insert__right__if1,axiom,
% 2.39/2.81 ! [A: produc3658429121746597890et_nat > $o,A3: set_Pr4532377907799695533_nat_o,B3: set_Pr4532377907799695533_nat_o] :
% 2.39/2.81 ( ( member6576561426505652726_nat_o @ A @ A3 )
% 2.39/2.81 => ( ( inf_in1906310914598751387_nat_o @ A3 @ ( insert5175938949040314269_nat_o @ A @ B3 ) )
% 2.39/2.81 = ( insert5175938949040314269_nat_o @ A @ ( inf_in1906310914598751387_nat_o @ A3 @ B3 ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % Int_insert_right_if1
% 2.39/2.81 thf(fact_4517_Int__insert__right__if1,axiom,
% 2.39/2.81 ! [A: int,A3: set_int,B3: set_int] :
% 2.39/2.81 ( ( member_int2 @ A @ A3 )
% 2.39/2.81 => ( ( inf_inf_set_int @ A3 @ ( insert_int2 @ A @ B3 ) )
% 2.39/2.81 = ( insert_int2 @ A @ ( inf_inf_set_int @ A3 @ B3 ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % Int_insert_right_if1
% 2.39/2.81 thf(fact_4518_Int__insert__right__if1,axiom,
% 2.39/2.81 ! [A: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.81 ( ( member8440522571783428010at_nat @ A @ A3 )
% 2.39/2.81 => ( ( inf_in2572325071724192079at_nat @ A3 @ ( insert8211810215607154385at_nat @ A @ B3 ) )
% 2.39/2.81 = ( insert8211810215607154385at_nat @ A @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % Int_insert_right_if1
% 2.39/2.81 thf(fact_4519_Int__insert__right__if1,axiom,
% 2.39/2.81 ! [A: nat,A3: set_nat,B3: set_nat] :
% 2.39/2.81 ( ( member_nat2 @ A @ A3 )
% 2.39/2.81 => ( ( inf_inf_set_nat @ A3 @ ( insert_nat2 @ A @ B3 ) )
% 2.39/2.81 = ( insert_nat2 @ A @ ( inf_inf_set_nat @ A3 @ B3 ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % Int_insert_right_if1
% 2.39/2.81 thf(fact_4520_Int__insert__right__if0,axiom,
% 2.39/2.81 ! [A: produc3658429121746597890et_nat > $o,A3: set_Pr4532377907799695533_nat_o,B3: set_Pr4532377907799695533_nat_o] :
% 2.39/2.81 ( ~ ( member6576561426505652726_nat_o @ A @ A3 )
% 2.39/2.81 => ( ( inf_in1906310914598751387_nat_o @ A3 @ ( insert5175938949040314269_nat_o @ A @ B3 ) )
% 2.39/2.81 = ( inf_in1906310914598751387_nat_o @ A3 @ B3 ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % Int_insert_right_if0
% 2.39/2.81 thf(fact_4521_Int__insert__right__if0,axiom,
% 2.39/2.81 ! [A: int,A3: set_int,B3: set_int] :
% 2.39/2.81 ( ~ ( member_int2 @ A @ A3 )
% 2.39/2.81 => ( ( inf_inf_set_int @ A3 @ ( insert_int2 @ A @ B3 ) )
% 2.39/2.81 = ( inf_inf_set_int @ A3 @ B3 ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % Int_insert_right_if0
% 2.39/2.81 thf(fact_4522_Int__insert__right__if0,axiom,
% 2.39/2.81 ! [A: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.81 ( ~ ( member8440522571783428010at_nat @ A @ A3 )
% 2.39/2.81 => ( ( inf_in2572325071724192079at_nat @ A3 @ ( insert8211810215607154385at_nat @ A @ B3 ) )
% 2.39/2.81 = ( inf_in2572325071724192079at_nat @ A3 @ B3 ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % Int_insert_right_if0
% 2.39/2.81 thf(fact_4523_Int__insert__right__if0,axiom,
% 2.39/2.81 ! [A: nat,A3: set_nat,B3: set_nat] :
% 2.39/2.81 ( ~ ( member_nat2 @ A @ A3 )
% 2.39/2.81 => ( ( inf_inf_set_nat @ A3 @ ( insert_nat2 @ A @ B3 ) )
% 2.39/2.81 = ( inf_inf_set_nat @ A3 @ B3 ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % Int_insert_right_if0
% 2.39/2.81 thf(fact_4524_insert__inter__insert,axiom,
% 2.39/2.81 ! [A: int,A3: set_int,B3: set_int] :
% 2.39/2.81 ( ( inf_inf_set_int @ ( insert_int2 @ A @ A3 ) @ ( insert_int2 @ A @ B3 ) )
% 2.39/2.81 = ( insert_int2 @ A @ ( inf_inf_set_int @ A3 @ B3 ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % insert_inter_insert
% 2.39/2.81 thf(fact_4525_insert__inter__insert,axiom,
% 2.39/2.81 ! [A: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.81 ( ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A @ A3 ) @ ( insert8211810215607154385at_nat @ A @ B3 ) )
% 2.39/2.81 = ( insert8211810215607154385at_nat @ A @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % insert_inter_insert
% 2.39/2.81 thf(fact_4526_insert__inter__insert,axiom,
% 2.39/2.81 ! [A: nat,A3: set_nat,B3: set_nat] :
% 2.39/2.81 ( ( inf_inf_set_nat @ ( insert_nat2 @ A @ A3 ) @ ( insert_nat2 @ A @ B3 ) )
% 2.39/2.81 = ( insert_nat2 @ A @ ( inf_inf_set_nat @ A3 @ B3 ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % insert_inter_insert
% 2.39/2.81 thf(fact_4527_Int__insert__left__if1,axiom,
% 2.39/2.81 ! [A: produc3658429121746597890et_nat > $o,C2: set_Pr4532377907799695533_nat_o,B3: set_Pr4532377907799695533_nat_o] :
% 2.39/2.81 ( ( member6576561426505652726_nat_o @ A @ C2 )
% 2.39/2.81 => ( ( inf_in1906310914598751387_nat_o @ ( insert5175938949040314269_nat_o @ A @ B3 ) @ C2 )
% 2.39/2.81 = ( insert5175938949040314269_nat_o @ A @ ( inf_in1906310914598751387_nat_o @ B3 @ C2 ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % Int_insert_left_if1
% 2.39/2.81 thf(fact_4528_Int__insert__left__if1,axiom,
% 2.39/2.81 ! [A: int,C2: set_int,B3: set_int] :
% 2.39/2.81 ( ( member_int2 @ A @ C2 )
% 2.39/2.81 => ( ( inf_inf_set_int @ ( insert_int2 @ A @ B3 ) @ C2 )
% 2.39/2.81 = ( insert_int2 @ A @ ( inf_inf_set_int @ B3 @ C2 ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % Int_insert_left_if1
% 2.39/2.81 thf(fact_4529_Int__insert__left__if1,axiom,
% 2.39/2.81 ! [A: product_prod_nat_nat,C2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.81 ( ( member8440522571783428010at_nat @ A @ C2 )
% 2.39/2.81 => ( ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A @ B3 ) @ C2 )
% 2.39/2.81 = ( insert8211810215607154385at_nat @ A @ ( inf_in2572325071724192079at_nat @ B3 @ C2 ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % Int_insert_left_if1
% 2.39/2.81 thf(fact_4530_Int__insert__left__if1,axiom,
% 2.39/2.81 ! [A: nat,C2: set_nat,B3: set_nat] :
% 2.39/2.81 ( ( member_nat2 @ A @ C2 )
% 2.39/2.81 => ( ( inf_inf_set_nat @ ( insert_nat2 @ A @ B3 ) @ C2 )
% 2.39/2.81 = ( insert_nat2 @ A @ ( inf_inf_set_nat @ B3 @ C2 ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % Int_insert_left_if1
% 2.39/2.81 thf(fact_4531_Int__insert__left__if0,axiom,
% 2.39/2.81 ! [A: produc3658429121746597890et_nat > $o,C2: set_Pr4532377907799695533_nat_o,B3: set_Pr4532377907799695533_nat_o] :
% 2.39/2.81 ( ~ ( member6576561426505652726_nat_o @ A @ C2 )
% 2.39/2.81 => ( ( inf_in1906310914598751387_nat_o @ ( insert5175938949040314269_nat_o @ A @ B3 ) @ C2 )
% 2.39/2.81 = ( inf_in1906310914598751387_nat_o @ B3 @ C2 ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % Int_insert_left_if0
% 2.39/2.81 thf(fact_4532_Int__insert__left__if0,axiom,
% 2.39/2.81 ! [A: int,C2: set_int,B3: set_int] :
% 2.39/2.81 ( ~ ( member_int2 @ A @ C2 )
% 2.39/2.81 => ( ( inf_inf_set_int @ ( insert_int2 @ A @ B3 ) @ C2 )
% 2.39/2.81 = ( inf_inf_set_int @ B3 @ C2 ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % Int_insert_left_if0
% 2.39/2.81 thf(fact_4533_Int__insert__left__if0,axiom,
% 2.39/2.81 ! [A: product_prod_nat_nat,C2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.81 ( ~ ( member8440522571783428010at_nat @ A @ C2 )
% 2.39/2.81 => ( ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A @ B3 ) @ C2 )
% 2.39/2.81 = ( inf_in2572325071724192079at_nat @ B3 @ C2 ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % Int_insert_left_if0
% 2.39/2.81 thf(fact_4534_Int__insert__left__if0,axiom,
% 2.39/2.81 ! [A: nat,C2: set_nat,B3: set_nat] :
% 2.39/2.81 ( ~ ( member_nat2 @ A @ C2 )
% 2.39/2.81 => ( ( inf_inf_set_nat @ ( insert_nat2 @ A @ B3 ) @ C2 )
% 2.39/2.81 = ( inf_inf_set_nat @ B3 @ C2 ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % Int_insert_left_if0
% 2.39/2.81 thf(fact_4535_insert__disjoint_I1_J,axiom,
% 2.39/2.81 ! [A: produc3658429121746597890et_nat > $o,A3: set_Pr4532377907799695533_nat_o,B3: set_Pr4532377907799695533_nat_o] :
% 2.39/2.81 ( ( ( inf_in1906310914598751387_nat_o @ ( insert5175938949040314269_nat_o @ A @ A3 ) @ B3 )
% 2.39/2.81 = bot_bo7824918357723582233_nat_o )
% 2.39/2.81 = ( ~ ( member6576561426505652726_nat_o @ A @ B3 )
% 2.39/2.81 & ( ( inf_in1906310914598751387_nat_o @ A3 @ B3 )
% 2.39/2.81 = bot_bo7824918357723582233_nat_o ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % insert_disjoint(1)
% 2.39/2.81 thf(fact_4536_insert__disjoint_I1_J,axiom,
% 2.39/2.81 ! [A: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.81 ( ( ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A @ A3 ) @ B3 )
% 2.39/2.81 = bot_bo2099793752762293965at_nat )
% 2.39/2.81 = ( ~ ( member8440522571783428010at_nat @ A @ B3 )
% 2.39/2.81 & ( ( inf_in2572325071724192079at_nat @ A3 @ B3 )
% 2.39/2.81 = bot_bo2099793752762293965at_nat ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % insert_disjoint(1)
% 2.39/2.81 thf(fact_4537_insert__disjoint_I1_J,axiom,
% 2.39/2.81 ! [A: nat,A3: set_nat,B3: set_nat] :
% 2.39/2.81 ( ( ( inf_inf_set_nat @ ( insert_nat2 @ A @ A3 ) @ B3 )
% 2.39/2.81 = bot_bot_set_nat )
% 2.39/2.81 = ( ~ ( member_nat2 @ A @ B3 )
% 2.39/2.81 & ( ( inf_inf_set_nat @ A3 @ B3 )
% 2.39/2.81 = bot_bot_set_nat ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % insert_disjoint(1)
% 2.39/2.81 thf(fact_4538_insert__disjoint_I1_J,axiom,
% 2.39/2.81 ! [A: int,A3: set_int,B3: set_int] :
% 2.39/2.81 ( ( ( inf_inf_set_int @ ( insert_int2 @ A @ A3 ) @ B3 )
% 2.39/2.81 = bot_bot_set_int )
% 2.39/2.81 = ( ~ ( member_int2 @ A @ B3 )
% 2.39/2.81 & ( ( inf_inf_set_int @ A3 @ B3 )
% 2.39/2.81 = bot_bot_set_int ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % insert_disjoint(1)
% 2.39/2.81 thf(fact_4539_insert__disjoint_I2_J,axiom,
% 2.39/2.81 ! [A: produc3658429121746597890et_nat > $o,A3: set_Pr4532377907799695533_nat_o,B3: set_Pr4532377907799695533_nat_o] :
% 2.39/2.81 ( ( bot_bo7824918357723582233_nat_o
% 2.39/2.81 = ( inf_in1906310914598751387_nat_o @ ( insert5175938949040314269_nat_o @ A @ A3 ) @ B3 ) )
% 2.39/2.81 = ( ~ ( member6576561426505652726_nat_o @ A @ B3 )
% 2.39/2.81 & ( bot_bo7824918357723582233_nat_o
% 2.39/2.81 = ( inf_in1906310914598751387_nat_o @ A3 @ B3 ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % insert_disjoint(2)
% 2.39/2.81 thf(fact_4540_insert__disjoint_I2_J,axiom,
% 2.39/2.81 ! [A: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.81 ( ( bot_bo2099793752762293965at_nat
% 2.39/2.81 = ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A @ A3 ) @ B3 ) )
% 2.39/2.81 = ( ~ ( member8440522571783428010at_nat @ A @ B3 )
% 2.39/2.81 & ( bot_bo2099793752762293965at_nat
% 2.39/2.81 = ( inf_in2572325071724192079at_nat @ A3 @ B3 ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % insert_disjoint(2)
% 2.39/2.81 thf(fact_4541_insert__disjoint_I2_J,axiom,
% 2.39/2.81 ! [A: nat,A3: set_nat,B3: set_nat] :
% 2.39/2.81 ( ( bot_bot_set_nat
% 2.39/2.81 = ( inf_inf_set_nat @ ( insert_nat2 @ A @ A3 ) @ B3 ) )
% 2.39/2.81 = ( ~ ( member_nat2 @ A @ B3 )
% 2.39/2.81 & ( bot_bot_set_nat
% 2.39/2.81 = ( inf_inf_set_nat @ A3 @ B3 ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % insert_disjoint(2)
% 2.39/2.81 thf(fact_4542_insert__disjoint_I2_J,axiom,
% 2.39/2.81 ! [A: int,A3: set_int,B3: set_int] :
% 2.39/2.81 ( ( bot_bot_set_int
% 2.39/2.81 = ( inf_inf_set_int @ ( insert_int2 @ A @ A3 ) @ B3 ) )
% 2.39/2.81 = ( ~ ( member_int2 @ A @ B3 )
% 2.39/2.81 & ( bot_bot_set_int
% 2.39/2.81 = ( inf_inf_set_int @ A3 @ B3 ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % insert_disjoint(2)
% 2.39/2.81 thf(fact_4543_disjoint__insert_I1_J,axiom,
% 2.39/2.81 ! [B3: set_Pr4532377907799695533_nat_o,A: produc3658429121746597890et_nat > $o,A3: set_Pr4532377907799695533_nat_o] :
% 2.39/2.81 ( ( ( inf_in1906310914598751387_nat_o @ B3 @ ( insert5175938949040314269_nat_o @ A @ A3 ) )
% 2.39/2.81 = bot_bo7824918357723582233_nat_o )
% 2.39/2.81 = ( ~ ( member6576561426505652726_nat_o @ A @ B3 )
% 2.39/2.81 & ( ( inf_in1906310914598751387_nat_o @ B3 @ A3 )
% 2.39/2.81 = bot_bo7824918357723582233_nat_o ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % disjoint_insert(1)
% 2.39/2.81 thf(fact_4544_disjoint__insert_I1_J,axiom,
% 2.39/2.81 ! [B3: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat] :
% 2.39/2.81 ( ( ( inf_in2572325071724192079at_nat @ B3 @ ( insert8211810215607154385at_nat @ A @ A3 ) )
% 2.39/2.81 = bot_bo2099793752762293965at_nat )
% 2.39/2.81 = ( ~ ( member8440522571783428010at_nat @ A @ B3 )
% 2.39/2.81 & ( ( inf_in2572325071724192079at_nat @ B3 @ A3 )
% 2.39/2.81 = bot_bo2099793752762293965at_nat ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % disjoint_insert(1)
% 2.39/2.81 thf(fact_4545_disjoint__insert_I1_J,axiom,
% 2.39/2.81 ! [B3: set_nat,A: nat,A3: set_nat] :
% 2.39/2.81 ( ( ( inf_inf_set_nat @ B3 @ ( insert_nat2 @ A @ A3 ) )
% 2.39/2.81 = bot_bot_set_nat )
% 2.39/2.81 = ( ~ ( member_nat2 @ A @ B3 )
% 2.39/2.81 & ( ( inf_inf_set_nat @ B3 @ A3 )
% 2.39/2.81 = bot_bot_set_nat ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % disjoint_insert(1)
% 2.39/2.81 thf(fact_4546_disjoint__insert_I1_J,axiom,
% 2.39/2.81 ! [B3: set_int,A: int,A3: set_int] :
% 2.39/2.81 ( ( ( inf_inf_set_int @ B3 @ ( insert_int2 @ A @ A3 ) )
% 2.39/2.81 = bot_bot_set_int )
% 2.39/2.81 = ( ~ ( member_int2 @ A @ B3 )
% 2.39/2.81 & ( ( inf_inf_set_int @ B3 @ A3 )
% 2.39/2.81 = bot_bot_set_int ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % disjoint_insert(1)
% 2.39/2.81 thf(fact_4547_disjoint__insert_I2_J,axiom,
% 2.39/2.81 ! [A3: set_Pr4532377907799695533_nat_o,B: produc3658429121746597890et_nat > $o,B3: set_Pr4532377907799695533_nat_o] :
% 2.39/2.81 ( ( bot_bo7824918357723582233_nat_o
% 2.39/2.81 = ( inf_in1906310914598751387_nat_o @ A3 @ ( insert5175938949040314269_nat_o @ B @ B3 ) ) )
% 2.39/2.81 = ( ~ ( member6576561426505652726_nat_o @ B @ A3 )
% 2.39/2.81 & ( bot_bo7824918357723582233_nat_o
% 2.39/2.81 = ( inf_in1906310914598751387_nat_o @ A3 @ B3 ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % disjoint_insert(2)
% 2.39/2.81 thf(fact_4548_disjoint__insert_I2_J,axiom,
% 2.39/2.81 ! [A3: set_Pr1261947904930325089at_nat,B: product_prod_nat_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.81 ( ( bot_bo2099793752762293965at_nat
% 2.39/2.81 = ( inf_in2572325071724192079at_nat @ A3 @ ( insert8211810215607154385at_nat @ B @ B3 ) ) )
% 2.39/2.81 = ( ~ ( member8440522571783428010at_nat @ B @ A3 )
% 2.39/2.81 & ( bot_bo2099793752762293965at_nat
% 2.39/2.81 = ( inf_in2572325071724192079at_nat @ A3 @ B3 ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % disjoint_insert(2)
% 2.39/2.81 thf(fact_4549_disjoint__insert_I2_J,axiom,
% 2.39/2.81 ! [A3: set_nat,B: nat,B3: set_nat] :
% 2.39/2.81 ( ( bot_bot_set_nat
% 2.39/2.81 = ( inf_inf_set_nat @ A3 @ ( insert_nat2 @ B @ B3 ) ) )
% 2.39/2.81 = ( ~ ( member_nat2 @ B @ A3 )
% 2.39/2.81 & ( bot_bot_set_nat
% 2.39/2.81 = ( inf_inf_set_nat @ A3 @ B3 ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % disjoint_insert(2)
% 2.39/2.81 thf(fact_4550_disjoint__insert_I2_J,axiom,
% 2.39/2.81 ! [A3: set_int,B: int,B3: set_int] :
% 2.39/2.81 ( ( bot_bot_set_int
% 2.39/2.81 = ( inf_inf_set_int @ A3 @ ( insert_int2 @ B @ B3 ) ) )
% 2.39/2.81 = ( ~ ( member_int2 @ B @ A3 )
% 2.39/2.81 & ( bot_bot_set_int
% 2.39/2.81 = ( inf_inf_set_int @ A3 @ B3 ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % disjoint_insert(2)
% 2.39/2.81 thf(fact_4551_upto__Nil,axiom,
% 2.39/2.81 ! [I2: int,J: int] :
% 2.39/2.81 ( ( ( upto @ I2 @ J )
% 2.39/2.81 = nil_int )
% 2.39/2.81 = ( ord_less_int @ J @ I2 ) ) ).
% 2.39/2.81
% 2.39/2.81 % upto_Nil
% 2.39/2.81 thf(fact_4552_upto__Nil2,axiom,
% 2.39/2.81 ! [I2: int,J: int] :
% 2.39/2.81 ( ( nil_int
% 2.39/2.81 = ( upto @ I2 @ J ) )
% 2.39/2.81 = ( ord_less_int @ J @ I2 ) ) ).
% 2.39/2.81
% 2.39/2.81 % upto_Nil2
% 2.39/2.81 thf(fact_4553_upto__empty,axiom,
% 2.39/2.81 ! [J: int,I2: int] :
% 2.39/2.81 ( ( ord_less_int @ J @ I2 )
% 2.39/2.81 => ( ( upto @ I2 @ J )
% 2.39/2.81 = nil_int ) ) ).
% 2.39/2.81
% 2.39/2.81 % upto_empty
% 2.39/2.81 thf(fact_4554_upto__single,axiom,
% 2.39/2.81 ! [I2: int] :
% 2.39/2.81 ( ( upto @ I2 @ I2 )
% 2.39/2.81 = ( cons_int @ I2 @ nil_int ) ) ).
% 2.39/2.81
% 2.39/2.81 % upto_single
% 2.39/2.81 thf(fact_4555_and__nat__numerals_I2_J,axiom,
% 2.39/2.81 ! [Y: num] :
% 2.39/2.81 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 2.39/2.81 = one_one_nat ) ).
% 2.39/2.81
% 2.39/2.81 % and_nat_numerals(2)
% 2.39/2.81 thf(fact_4556_and__nat__numerals_I4_J,axiom,
% 2.39/2.81 ! [X: num] :
% 2.39/2.81 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 2.39/2.81 = one_one_nat ) ).
% 2.39/2.81
% 2.39/2.81 % and_nat_numerals(4)
% 2.39/2.81 thf(fact_4557_upto__rec__numeral_I1_J,axiom,
% 2.39/2.81 ! [M2: num,N: num] :
% 2.39/2.81 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) )
% 2.39/2.81 => ( ( upto @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) )
% 2.39/2.81 = ( cons_int @ ( numeral_numeral_int @ M2 ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M2 ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 2.39/2.81 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) )
% 2.39/2.81 => ( ( upto @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) )
% 2.39/2.81 = nil_int ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % upto_rec_numeral(1)
% 2.39/2.81 thf(fact_4558_upto__rec__numeral_I2_J,axiom,
% 2.39/2.81 ! [M2: num,N: num] :
% 2.39/2.81 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 2.39/2.81 => ( ( upto @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 2.39/2.81 = ( cons_int @ ( numeral_numeral_int @ M2 ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M2 ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 2.39/2.81 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 2.39/2.81 => ( ( upto @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 2.39/2.81 = nil_int ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % upto_rec_numeral(2)
% 2.39/2.81 thf(fact_4559_Int__insert__right,axiom,
% 2.39/2.81 ! [A: produc3658429121746597890et_nat > $o,A3: set_Pr4532377907799695533_nat_o,B3: set_Pr4532377907799695533_nat_o] :
% 2.39/2.81 ( ( ( member6576561426505652726_nat_o @ A @ A3 )
% 2.39/2.81 => ( ( inf_in1906310914598751387_nat_o @ A3 @ ( insert5175938949040314269_nat_o @ A @ B3 ) )
% 2.39/2.81 = ( insert5175938949040314269_nat_o @ A @ ( inf_in1906310914598751387_nat_o @ A3 @ B3 ) ) ) )
% 2.39/2.81 & ( ~ ( member6576561426505652726_nat_o @ A @ A3 )
% 2.39/2.81 => ( ( inf_in1906310914598751387_nat_o @ A3 @ ( insert5175938949040314269_nat_o @ A @ B3 ) )
% 2.39/2.81 = ( inf_in1906310914598751387_nat_o @ A3 @ B3 ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % Int_insert_right
% 2.39/2.81 thf(fact_4560_Int__insert__right,axiom,
% 2.39/2.81 ! [A: int,A3: set_int,B3: set_int] :
% 2.39/2.81 ( ( ( member_int2 @ A @ A3 )
% 2.39/2.81 => ( ( inf_inf_set_int @ A3 @ ( insert_int2 @ A @ B3 ) )
% 2.39/2.81 = ( insert_int2 @ A @ ( inf_inf_set_int @ A3 @ B3 ) ) ) )
% 2.39/2.81 & ( ~ ( member_int2 @ A @ A3 )
% 2.39/2.81 => ( ( inf_inf_set_int @ A3 @ ( insert_int2 @ A @ B3 ) )
% 2.39/2.81 = ( inf_inf_set_int @ A3 @ B3 ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % Int_insert_right
% 2.39/2.81 thf(fact_4561_Int__insert__right,axiom,
% 2.39/2.81 ! [A: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.81 ( ( ( member8440522571783428010at_nat @ A @ A3 )
% 2.39/2.81 => ( ( inf_in2572325071724192079at_nat @ A3 @ ( insert8211810215607154385at_nat @ A @ B3 ) )
% 2.39/2.81 = ( insert8211810215607154385at_nat @ A @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) ) ) )
% 2.39/2.81 & ( ~ ( member8440522571783428010at_nat @ A @ A3 )
% 2.39/2.81 => ( ( inf_in2572325071724192079at_nat @ A3 @ ( insert8211810215607154385at_nat @ A @ B3 ) )
% 2.39/2.81 = ( inf_in2572325071724192079at_nat @ A3 @ B3 ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % Int_insert_right
% 2.39/2.81 thf(fact_4562_Int__insert__right,axiom,
% 2.39/2.81 ! [A: nat,A3: set_nat,B3: set_nat] :
% 2.39/2.81 ( ( ( member_nat2 @ A @ A3 )
% 2.39/2.81 => ( ( inf_inf_set_nat @ A3 @ ( insert_nat2 @ A @ B3 ) )
% 2.39/2.81 = ( insert_nat2 @ A @ ( inf_inf_set_nat @ A3 @ B3 ) ) ) )
% 2.39/2.81 & ( ~ ( member_nat2 @ A @ A3 )
% 2.39/2.81 => ( ( inf_inf_set_nat @ A3 @ ( insert_nat2 @ A @ B3 ) )
% 2.39/2.81 = ( inf_inf_set_nat @ A3 @ B3 ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % Int_insert_right
% 2.39/2.81 thf(fact_4563_Int__insert__left,axiom,
% 2.39/2.81 ! [A: produc3658429121746597890et_nat > $o,C2: set_Pr4532377907799695533_nat_o,B3: set_Pr4532377907799695533_nat_o] :
% 2.39/2.81 ( ( ( member6576561426505652726_nat_o @ A @ C2 )
% 2.39/2.81 => ( ( inf_in1906310914598751387_nat_o @ ( insert5175938949040314269_nat_o @ A @ B3 ) @ C2 )
% 2.39/2.81 = ( insert5175938949040314269_nat_o @ A @ ( inf_in1906310914598751387_nat_o @ B3 @ C2 ) ) ) )
% 2.39/2.81 & ( ~ ( member6576561426505652726_nat_o @ A @ C2 )
% 2.39/2.81 => ( ( inf_in1906310914598751387_nat_o @ ( insert5175938949040314269_nat_o @ A @ B3 ) @ C2 )
% 2.39/2.81 = ( inf_in1906310914598751387_nat_o @ B3 @ C2 ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % Int_insert_left
% 2.39/2.81 thf(fact_4564_Int__insert__left,axiom,
% 2.39/2.81 ! [A: int,C2: set_int,B3: set_int] :
% 2.39/2.81 ( ( ( member_int2 @ A @ C2 )
% 2.39/2.81 => ( ( inf_inf_set_int @ ( insert_int2 @ A @ B3 ) @ C2 )
% 2.39/2.81 = ( insert_int2 @ A @ ( inf_inf_set_int @ B3 @ C2 ) ) ) )
% 2.39/2.81 & ( ~ ( member_int2 @ A @ C2 )
% 2.39/2.81 => ( ( inf_inf_set_int @ ( insert_int2 @ A @ B3 ) @ C2 )
% 2.39/2.81 = ( inf_inf_set_int @ B3 @ C2 ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % Int_insert_left
% 2.39/2.81 thf(fact_4565_Int__insert__left,axiom,
% 2.39/2.81 ! [A: product_prod_nat_nat,C2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 2.39/2.81 ( ( ( member8440522571783428010at_nat @ A @ C2 )
% 2.39/2.81 => ( ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A @ B3 ) @ C2 )
% 2.39/2.81 = ( insert8211810215607154385at_nat @ A @ ( inf_in2572325071724192079at_nat @ B3 @ C2 ) ) ) )
% 2.39/2.81 & ( ~ ( member8440522571783428010at_nat @ A @ C2 )
% 2.39/2.81 => ( ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A @ B3 ) @ C2 )
% 2.39/2.81 = ( inf_in2572325071724192079at_nat @ B3 @ C2 ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % Int_insert_left
% 2.39/2.81 thf(fact_4566_Int__insert__left,axiom,
% 2.39/2.81 ! [A: nat,C2: set_nat,B3: set_nat] :
% 2.39/2.81 ( ( ( member_nat2 @ A @ C2 )
% 2.39/2.81 => ( ( inf_inf_set_nat @ ( insert_nat2 @ A @ B3 ) @ C2 )
% 2.39/2.81 = ( insert_nat2 @ A @ ( inf_inf_set_nat @ B3 @ C2 ) ) ) )
% 2.39/2.81 & ( ~ ( member_nat2 @ A @ C2 )
% 2.39/2.81 => ( ( inf_inf_set_nat @ ( insert_nat2 @ A @ B3 ) @ C2 )
% 2.39/2.81 = ( inf_inf_set_nat @ B3 @ C2 ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % Int_insert_left
% 2.39/2.81 thf(fact_4567_upto__code,axiom,
% 2.39/2.81 ( upto
% 2.39/2.81 = ( ^ [I4: int,J2: int] : ( upto_aux @ I4 @ J2 @ nil_int ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % upto_code
% 2.39/2.81 thf(fact_4568_pred__numeral__def,axiom,
% 2.39/2.81 ( pred_numeral
% 2.39/2.81 = ( ^ [K4: num] : ( minus_minus_nat @ ( numeral_numeral_nat @ K4 ) @ one_one_nat ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % pred_numeral_def
% 2.39/2.81 thf(fact_4569_upto_Oelims,axiom,
% 2.39/2.81 ! [X: int,Xa: int,Y: list_int] :
% 2.39/2.81 ( ( ( upto @ X @ Xa )
% 2.39/2.81 = Y )
% 2.39/2.81 => ( ( ( ord_less_eq_int @ X @ Xa )
% 2.39/2.81 => ( Y
% 2.39/2.81 = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa ) ) ) )
% 2.39/2.81 & ( ~ ( ord_less_eq_int @ X @ Xa )
% 2.39/2.81 => ( Y = nil_int ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % upto.elims
% 2.39/2.81 thf(fact_4570_upto_Osimps,axiom,
% 2.39/2.81 ( upto
% 2.39/2.81 = ( ^ [I4: int,J2: int] : ( if_list_int @ ( ord_less_eq_int @ I4 @ J2 ) @ ( cons_int @ I4 @ ( upto @ ( plus_plus_int @ I4 @ one_one_int ) @ J2 ) ) @ nil_int ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % upto.simps
% 2.39/2.81 thf(fact_4571_upto__rec1,axiom,
% 2.39/2.81 ! [I2: int,J: int] :
% 2.39/2.81 ( ( ord_less_eq_int @ I2 @ J )
% 2.39/2.81 => ( ( upto @ I2 @ J )
% 2.39/2.81 = ( cons_int @ I2 @ ( upto @ ( plus_plus_int @ I2 @ one_one_int ) @ J ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % upto_rec1
% 2.39/2.81 thf(fact_4572_take__bit__numeral__bit0,axiom,
% 2.39/2.81 ! [L: num,K: num] :
% 2.39/2.81 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 2.39/2.81 = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_numeral_bit0
% 2.39/2.81 thf(fact_4573_take__bit__numeral__bit0,axiom,
% 2.39/2.81 ! [L: num,K: num] :
% 2.39/2.81 ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ L ) @ ( numera6620942414471956472nteger @ ( bit0 @ K ) ) )
% 2.39/2.81 = ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ ( pred_numeral @ L ) @ ( numera6620942414471956472nteger @ K ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_numeral_bit0
% 2.39/2.81 thf(fact_4574_take__bit__numeral__bit0,axiom,
% 2.39/2.81 ! [L: num,K: num] :
% 2.39/2.81 ( ( bit_se569199155075624693atural @ ( numeral_numeral_nat @ L ) @ ( numera5444537566228673987atural @ ( bit0 @ K ) ) )
% 2.39/2.81 = ( times_2397367101498566445atural @ ( bit_se569199155075624693atural @ ( pred_numeral @ L ) @ ( numera5444537566228673987atural @ K ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_numeral_bit0
% 2.39/2.81 thf(fact_4575_take__bit__numeral__bit0,axiom,
% 2.39/2.81 ! [L: num,K: num] :
% 2.39/2.81 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 2.39/2.81 = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_numeral_bit0
% 2.39/2.81 thf(fact_4576_and__int_Opsimps,axiom,
% 2.39/2.81 ! [K: int,L: int] :
% 2.39/2.81 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L ) )
% 2.39/2.81 => ( ( ( ( member_int2 @ K @ ( insert_int2 @ zero_zero_int @ ( insert_int2 @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 2.39/2.81 & ( member_int2 @ L @ ( insert_int2 @ zero_zero_int @ ( insert_int2 @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 2.39/2.81 => ( ( bit_se725231765392027082nd_int @ K @ L )
% 2.39/2.81 = ( uminus_uminus_int
% 2.39/2.81 @ ( zero_n2684676970156552555ol_int
% 2.39/2.81 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 2.39/2.81 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ) ) )
% 2.39/2.81 & ( ~ ( ( member_int2 @ K @ ( insert_int2 @ zero_zero_int @ ( insert_int2 @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 2.39/2.81 & ( member_int2 @ L @ ( insert_int2 @ zero_zero_int @ ( insert_int2 @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 2.39/2.81 => ( ( bit_se725231765392027082nd_int @ K @ L )
% 2.39/2.81 = ( plus_plus_int
% 2.39/2.81 @ ( zero_n2684676970156552555ol_int
% 2.39/2.81 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 2.39/2.81 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 2.39/2.81 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % and_int.psimps
% 2.39/2.81 thf(fact_4577_and__int_Opelims,axiom,
% 2.39/2.81 ! [X: int,Xa: int,Y: int] :
% 2.39/2.81 ( ( ( bit_se725231765392027082nd_int @ X @ Xa )
% 2.39/2.81 = Y )
% 2.39/2.81 => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa ) )
% 2.39/2.81 => ~ ( ( ( ( ( member_int2 @ X @ ( insert_int2 @ zero_zero_int @ ( insert_int2 @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 2.39/2.81 & ( member_int2 @ Xa @ ( insert_int2 @ zero_zero_int @ ( insert_int2 @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 2.39/2.81 => ( Y
% 2.39/2.81 = ( uminus_uminus_int
% 2.39/2.81 @ ( zero_n2684676970156552555ol_int
% 2.39/2.81 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 2.39/2.81 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ) )
% 2.39/2.81 & ( ~ ( ( member_int2 @ X @ ( insert_int2 @ zero_zero_int @ ( insert_int2 @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 2.39/2.81 & ( member_int2 @ Xa @ ( insert_int2 @ zero_zero_int @ ( insert_int2 @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 2.39/2.81 => ( Y
% 2.39/2.81 = ( plus_plus_int
% 2.39/2.81 @ ( zero_n2684676970156552555ol_int
% 2.39/2.81 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 2.39/2.81 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) )
% 2.39/2.81 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 2.39/2.81 => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % and_int.pelims
% 2.39/2.81 thf(fact_4578_mask__numeral,axiom,
% 2.39/2.81 ! [N: num] :
% 2.39/2.81 ( ( bit_se2119862282449309892nteger @ ( numeral_numeral_nat @ N ) )
% 2.39/2.81 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2119862282449309892nteger @ ( pred_numeral @ N ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % mask_numeral
% 2.39/2.81 thf(fact_4579_mask__numeral,axiom,
% 2.39/2.81 ! [N: num] :
% 2.39/2.81 ( ( bit_se943457434206027407atural @ ( numeral_numeral_nat @ N ) )
% 2.39/2.81 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se943457434206027407atural @ ( pred_numeral @ N ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % mask_numeral
% 2.39/2.81 thf(fact_4580_mask__numeral,axiom,
% 2.39/2.81 ! [N: num] :
% 2.39/2.81 ( ( bit_se2000444600071755411sk_int @ ( numeral_numeral_nat @ N ) )
% 2.39/2.81 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ ( pred_numeral @ N ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % mask_numeral
% 2.39/2.81 thf(fact_4581_mask__numeral,axiom,
% 2.39/2.81 ! [N: num] :
% 2.39/2.81 ( ( bit_se2002935070580805687sk_nat @ ( numeral_numeral_nat @ N ) )
% 2.39/2.81 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ ( pred_numeral @ N ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % mask_numeral
% 2.39/2.81 thf(fact_4582_take__bit__eq__mask__iff__exp__dvd,axiom,
% 2.39/2.81 ! [N: nat,K: int] :
% 2.39/2.81 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 2.39/2.81 = ( bit_se2000444600071755411sk_int @ N ) )
% 2.39/2.81 = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( plus_plus_int @ K @ one_one_int ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % take_bit_eq_mask_iff_exp_dvd
% 2.39/2.81 thf(fact_4583_xor__numerals_I4_J,axiom,
% 2.39/2.81 ! [X: num,Y: num] :
% 2.39/2.81 ( ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 2.39/2.81 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % xor_numerals(4)
% 2.39/2.81 thf(fact_4584_xor__numerals_I4_J,axiom,
% 2.39/2.81 ! [X: num,Y: num] :
% 2.39/2.81 ( ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ ( bit0 @ X ) ) @ ( numera5444537566228673987atural @ ( bit1 @ Y ) ) )
% 2.39/2.81 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % xor_numerals(4)
% 2.39/2.81 thf(fact_4585_xor__numerals_I4_J,axiom,
% 2.39/2.81 ! [X: num,Y: num] :
% 2.39/2.81 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 2.39/2.81 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % xor_numerals(4)
% 2.39/2.81 thf(fact_4586_xor__numerals_I4_J,axiom,
% 2.39/2.81 ! [X: num,Y: num] :
% 2.39/2.81 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 2.39/2.81 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % xor_numerals(4)
% 2.39/2.81 thf(fact_4587_xor__numerals_I6_J,axiom,
% 2.39/2.81 ! [X: num,Y: num] :
% 2.39/2.81 ( ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 2.39/2.81 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % xor_numerals(6)
% 2.39/2.81 thf(fact_4588_xor__numerals_I6_J,axiom,
% 2.39/2.81 ! [X: num,Y: num] :
% 2.39/2.81 ( ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ ( bit1 @ X ) ) @ ( numera5444537566228673987atural @ ( bit0 @ Y ) ) )
% 2.39/2.81 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % xor_numerals(6)
% 2.39/2.81 thf(fact_4589_xor__numerals_I6_J,axiom,
% 2.39/2.81 ! [X: num,Y: num] :
% 2.39/2.81 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 2.39/2.81 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % xor_numerals(6)
% 2.39/2.81 thf(fact_4590_xor__numerals_I6_J,axiom,
% 2.39/2.81 ! [X: num,Y: num] :
% 2.39/2.81 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 2.39/2.81 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % xor_numerals(6)
% 2.39/2.81 thf(fact_4591_xor__one__eq,axiom,
% 2.39/2.81 ! [A: code_integer] :
% 2.39/2.81 ( ( bit_se3222712562003087583nteger @ A @ one_one_Code_integer )
% 2.39/2.81 = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) )
% 2.39/2.81 @ ( zero_n356916108424825756nteger
% 2.39/2.81 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % xor_one_eq
% 2.39/2.81 thf(fact_4592_xor__one__eq,axiom,
% 2.39/2.81 ! [A: code_natural] :
% 2.39/2.81 ( ( bit_se2046307713759805098atural @ A @ one_one_Code_natural )
% 2.39/2.81 = ( minus_7197305767214868737atural @ ( plus_p4538020629002901425atural @ A @ ( zero_n8403883297036319079atural @ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) )
% 2.39/2.81 @ ( zero_n8403883297036319079atural
% 2.39/2.81 @ ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % xor_one_eq
% 2.39/2.81 thf(fact_4593_xor__one__eq,axiom,
% 2.39/2.81 ! [A: nat] :
% 2.39/2.81 ( ( bit_se6528837805403552850or_nat @ A @ one_one_nat )
% 2.39/2.81 = ( minus_minus_nat @ ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) )
% 2.39/2.81 @ ( zero_n2687167440665602831ol_nat
% 2.39/2.81 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % xor_one_eq
% 2.39/2.81 thf(fact_4594_xor__one__eq,axiom,
% 2.39/2.81 ! [A: int] :
% 2.39/2.81 ( ( bit_se6526347334894502574or_int @ A @ one_one_int )
% 2.39/2.81 = ( minus_minus_int @ ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) )
% 2.39/2.81 @ ( zero_n2684676970156552555ol_int
% 2.39/2.81 @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % xor_one_eq
% 2.39/2.81 thf(fact_4595_one__xor__eq,axiom,
% 2.39/2.81 ! [A: code_integer] :
% 2.39/2.81 ( ( bit_se3222712562003087583nteger @ one_one_Code_integer @ A )
% 2.39/2.81 = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) )
% 2.39/2.81 @ ( zero_n356916108424825756nteger
% 2.39/2.81 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % one_xor_eq
% 2.39/2.81 thf(fact_4596_one__xor__eq,axiom,
% 2.39/2.81 ! [A: code_natural] :
% 2.39/2.81 ( ( bit_se2046307713759805098atural @ one_one_Code_natural @ A )
% 2.39/2.81 = ( minus_7197305767214868737atural @ ( plus_p4538020629002901425atural @ A @ ( zero_n8403883297036319079atural @ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) )
% 2.39/2.81 @ ( zero_n8403883297036319079atural
% 2.39/2.81 @ ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % one_xor_eq
% 2.39/2.81 thf(fact_4597_one__xor__eq,axiom,
% 2.39/2.81 ! [A: nat] :
% 2.39/2.81 ( ( bit_se6528837805403552850or_nat @ one_one_nat @ A )
% 2.39/2.81 = ( minus_minus_nat @ ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) )
% 2.39/2.81 @ ( zero_n2687167440665602831ol_nat
% 2.39/2.81 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 2.39/2.81
% 2.39/2.81 % one_xor_eq
% 2.39/2.81 thf(fact_4598_one__xor__eq,axiom,
% 2.39/2.81 ! [A: int] :
% 2.39/2.81 ( ( bit_se6526347334894502574or_int @ one_one_int @ A )
% 2.39/2.81 = ( minus_minus_int @ ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) )
% 2.39/2.81 @ ( zero_n2684676970156552555ol_int
% 2.39/2.81 @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % one_xor_eq
% 2.39/2.82 thf(fact_4599_mask__Suc__0,axiom,
% 2.39/2.82 ( ( bit_se2119862282449309892nteger @ ( suc @ zero_zero_nat ) )
% 2.39/2.82 = one_one_Code_integer ) ).
% 2.39/2.82
% 2.39/2.82 % mask_Suc_0
% 2.39/2.82 thf(fact_4600_mask__Suc__0,axiom,
% 2.39/2.82 ( ( bit_se2000444600071755411sk_int @ ( suc @ zero_zero_nat ) )
% 2.39/2.82 = one_one_int ) ).
% 2.39/2.82
% 2.39/2.82 % mask_Suc_0
% 2.39/2.82 thf(fact_4601_mask__Suc__0,axiom,
% 2.39/2.82 ( ( bit_se2002935070580805687sk_nat @ ( suc @ zero_zero_nat ) )
% 2.39/2.82 = one_one_nat ) ).
% 2.39/2.82
% 2.39/2.82 % mask_Suc_0
% 2.39/2.82 thf(fact_4602_take__bit__minus__one__eq__mask,axiom,
% 2.39/2.82 ! [N: nat] :
% 2.39/2.82 ( ( bit_se1745604003318907178nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 2.39/2.82 = ( bit_se2119862282449309892nteger @ N ) ) ).
% 2.39/2.82
% 2.39/2.82 % take_bit_minus_one_eq_mask
% 2.39/2.82 thf(fact_4603_take__bit__minus__one__eq__mask,axiom,
% 2.39/2.82 ! [N: nat] :
% 2.39/2.82 ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 2.39/2.82 = ( bit_se2000444600071755411sk_int @ N ) ) ).
% 2.39/2.82
% 2.39/2.82 % take_bit_minus_one_eq_mask
% 2.39/2.82 thf(fact_4604_xor__numerals_I3_J,axiom,
% 2.39/2.82 ! [X: num,Y: num] :
% 2.39/2.82 ( ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 2.39/2.82 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % xor_numerals(3)
% 2.39/2.82 thf(fact_4605_xor__numerals_I3_J,axiom,
% 2.39/2.82 ! [X: num,Y: num] :
% 2.39/2.82 ( ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ ( bit0 @ X ) ) @ ( numera5444537566228673987atural @ ( bit0 @ Y ) ) )
% 2.39/2.82 = ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % xor_numerals(3)
% 2.39/2.82 thf(fact_4606_xor__numerals_I3_J,axiom,
% 2.39/2.82 ! [X: num,Y: num] :
% 2.39/2.82 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 2.39/2.82 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % xor_numerals(3)
% 2.39/2.82 thf(fact_4607_xor__numerals_I3_J,axiom,
% 2.39/2.82 ! [X: num,Y: num] :
% 2.39/2.82 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 2.39/2.82 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % xor_numerals(3)
% 2.39/2.82 thf(fact_4608_xor__numerals_I1_J,axiom,
% 2.39/2.82 ! [Y: num] :
% 2.39/2.82 ( ( bit_se3222712562003087583nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 2.39/2.82 = ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % xor_numerals(1)
% 2.39/2.82 thf(fact_4609_xor__numerals_I1_J,axiom,
% 2.39/2.82 ! [Y: num] :
% 2.39/2.82 ( ( bit_se2046307713759805098atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ Y ) ) )
% 2.39/2.82 = ( numera5444537566228673987atural @ ( bit1 @ Y ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % xor_numerals(1)
% 2.39/2.82 thf(fact_4610_xor__numerals_I1_J,axiom,
% 2.39/2.82 ! [Y: num] :
% 2.39/2.82 ( ( bit_se6528837805403552850or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 2.39/2.82 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % xor_numerals(1)
% 2.39/2.82 thf(fact_4611_xor__numerals_I1_J,axiom,
% 2.39/2.82 ! [Y: num] :
% 2.39/2.82 ( ( bit_se6526347334894502574or_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 2.39/2.82 = ( numeral_numeral_int @ ( bit1 @ Y ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % xor_numerals(1)
% 2.39/2.82 thf(fact_4612_xor__numerals_I2_J,axiom,
% 2.39/2.82 ! [Y: num] :
% 2.39/2.82 ( ( bit_se3222712562003087583nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 2.39/2.82 = ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % xor_numerals(2)
% 2.39/2.82 thf(fact_4613_xor__numerals_I2_J,axiom,
% 2.39/2.82 ! [Y: num] :
% 2.39/2.82 ( ( bit_se2046307713759805098atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit1 @ Y ) ) )
% 2.39/2.82 = ( numera5444537566228673987atural @ ( bit0 @ Y ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % xor_numerals(2)
% 2.39/2.82 thf(fact_4614_xor__numerals_I2_J,axiom,
% 2.39/2.82 ! [Y: num] :
% 2.39/2.82 ( ( bit_se6528837805403552850or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 2.39/2.82 = ( numeral_numeral_nat @ ( bit0 @ Y ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % xor_numerals(2)
% 2.39/2.82 thf(fact_4615_xor__numerals_I2_J,axiom,
% 2.39/2.82 ! [Y: num] :
% 2.39/2.82 ( ( bit_se6526347334894502574or_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 2.39/2.82 = ( numeral_numeral_int @ ( bit0 @ Y ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % xor_numerals(2)
% 2.39/2.82 thf(fact_4616_xor__numerals_I5_J,axiom,
% 2.39/2.82 ! [X: num] :
% 2.39/2.82 ( ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X ) ) @ one_one_Code_integer )
% 2.39/2.82 = ( numera6620942414471956472nteger @ ( bit1 @ X ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % xor_numerals(5)
% 2.39/2.82 thf(fact_4617_xor__numerals_I5_J,axiom,
% 2.39/2.82 ! [X: num] :
% 2.39/2.82 ( ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ ( bit0 @ X ) ) @ one_one_Code_natural )
% 2.39/2.82 = ( numera5444537566228673987atural @ ( bit1 @ X ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % xor_numerals(5)
% 2.39/2.82 thf(fact_4618_xor__numerals_I5_J,axiom,
% 2.39/2.82 ! [X: num] :
% 2.39/2.82 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ one_one_nat )
% 2.39/2.82 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % xor_numerals(5)
% 2.39/2.82 thf(fact_4619_xor__numerals_I5_J,axiom,
% 2.39/2.82 ! [X: num] :
% 2.39/2.82 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ one_one_int )
% 2.39/2.82 = ( numeral_numeral_int @ ( bit1 @ X ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % xor_numerals(5)
% 2.39/2.82 thf(fact_4620_xor__numerals_I8_J,axiom,
% 2.39/2.82 ! [X: num] :
% 2.39/2.82 ( ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ one_one_Code_integer )
% 2.39/2.82 = ( numera6620942414471956472nteger @ ( bit0 @ X ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % xor_numerals(8)
% 2.39/2.82 thf(fact_4621_xor__numerals_I8_J,axiom,
% 2.39/2.82 ! [X: num] :
% 2.39/2.82 ( ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ ( bit1 @ X ) ) @ one_one_Code_natural )
% 2.39/2.82 = ( numera5444537566228673987atural @ ( bit0 @ X ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % xor_numerals(8)
% 2.39/2.82 thf(fact_4622_xor__numerals_I8_J,axiom,
% 2.39/2.82 ! [X: num] :
% 2.39/2.82 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ one_one_nat )
% 2.39/2.82 = ( numeral_numeral_nat @ ( bit0 @ X ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % xor_numerals(8)
% 2.39/2.82 thf(fact_4623_xor__numerals_I8_J,axiom,
% 2.39/2.82 ! [X: num] :
% 2.39/2.82 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ one_one_int )
% 2.39/2.82 = ( numeral_numeral_int @ ( bit0 @ X ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % xor_numerals(8)
% 2.39/2.82 thf(fact_4624_xor__numerals_I7_J,axiom,
% 2.39/2.82 ! [X: num,Y: num] :
% 2.39/2.82 ( ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 2.39/2.82 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % xor_numerals(7)
% 2.39/2.82 thf(fact_4625_xor__numerals_I7_J,axiom,
% 2.39/2.82 ! [X: num,Y: num] :
% 2.39/2.82 ( ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ ( bit1 @ X ) ) @ ( numera5444537566228673987atural @ ( bit1 @ Y ) ) )
% 2.39/2.82 = ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % xor_numerals(7)
% 2.39/2.82 thf(fact_4626_xor__numerals_I7_J,axiom,
% 2.39/2.82 ! [X: num,Y: num] :
% 2.39/2.82 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 2.39/2.82 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % xor_numerals(7)
% 2.39/2.82 thf(fact_4627_xor__numerals_I7_J,axiom,
% 2.39/2.82 ! [X: num,Y: num] :
% 2.39/2.82 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 2.39/2.82 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % xor_numerals(7)
% 2.39/2.82 thf(fact_4628_flip__bit__nat__def,axiom,
% 2.39/2.82 ( bit_se2161824704523386999it_nat
% 2.39/2.82 = ( ^ [M3: nat,N3: nat] : ( bit_se6528837805403552850or_nat @ N3 @ ( bit_se547839408752420682it_nat @ M3 @ one_one_nat ) ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % flip_bit_nat_def
% 2.39/2.82 thf(fact_4629_flip__bit__int__def,axiom,
% 2.39/2.82 ( bit_se2159334234014336723it_int
% 2.39/2.82 = ( ^ [N3: nat,K4: int] : ( bit_se6526347334894502574or_int @ K4 @ ( bit_se545348938243370406it_int @ N3 @ one_one_int ) ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % flip_bit_int_def
% 2.39/2.82 thf(fact_4630_flip__bit__eq__xor,axiom,
% 2.39/2.82 ( bit_se1345352211410354436nteger
% 2.39/2.82 = ( ^ [N3: nat,A2: code_integer] : ( bit_se3222712562003087583nteger @ A2 @ ( bit_se7788150548672797655nteger @ N3 @ one_one_Code_integer ) ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % flip_bit_eq_xor
% 2.39/2.82 thf(fact_4631_flip__bit__eq__xor,axiom,
% 2.39/2.82 ( bit_se2159334234014336723it_int
% 2.39/2.82 = ( ^ [N3: nat,A2: int] : ( bit_se6526347334894502574or_int @ A2 @ ( bit_se545348938243370406it_int @ N3 @ one_one_int ) ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % flip_bit_eq_xor
% 2.39/2.82 thf(fact_4632_flip__bit__eq__xor,axiom,
% 2.39/2.82 ( bit_se2161824704523386999it_nat
% 2.39/2.82 = ( ^ [N3: nat,A2: nat] : ( bit_se6528837805403552850or_nat @ A2 @ ( bit_se547839408752420682it_nat @ N3 @ one_one_nat ) ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % flip_bit_eq_xor
% 2.39/2.82 thf(fact_4633_take__bit__eq__mask__iff,axiom,
% 2.39/2.82 ! [N: nat,K: int] :
% 2.39/2.82 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 2.39/2.82 = ( bit_se2000444600071755411sk_int @ N ) )
% 2.39/2.82 = ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 2.39/2.82 = zero_zero_int ) ) ).
% 2.39/2.82
% 2.39/2.82 % take_bit_eq_mask_iff
% 2.39/2.82 thf(fact_4634_mask__half__int,axiom,
% 2.39/2.82 ! [N: nat] :
% 2.39/2.82 ( ( divide_divide_int @ ( bit_se2000444600071755411sk_int @ N ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 2.39/2.82 = ( bit_se2000444600071755411sk_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % mask_half_int
% 2.39/2.82 thf(fact_4635_mask__nat__def,axiom,
% 2.39/2.82 ( bit_se2002935070580805687sk_nat
% 2.39/2.82 = ( ^ [N3: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ one_one_nat ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % mask_nat_def
% 2.39/2.82 thf(fact_4636_mask__int__def,axiom,
% 2.39/2.82 ( bit_se2000444600071755411sk_int
% 2.39/2.82 = ( ^ [N3: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) @ one_one_int ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % mask_int_def
% 2.39/2.82 thf(fact_4637_mask__eq__exp__minus__1,axiom,
% 2.39/2.82 ( bit_se2119862282449309892nteger
% 2.39/2.82 = ( ^ [N3: nat] : ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N3 ) @ one_one_Code_integer ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % mask_eq_exp_minus_1
% 2.39/2.82 thf(fact_4638_mask__eq__exp__minus__1,axiom,
% 2.39/2.82 ( bit_se943457434206027407atural
% 2.39/2.82 = ( ^ [N3: nat] : ( minus_7197305767214868737atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N3 ) @ one_one_Code_natural ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % mask_eq_exp_minus_1
% 2.39/2.82 thf(fact_4639_mask__eq__exp__minus__1,axiom,
% 2.39/2.82 ( bit_se2000444600071755411sk_int
% 2.39/2.82 = ( ^ [N3: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) @ one_one_int ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % mask_eq_exp_minus_1
% 2.39/2.82 thf(fact_4640_mask__eq__exp__minus__1,axiom,
% 2.39/2.82 ( bit_se2002935070580805687sk_nat
% 2.39/2.82 = ( ^ [N3: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ one_one_nat ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % mask_eq_exp_minus_1
% 2.39/2.82 thf(fact_4641_and__int_Opinduct,axiom,
% 2.39/2.82 ! [A0: int,A1: int,P2: int > int > $o] :
% 2.39/2.82 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A1 ) )
% 2.39/2.82 => ( ! [K2: int,L4: int] :
% 2.39/2.82 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K2 @ L4 ) )
% 2.39/2.82 => ( ( ~ ( ( member_int2 @ K2 @ ( insert_int2 @ zero_zero_int @ ( insert_int2 @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 2.39/2.82 & ( member_int2 @ L4 @ ( insert_int2 @ zero_zero_int @ ( insert_int2 @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 2.39/2.82 => ( P2 @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 2.39/2.82 => ( P2 @ K2 @ L4 ) ) )
% 2.39/2.82 => ( P2 @ A0 @ A1 ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % and_int.pinduct
% 2.39/2.82 thf(fact_4642_upto_Opsimps,axiom,
% 2.39/2.82 ! [I2: int,J: int] :
% 2.39/2.82 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I2 @ J ) )
% 2.39/2.82 => ( ( ( ord_less_eq_int @ I2 @ J )
% 2.39/2.82 => ( ( upto @ I2 @ J )
% 2.39/2.82 = ( cons_int @ I2 @ ( upto @ ( plus_plus_int @ I2 @ one_one_int ) @ J ) ) ) )
% 2.39/2.82 & ( ~ ( ord_less_eq_int @ I2 @ J )
% 2.39/2.82 => ( ( upto @ I2 @ J )
% 2.39/2.82 = nil_int ) ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % upto.psimps
% 2.39/2.82 thf(fact_4643_upto_Opelims,axiom,
% 2.39/2.82 ! [X: int,Xa: int,Y: list_int] :
% 2.39/2.82 ( ( ( upto @ X @ Xa )
% 2.39/2.82 = Y )
% 2.39/2.82 => ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa ) )
% 2.39/2.82 => ~ ( ( ( ( ord_less_eq_int @ X @ Xa )
% 2.39/2.82 => ( Y
% 2.39/2.82 = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa ) ) ) )
% 2.39/2.82 & ( ~ ( ord_less_eq_int @ X @ Xa )
% 2.39/2.82 => ( Y = nil_int ) ) )
% 2.39/2.82 => ~ ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa ) ) ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % upto.pelims
% 2.39/2.82 thf(fact_4644_upto_Opinduct,axiom,
% 2.39/2.82 ! [A0: int,A1: int,P2: int > int > $o] :
% 2.39/2.82 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ A0 @ A1 ) )
% 2.39/2.82 => ( ! [I3: int,J3: int] :
% 2.39/2.82 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I3 @ J3 ) )
% 2.39/2.82 => ( ( ( ord_less_eq_int @ I3 @ J3 )
% 2.39/2.82 => ( P2 @ ( plus_plus_int @ I3 @ one_one_int ) @ J3 ) )
% 2.39/2.82 => ( P2 @ I3 @ J3 ) ) )
% 2.39/2.82 => ( P2 @ A0 @ A1 ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % upto.pinduct
% 2.39/2.82 thf(fact_4645_nat0__intermed__int__val,axiom,
% 2.39/2.82 ! [N: nat,F2: nat > int,K: int] :
% 2.39/2.82 ( ! [I3: nat] :
% 2.39/2.82 ( ( ord_less_nat @ I3 @ N )
% 2.39/2.82 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F2 @ ( plus_plus_nat @ I3 @ one_one_nat ) ) @ ( F2 @ I3 ) ) ) @ one_one_int ) )
% 2.39/2.82 => ( ( ord_less_eq_int @ ( F2 @ zero_zero_nat ) @ K )
% 2.39/2.82 => ( ( ord_less_eq_int @ K @ ( F2 @ N ) )
% 2.39/2.82 => ? [I3: nat] :
% 2.39/2.82 ( ( ord_less_eq_nat @ I3 @ N )
% 2.39/2.82 & ( ( F2 @ I3 )
% 2.39/2.82 = K ) ) ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % nat0_intermed_int_val
% 2.39/2.82 thf(fact_4646_or__numerals_I7_J,axiom,
% 2.39/2.82 ! [X: num,Y: num] :
% 2.39/2.82 ( ( bit_se1080825931792720795nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 2.39/2.82 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1080825931792720795nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % or_numerals(7)
% 2.39/2.82 thf(fact_4647_or__numerals_I7_J,axiom,
% 2.39/2.82 ! [X: num,Y: num] :
% 2.39/2.82 ( ( bit_se9127793120404214118atural @ ( numera5444537566228673987atural @ ( bit1 @ X ) ) @ ( numera5444537566228673987atural @ ( bit1 @ Y ) ) )
% 2.39/2.82 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se9127793120404214118atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % or_numerals(7)
% 2.39/2.82 thf(fact_4648_or__numerals_I7_J,axiom,
% 2.39/2.82 ! [X: num,Y: num] :
% 2.39/2.82 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 2.39/2.82 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % or_numerals(7)
% 2.39/2.82 thf(fact_4649_or__numerals_I7_J,axiom,
% 2.39/2.82 ! [X: num,Y: num] :
% 2.39/2.82 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 2.39/2.82 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % or_numerals(7)
% 2.39/2.82 thf(fact_4650_or__numerals_I6_J,axiom,
% 2.39/2.82 ! [X: num,Y: num] :
% 2.39/2.82 ( ( bit_se1080825931792720795nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 2.39/2.82 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1080825931792720795nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % or_numerals(6)
% 2.39/2.82 thf(fact_4651_or__numerals_I6_J,axiom,
% 2.39/2.82 ! [X: num,Y: num] :
% 2.39/2.82 ( ( bit_se9127793120404214118atural @ ( numera5444537566228673987atural @ ( bit1 @ X ) ) @ ( numera5444537566228673987atural @ ( bit0 @ Y ) ) )
% 2.39/2.82 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se9127793120404214118atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % or_numerals(6)
% 2.39/2.82 thf(fact_4652_or__numerals_I6_J,axiom,
% 2.39/2.82 ! [X: num,Y: num] :
% 2.39/2.82 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 2.39/2.82 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % or_numerals(6)
% 2.39/2.82 thf(fact_4653_or__numerals_I6_J,axiom,
% 2.39/2.82 ! [X: num,Y: num] :
% 2.39/2.82 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 2.39/2.82 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % or_numerals(6)
% 2.39/2.82 thf(fact_4654_or__numerals_I4_J,axiom,
% 2.39/2.82 ! [X: num,Y: num] :
% 2.39/2.82 ( ( bit_se1080825931792720795nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 2.39/2.82 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1080825931792720795nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % or_numerals(4)
% 2.39/2.82 thf(fact_4655_or__numerals_I4_J,axiom,
% 2.39/2.82 ! [X: num,Y: num] :
% 2.39/2.82 ( ( bit_se9127793120404214118atural @ ( numera5444537566228673987atural @ ( bit0 @ X ) ) @ ( numera5444537566228673987atural @ ( bit1 @ Y ) ) )
% 2.39/2.82 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se9127793120404214118atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % or_numerals(4)
% 2.39/2.82 thf(fact_4656_or__numerals_I4_J,axiom,
% 2.39/2.82 ! [X: num,Y: num] :
% 2.39/2.82 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 2.39/2.82 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % or_numerals(4)
% 2.39/2.82 thf(fact_4657_or__numerals_I4_J,axiom,
% 2.39/2.82 ! [X: num,Y: num] :
% 2.39/2.82 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 2.39/2.82 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % or_numerals(4)
% 2.39/2.82 thf(fact_4658_and__not__numerals_I8_J,axiom,
% 2.39/2.82 ! [M2: num,N: num] :
% 2.39/2.82 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 2.39/2.82 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % and_not_numerals(8)
% 2.39/2.82 thf(fact_4659_abs__idempotent,axiom,
% 2.39/2.82 ! [A: int] :
% 2.39/2.82 ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 2.39/2.82 = ( abs_abs_int @ A ) ) ).
% 2.39/2.82
% 2.39/2.82 % abs_idempotent
% 2.39/2.82 thf(fact_4660_abs__idempotent,axiom,
% 2.39/2.82 ! [A: code_integer] :
% 2.39/2.82 ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 2.39/2.82 = ( abs_abs_Code_integer @ A ) ) ).
% 2.39/2.82
% 2.39/2.82 % abs_idempotent
% 2.39/2.82 thf(fact_4661_abs__0__eq,axiom,
% 2.39/2.82 ! [A: int] :
% 2.39/2.82 ( ( zero_zero_int
% 2.39/2.82 = ( abs_abs_int @ A ) )
% 2.39/2.82 = ( A = zero_zero_int ) ) ).
% 2.39/2.82
% 2.39/2.82 % abs_0_eq
% 2.39/2.82 thf(fact_4662_abs__0__eq,axiom,
% 2.39/2.82 ! [A: rat] :
% 2.39/2.82 ( ( zero_zero_rat
% 2.39/2.82 = ( abs_abs_rat @ A ) )
% 2.39/2.82 = ( A = zero_zero_rat ) ) ).
% 2.39/2.82
% 2.39/2.82 % abs_0_eq
% 2.39/2.82 thf(fact_4663_abs__0__eq,axiom,
% 2.39/2.82 ! [A: code_integer] :
% 2.39/2.82 ( ( zero_z3403309356797280102nteger
% 2.39/2.82 = ( abs_abs_Code_integer @ A ) )
% 2.39/2.82 = ( A = zero_z3403309356797280102nteger ) ) ).
% 2.39/2.82
% 2.39/2.82 % abs_0_eq
% 2.39/2.82 thf(fact_4664_abs__eq__0,axiom,
% 2.39/2.82 ! [A: int] :
% 2.39/2.82 ( ( ( abs_abs_int @ A )
% 2.39/2.82 = zero_zero_int )
% 2.39/2.82 = ( A = zero_zero_int ) ) ).
% 2.39/2.82
% 2.39/2.82 % abs_eq_0
% 2.39/2.82 thf(fact_4665_abs__eq__0,axiom,
% 2.39/2.82 ! [A: rat] :
% 2.39/2.82 ( ( ( abs_abs_rat @ A )
% 2.39/2.82 = zero_zero_rat )
% 2.39/2.82 = ( A = zero_zero_rat ) ) ).
% 2.39/2.82
% 2.39/2.82 % abs_eq_0
% 2.39/2.82 thf(fact_4666_abs__eq__0,axiom,
% 2.39/2.82 ! [A: code_integer] :
% 2.39/2.82 ( ( ( abs_abs_Code_integer @ A )
% 2.39/2.82 = zero_z3403309356797280102nteger )
% 2.39/2.82 = ( A = zero_z3403309356797280102nteger ) ) ).
% 2.39/2.82
% 2.39/2.82 % abs_eq_0
% 2.39/2.82 thf(fact_4667_abs__zero,axiom,
% 2.39/2.82 ( ( abs_abs_int @ zero_zero_int )
% 2.39/2.82 = zero_zero_int ) ).
% 2.39/2.82
% 2.39/2.82 % abs_zero
% 2.39/2.82 thf(fact_4668_abs__zero,axiom,
% 2.39/2.82 ( ( abs_abs_rat @ zero_zero_rat )
% 2.39/2.82 = zero_zero_rat ) ).
% 2.39/2.82
% 2.39/2.82 % abs_zero
% 2.39/2.82 thf(fact_4669_abs__zero,axiom,
% 2.39/2.82 ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 2.39/2.82 = zero_z3403309356797280102nteger ) ).
% 2.39/2.82
% 2.39/2.82 % abs_zero
% 2.39/2.82 thf(fact_4670_abs__add__abs,axiom,
% 2.39/2.82 ! [A: code_integer,B: code_integer] :
% 2.39/2.82 ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) )
% 2.39/2.82 = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % abs_add_abs
% 2.39/2.82 thf(fact_4671_abs__add__abs,axiom,
% 2.39/2.82 ! [A: rat,B: rat] :
% 2.39/2.82 ( ( abs_abs_rat @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) )
% 2.39/2.82 = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % abs_add_abs
% 2.39/2.82 thf(fact_4672_abs__add__abs,axiom,
% 2.39/2.82 ! [A: int,B: int] :
% 2.39/2.82 ( ( abs_abs_int @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) )
% 2.39/2.82 = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % abs_add_abs
% 2.39/2.82 thf(fact_4673_abs__mult__self__eq,axiom,
% 2.39/2.82 ! [A: int] :
% 2.39/2.82 ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ A ) )
% 2.39/2.82 = ( times_times_int @ A @ A ) ) ).
% 2.39/2.82
% 2.39/2.82 % abs_mult_self_eq
% 2.39/2.82 thf(fact_4674_abs__mult__self__eq,axiom,
% 2.39/2.82 ! [A: code_integer] :
% 2.39/2.82 ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 2.39/2.82 = ( times_3573771949741848930nteger @ A @ A ) ) ).
% 2.39/2.82
% 2.39/2.82 % abs_mult_self_eq
% 2.39/2.82 thf(fact_4675_abs__1,axiom,
% 2.39/2.82 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 2.39/2.82 = one_one_Code_integer ) ).
% 2.39/2.82
% 2.39/2.82 % abs_1
% 2.39/2.82 thf(fact_4676_abs__1,axiom,
% 2.39/2.82 ( ( abs_abs_rat @ one_one_rat )
% 2.39/2.82 = one_one_rat ) ).
% 2.39/2.82
% 2.39/2.82 % abs_1
% 2.39/2.82 thf(fact_4677_abs__1,axiom,
% 2.39/2.82 ( ( abs_abs_int @ one_one_int )
% 2.39/2.82 = one_one_int ) ).
% 2.39/2.82
% 2.39/2.82 % abs_1
% 2.39/2.82 thf(fact_4678_abs__minus__cancel,axiom,
% 2.39/2.82 ! [A: int] :
% 2.39/2.82 ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 2.39/2.82 = ( abs_abs_int @ A ) ) ).
% 2.39/2.82
% 2.39/2.82 % abs_minus_cancel
% 2.39/2.82 thf(fact_4679_abs__minus__cancel,axiom,
% 2.39/2.82 ! [A: rat] :
% 2.39/2.82 ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 2.39/2.82 = ( abs_abs_rat @ A ) ) ).
% 2.39/2.82
% 2.39/2.82 % abs_minus_cancel
% 2.39/2.82 thf(fact_4680_abs__minus__cancel,axiom,
% 2.39/2.82 ! [A: code_integer] :
% 2.39/2.82 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 2.39/2.82 = ( abs_abs_Code_integer @ A ) ) ).
% 2.39/2.82
% 2.39/2.82 % abs_minus_cancel
% 2.39/2.82 thf(fact_4681_abs__of__nonneg,axiom,
% 2.39/2.82 ! [A: code_integer] :
% 2.39/2.82 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 2.39/2.82 => ( ( abs_abs_Code_integer @ A )
% 2.39/2.82 = A ) ) ).
% 2.39/2.82
% 2.39/2.82 % abs_of_nonneg
% 2.39/2.82 thf(fact_4682_abs__of__nonneg,axiom,
% 2.39/2.82 ! [A: rat] :
% 2.39/2.82 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 2.39/2.82 => ( ( abs_abs_rat @ A )
% 2.39/2.82 = A ) ) ).
% 2.39/2.82
% 2.39/2.82 % abs_of_nonneg
% 2.39/2.82 thf(fact_4683_abs__of__nonneg,axiom,
% 2.39/2.82 ! [A: int] :
% 2.39/2.82 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 2.39/2.82 => ( ( abs_abs_int @ A )
% 2.39/2.82 = A ) ) ).
% 2.39/2.82
% 2.39/2.82 % abs_of_nonneg
% 2.39/2.82 thf(fact_4684_abs__le__self__iff,axiom,
% 2.39/2.82 ! [A: code_integer] :
% 2.39/2.82 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ A )
% 2.39/2.82 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 2.39/2.82
% 2.39/2.82 % abs_le_self_iff
% 2.39/2.82 thf(fact_4685_abs__le__self__iff,axiom,
% 2.39/2.82 ! [A: rat] :
% 2.39/2.82 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ A )
% 2.39/2.82 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 2.39/2.82
% 2.39/2.82 % abs_le_self_iff
% 2.39/2.82 thf(fact_4686_abs__le__self__iff,axiom,
% 2.39/2.82 ! [A: int] :
% 2.39/2.82 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ A )
% 2.39/2.82 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 2.39/2.82
% 2.39/2.82 % abs_le_self_iff
% 2.39/2.82 thf(fact_4687_abs__le__zero__iff,axiom,
% 2.39/2.82 ! [A: code_integer] :
% 2.39/2.82 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 2.39/2.82 = ( A = zero_z3403309356797280102nteger ) ) ).
% 2.39/2.82
% 2.39/2.82 % abs_le_zero_iff
% 2.39/2.82 thf(fact_4688_abs__le__zero__iff,axiom,
% 2.39/2.82 ! [A: rat] :
% 2.39/2.82 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat )
% 2.39/2.82 = ( A = zero_zero_rat ) ) ).
% 2.39/2.82
% 2.39/2.82 % abs_le_zero_iff
% 2.39/2.82 thf(fact_4689_abs__le__zero__iff,axiom,
% 2.39/2.82 ! [A: int] :
% 2.39/2.82 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ zero_zero_int )
% 2.39/2.82 = ( A = zero_zero_int ) ) ).
% 2.39/2.82
% 2.39/2.82 % abs_le_zero_iff
% 2.39/2.82 thf(fact_4690_zero__less__abs__iff,axiom,
% 2.39/2.82 ! [A: code_integer] :
% 2.39/2.82 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) )
% 2.39/2.82 = ( A != zero_z3403309356797280102nteger ) ) ).
% 2.39/2.82
% 2.39/2.82 % zero_less_abs_iff
% 2.39/2.82 thf(fact_4691_zero__less__abs__iff,axiom,
% 2.39/2.82 ! [A: rat] :
% 2.39/2.82 ( ( ord_less_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) )
% 2.39/2.82 = ( A != zero_zero_rat ) ) ).
% 2.39/2.82
% 2.39/2.82 % zero_less_abs_iff
% 2.39/2.82 thf(fact_4692_zero__less__abs__iff,axiom,
% 2.39/2.82 ! [A: int] :
% 2.39/2.82 ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A ) )
% 2.39/2.82 = ( A != zero_zero_int ) ) ).
% 2.39/2.82
% 2.39/2.82 % zero_less_abs_iff
% 2.39/2.82 thf(fact_4693_abs__neg__one,axiom,
% 2.39/2.82 ( ( abs_abs_int @ ( uminus_uminus_int @ one_one_int ) )
% 2.39/2.82 = one_one_int ) ).
% 2.39/2.82
% 2.39/2.82 % abs_neg_one
% 2.39/2.82 thf(fact_4694_abs__neg__one,axiom,
% 2.39/2.82 ( ( abs_abs_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 2.39/2.82 = one_one_rat ) ).
% 2.39/2.82
% 2.39/2.82 % abs_neg_one
% 2.39/2.82 thf(fact_4695_abs__neg__one,axiom,
% 2.39/2.82 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 2.39/2.82 = one_one_Code_integer ) ).
% 2.39/2.82
% 2.39/2.82 % abs_neg_one
% 2.39/2.82 thf(fact_4696_bit_Odisj__one__right,axiom,
% 2.39/2.82 ! [X: code_integer] :
% 2.39/2.82 ( ( bit_se1080825931792720795nteger @ X @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 2.39/2.82 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 2.39/2.82
% 2.39/2.82 % bit.disj_one_right
% 2.39/2.82 thf(fact_4697_bit_Odisj__one__right,axiom,
% 2.39/2.82 ! [X: int] :
% 2.39/2.82 ( ( bit_se1409905431419307370or_int @ X @ ( uminus_uminus_int @ one_one_int ) )
% 2.39/2.82 = ( uminus_uminus_int @ one_one_int ) ) ).
% 2.39/2.82
% 2.39/2.82 % bit.disj_one_right
% 2.39/2.82 thf(fact_4698_bit_Odisj__one__left,axiom,
% 2.39/2.82 ! [X: code_integer] :
% 2.39/2.82 ( ( bit_se1080825931792720795nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X )
% 2.39/2.82 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 2.39/2.82
% 2.39/2.82 % bit.disj_one_left
% 2.39/2.82 thf(fact_4699_bit_Odisj__one__left,axiom,
% 2.39/2.82 ! [X: int] :
% 2.39/2.82 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ one_one_int ) @ X )
% 2.39/2.82 = ( uminus_uminus_int @ one_one_int ) ) ).
% 2.39/2.82
% 2.39/2.82 % bit.disj_one_left
% 2.39/2.82 thf(fact_4700_zdvd1__eq,axiom,
% 2.39/2.82 ! [X: int] :
% 2.39/2.82 ( ( dvd_dvd_int @ X @ one_one_int )
% 2.39/2.82 = ( ( abs_abs_int @ X )
% 2.39/2.82 = one_one_int ) ) ).
% 2.39/2.82
% 2.39/2.82 % zdvd1_eq
% 2.39/2.82 thf(fact_4701_abs__of__nonpos,axiom,
% 2.39/2.82 ! [A: code_integer] :
% 2.39/2.82 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 2.39/2.82 => ( ( abs_abs_Code_integer @ A )
% 2.39/2.82 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % abs_of_nonpos
% 2.39/2.82 thf(fact_4702_abs__of__nonpos,axiom,
% 2.39/2.82 ! [A: rat] :
% 2.39/2.82 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 2.39/2.82 => ( ( abs_abs_rat @ A )
% 2.39/2.82 = ( uminus_uminus_rat @ A ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % abs_of_nonpos
% 2.39/2.82 thf(fact_4703_abs__of__nonpos,axiom,
% 2.39/2.82 ! [A: int] :
% 2.39/2.82 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 2.39/2.82 => ( ( abs_abs_int @ A )
% 2.39/2.82 = ( uminus_uminus_int @ A ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % abs_of_nonpos
% 2.39/2.82 thf(fact_4704_bit_Ocompl__zero,axiom,
% 2.39/2.82 ( ( bit_ri7632146776885996613nteger @ zero_z3403309356797280102nteger )
% 2.39/2.82 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 2.39/2.82
% 2.39/2.82 % bit.compl_zero
% 2.39/2.82 thf(fact_4705_bit_Ocompl__zero,axiom,
% 2.39/2.82 ( ( bit_ri7919022796975470100ot_int @ zero_zero_int )
% 2.39/2.82 = ( uminus_uminus_int @ one_one_int ) ) ).
% 2.39/2.82
% 2.39/2.82 % bit.compl_zero
% 2.39/2.82 thf(fact_4706_bit_Ocompl__one,axiom,
% 2.39/2.82 ( ( bit_ri7632146776885996613nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 2.39/2.82 = zero_z3403309356797280102nteger ) ).
% 2.39/2.82
% 2.39/2.82 % bit.compl_one
% 2.39/2.82 thf(fact_4707_bit_Ocompl__one,axiom,
% 2.39/2.82 ( ( bit_ri7919022796975470100ot_int @ ( uminus_uminus_int @ one_one_int ) )
% 2.39/2.82 = zero_zero_int ) ).
% 2.39/2.82
% 2.39/2.82 % bit.compl_one
% 2.39/2.82 thf(fact_4708_or__numerals_I2_J,axiom,
% 2.39/2.82 ! [Y: num] :
% 2.39/2.82 ( ( bit_se1080825931792720795nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 2.39/2.82 = ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % or_numerals(2)
% 2.39/2.82 thf(fact_4709_or__numerals_I2_J,axiom,
% 2.39/2.82 ! [Y: num] :
% 2.39/2.82 ( ( bit_se9127793120404214118atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit1 @ Y ) ) )
% 2.39/2.82 = ( numera5444537566228673987atural @ ( bit1 @ Y ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % or_numerals(2)
% 2.39/2.82 thf(fact_4710_or__numerals_I2_J,axiom,
% 2.39/2.82 ! [Y: num] :
% 2.39/2.82 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 2.39/2.82 = ( numeral_numeral_int @ ( bit1 @ Y ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % or_numerals(2)
% 2.39/2.82 thf(fact_4711_or__numerals_I2_J,axiom,
% 2.39/2.82 ! [Y: num] :
% 2.39/2.82 ( ( bit_se1412395901928357646or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 2.39/2.82 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % or_numerals(2)
% 2.39/2.82 thf(fact_4712_or__numerals_I8_J,axiom,
% 2.39/2.82 ! [X: num] :
% 2.39/2.82 ( ( bit_se1080825931792720795nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ one_one_Code_integer )
% 2.39/2.82 = ( numera6620942414471956472nteger @ ( bit1 @ X ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % or_numerals(8)
% 2.39/2.82 thf(fact_4713_or__numerals_I8_J,axiom,
% 2.39/2.82 ! [X: num] :
% 2.39/2.82 ( ( bit_se9127793120404214118atural @ ( numera5444537566228673987atural @ ( bit1 @ X ) ) @ one_one_Code_natural )
% 2.39/2.82 = ( numera5444537566228673987atural @ ( bit1 @ X ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % or_numerals(8)
% 2.39/2.82 thf(fact_4714_or__numerals_I8_J,axiom,
% 2.39/2.82 ! [X: num] :
% 2.39/2.82 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ one_one_int )
% 2.39/2.82 = ( numeral_numeral_int @ ( bit1 @ X ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % or_numerals(8)
% 2.39/2.82 thf(fact_4715_or__numerals_I8_J,axiom,
% 2.39/2.82 ! [X: num] :
% 2.39/2.82 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ one_one_nat )
% 2.39/2.82 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % or_numerals(8)
% 2.39/2.82 thf(fact_4716_abs__sgn__eq__1,axiom,
% 2.39/2.82 ! [A: int] :
% 2.39/2.82 ( ( A != zero_zero_int )
% 2.39/2.82 => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 2.39/2.82 = one_one_int ) ) ).
% 2.39/2.82
% 2.39/2.82 % abs_sgn_eq_1
% 2.39/2.82 thf(fact_4717_abs__sgn__eq__1,axiom,
% 2.39/2.82 ! [A: rat] :
% 2.39/2.82 ( ( A != zero_zero_rat )
% 2.39/2.82 => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 2.39/2.82 = one_one_rat ) ) ).
% 2.39/2.82
% 2.39/2.82 % abs_sgn_eq_1
% 2.39/2.82 thf(fact_4718_abs__sgn__eq__1,axiom,
% 2.39/2.82 ! [A: code_integer] :
% 2.39/2.82 ( ( A != zero_z3403309356797280102nteger )
% 2.39/2.82 => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 2.39/2.82 = one_one_Code_integer ) ) ).
% 2.39/2.82
% 2.39/2.82 % abs_sgn_eq_1
% 2.39/2.82 thf(fact_4719_or__minus__numerals_I2_J,axiom,
% 2.39/2.82 ! [N: num] :
% 2.39/2.82 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 2.39/2.82 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % or_minus_numerals(2)
% 2.39/2.82 thf(fact_4720_or__minus__numerals_I6_J,axiom,
% 2.39/2.82 ! [N: num] :
% 2.39/2.82 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 2.39/2.82 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % or_minus_numerals(6)
% 2.39/2.82 thf(fact_4721_bit_Odisj__cancel__right,axiom,
% 2.39/2.82 ! [X: code_integer] :
% 2.39/2.82 ( ( bit_se1080825931792720795nteger @ X @ ( bit_ri7632146776885996613nteger @ X ) )
% 2.39/2.82 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 2.39/2.82
% 2.39/2.82 % bit.disj_cancel_right
% 2.39/2.82 thf(fact_4722_bit_Odisj__cancel__right,axiom,
% 2.39/2.82 ! [X: int] :
% 2.39/2.82 ( ( bit_se1409905431419307370or_int @ X @ ( bit_ri7919022796975470100ot_int @ X ) )
% 2.39/2.82 = ( uminus_uminus_int @ one_one_int ) ) ).
% 2.39/2.82
% 2.39/2.82 % bit.disj_cancel_right
% 2.39/2.82 thf(fact_4723_bit_Odisj__cancel__left,axiom,
% 2.39/2.82 ! [X: code_integer] :
% 2.39/2.82 ( ( bit_se1080825931792720795nteger @ ( bit_ri7632146776885996613nteger @ X ) @ X )
% 2.39/2.82 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 2.39/2.82
% 2.39/2.82 % bit.disj_cancel_left
% 2.39/2.82 thf(fact_4724_bit_Odisj__cancel__left,axiom,
% 2.39/2.82 ! [X: int] :
% 2.39/2.82 ( ( bit_se1409905431419307370or_int @ ( bit_ri7919022796975470100ot_int @ X ) @ X )
% 2.39/2.82 = ( uminus_uminus_int @ one_one_int ) ) ).
% 2.39/2.82
% 2.39/2.82 % bit.disj_cancel_left
% 2.39/2.82 thf(fact_4725_bit_Oxor__cancel__right,axiom,
% 2.39/2.82 ! [X: code_integer] :
% 2.39/2.82 ( ( bit_se3222712562003087583nteger @ X @ ( bit_ri7632146776885996613nteger @ X ) )
% 2.39/2.82 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 2.39/2.82
% 2.39/2.82 % bit.xor_cancel_right
% 2.39/2.82 thf(fact_4726_bit_Oxor__cancel__right,axiom,
% 2.39/2.82 ! [X: int] :
% 2.39/2.82 ( ( bit_se6526347334894502574or_int @ X @ ( bit_ri7919022796975470100ot_int @ X ) )
% 2.39/2.82 = ( uminus_uminus_int @ one_one_int ) ) ).
% 2.39/2.82
% 2.39/2.82 % bit.xor_cancel_right
% 2.39/2.82 thf(fact_4727_bit_Oxor__cancel__left,axiom,
% 2.39/2.82 ! [X: code_integer] :
% 2.39/2.82 ( ( bit_se3222712562003087583nteger @ ( bit_ri7632146776885996613nteger @ X ) @ X )
% 2.39/2.82 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 2.39/2.82
% 2.39/2.82 % bit.xor_cancel_left
% 2.39/2.82 thf(fact_4728_bit_Oxor__cancel__left,axiom,
% 2.39/2.82 ! [X: int] :
% 2.39/2.82 ( ( bit_se6526347334894502574or_int @ ( bit_ri7919022796975470100ot_int @ X ) @ X )
% 2.39/2.82 = ( uminus_uminus_int @ one_one_int ) ) ).
% 2.39/2.82
% 2.39/2.82 % bit.xor_cancel_left
% 2.39/2.82 thf(fact_4729_bit_Oxor__one__right,axiom,
% 2.39/2.82 ! [X: code_integer] :
% 2.39/2.82 ( ( bit_se3222712562003087583nteger @ X @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 2.39/2.82 = ( bit_ri7632146776885996613nteger @ X ) ) ).
% 2.39/2.82
% 2.39/2.82 % bit.xor_one_right
% 2.39/2.82 thf(fact_4730_bit_Oxor__one__right,axiom,
% 2.39/2.82 ! [X: int] :
% 2.39/2.82 ( ( bit_se6526347334894502574or_int @ X @ ( uminus_uminus_int @ one_one_int ) )
% 2.39/2.82 = ( bit_ri7919022796975470100ot_int @ X ) ) ).
% 2.39/2.82
% 2.39/2.82 % bit.xor_one_right
% 2.39/2.82 thf(fact_4731_bit_Oxor__one__left,axiom,
% 2.39/2.82 ! [X: code_integer] :
% 2.39/2.82 ( ( bit_se3222712562003087583nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X )
% 2.39/2.82 = ( bit_ri7632146776885996613nteger @ X ) ) ).
% 2.39/2.82
% 2.39/2.82 % bit.xor_one_left
% 2.39/2.82 thf(fact_4732_bit_Oxor__one__left,axiom,
% 2.39/2.82 ! [X: int] :
% 2.39/2.82 ( ( bit_se6526347334894502574or_int @ ( uminus_uminus_int @ one_one_int ) @ X )
% 2.39/2.82 = ( bit_ri7919022796975470100ot_int @ X ) ) ).
% 2.39/2.82
% 2.39/2.82 % bit.xor_one_left
% 2.39/2.82 thf(fact_4733_zabs__less__one__iff,axiom,
% 2.39/2.82 ! [Z: int] :
% 2.39/2.82 ( ( ord_less_int @ ( abs_abs_int @ Z ) @ one_one_int )
% 2.39/2.82 = ( Z = zero_zero_int ) ) ).
% 2.39/2.82
% 2.39/2.82 % zabs_less_one_iff
% 2.39/2.82 thf(fact_4734_or__numerals_I3_J,axiom,
% 2.39/2.82 ! [X: num,Y: num] :
% 2.39/2.82 ( ( bit_se1080825931792720795nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 2.39/2.82 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1080825931792720795nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % or_numerals(3)
% 2.39/2.82 thf(fact_4735_or__numerals_I3_J,axiom,
% 2.39/2.82 ! [X: num,Y: num] :
% 2.39/2.82 ( ( bit_se9127793120404214118atural @ ( numera5444537566228673987atural @ ( bit0 @ X ) ) @ ( numera5444537566228673987atural @ ( bit0 @ Y ) ) )
% 2.39/2.82 = ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se9127793120404214118atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % or_numerals(3)
% 2.39/2.82 thf(fact_4736_or__numerals_I3_J,axiom,
% 2.39/2.82 ! [X: num,Y: num] :
% 2.39/2.82 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 2.39/2.82 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % or_numerals(3)
% 2.39/2.82 thf(fact_4737_or__numerals_I3_J,axiom,
% 2.39/2.82 ! [X: num,Y: num] :
% 2.39/2.82 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 2.39/2.82 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % or_numerals(3)
% 2.39/2.82 thf(fact_4738_or__numerals_I5_J,axiom,
% 2.39/2.82 ! [X: num] :
% 2.39/2.82 ( ( bit_se1080825931792720795nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X ) ) @ one_one_Code_integer )
% 2.39/2.82 = ( numera6620942414471956472nteger @ ( bit1 @ X ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % or_numerals(5)
% 2.39/2.82 thf(fact_4739_or__numerals_I5_J,axiom,
% 2.39/2.82 ! [X: num] :
% 2.39/2.82 ( ( bit_se9127793120404214118atural @ ( numera5444537566228673987atural @ ( bit0 @ X ) ) @ one_one_Code_natural )
% 2.39/2.82 = ( numera5444537566228673987atural @ ( bit1 @ X ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % or_numerals(5)
% 2.39/2.82 thf(fact_4740_or__numerals_I5_J,axiom,
% 2.39/2.82 ! [X: num] :
% 2.39/2.82 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ one_one_int )
% 2.39/2.82 = ( numeral_numeral_int @ ( bit1 @ X ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % or_numerals(5)
% 2.39/2.82 thf(fact_4741_or__numerals_I5_J,axiom,
% 2.39/2.82 ! [X: num] :
% 2.39/2.82 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ one_one_nat )
% 2.39/2.82 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % or_numerals(5)
% 2.39/2.82 thf(fact_4742_or__numerals_I1_J,axiom,
% 2.39/2.82 ! [Y: num] :
% 2.39/2.82 ( ( bit_se1080825931792720795nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 2.39/2.82 = ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % or_numerals(1)
% 2.39/2.82 thf(fact_4743_or__numerals_I1_J,axiom,
% 2.39/2.82 ! [Y: num] :
% 2.39/2.82 ( ( bit_se9127793120404214118atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ Y ) ) )
% 2.39/2.82 = ( numera5444537566228673987atural @ ( bit1 @ Y ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % or_numerals(1)
% 2.39/2.82 thf(fact_4744_or__numerals_I1_J,axiom,
% 2.39/2.82 ! [Y: num] :
% 2.39/2.82 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 2.39/2.82 = ( numeral_numeral_int @ ( bit1 @ Y ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % or_numerals(1)
% 2.39/2.82 thf(fact_4745_or__numerals_I1_J,axiom,
% 2.39/2.82 ! [Y: num] :
% 2.39/2.82 ( ( bit_se1412395901928357646or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 2.39/2.82 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % or_numerals(1)
% 2.39/2.82 thf(fact_4746_push__bit__minus__one__eq__not__mask,axiom,
% 2.39/2.82 ! [N: nat] :
% 2.39/2.82 ( ( bit_se7788150548672797655nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 2.39/2.82 = ( bit_ri7632146776885996613nteger @ ( bit_se2119862282449309892nteger @ N ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % push_bit_minus_one_eq_not_mask
% 2.39/2.82 thf(fact_4747_push__bit__minus__one__eq__not__mask,axiom,
% 2.39/2.82 ! [N: nat] :
% 2.39/2.82 ( ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 2.39/2.82 = ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ N ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % push_bit_minus_one_eq_not_mask
% 2.39/2.82 thf(fact_4748_not__one__eq,axiom,
% 2.39/2.82 ( ( bit_ri7632146776885996613nteger @ one_one_Code_integer )
% 2.39/2.82 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % not_one_eq
% 2.39/2.82 thf(fact_4749_not__one__eq,axiom,
% 2.39/2.82 ( ( bit_ri7919022796975470100ot_int @ one_one_int )
% 2.39/2.82 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % not_one_eq
% 2.39/2.82 thf(fact_4750_or__minus__minus__numerals,axiom,
% 2.39/2.82 ! [M2: num,N: num] :
% 2.39/2.82 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 2.39/2.82 = ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % or_minus_minus_numerals
% 2.39/2.82 thf(fact_4751_and__minus__minus__numerals,axiom,
% 2.39/2.82 ! [M2: num,N: num] :
% 2.39/2.82 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 2.39/2.82 = ( bit_ri7919022796975470100ot_int @ ( bit_se1409905431419307370or_int @ ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % and_minus_minus_numerals
% 2.39/2.82 thf(fact_4752_or__not__numerals_I1_J,axiom,
% 2.39/2.82 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 2.39/2.82 = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 2.39/2.82
% 2.39/2.82 % or_not_numerals(1)
% 2.39/2.82 thf(fact_4753_abs__le__D1,axiom,
% 2.39/2.82 ! [A: code_integer,B: code_integer] :
% 2.39/2.82 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 2.39/2.82 => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 2.39/2.82
% 2.39/2.82 % abs_le_D1
% 2.39/2.82 thf(fact_4754_abs__le__D1,axiom,
% 2.39/2.82 ! [A: rat,B: rat] :
% 2.39/2.82 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 2.39/2.82 => ( ord_less_eq_rat @ A @ B ) ) ).
% 2.39/2.82
% 2.39/2.82 % abs_le_D1
% 2.39/2.82 thf(fact_4755_abs__le__D1,axiom,
% 2.39/2.82 ! [A: int,B: int] :
% 2.39/2.82 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 2.39/2.82 => ( ord_less_eq_int @ A @ B ) ) ).
% 2.39/2.82
% 2.39/2.82 % abs_le_D1
% 2.39/2.82 thf(fact_4756_abs__ge__self,axiom,
% 2.39/2.82 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( abs_abs_Code_integer @ A ) ) ).
% 2.39/2.82
% 2.39/2.82 % abs_ge_self
% 2.39/2.82 thf(fact_4757_abs__ge__self,axiom,
% 2.39/2.82 ! [A: rat] : ( ord_less_eq_rat @ A @ ( abs_abs_rat @ A ) ) ).
% 2.39/2.82
% 2.39/2.82 % abs_ge_self
% 2.39/2.82 thf(fact_4758_abs__ge__self,axiom,
% 2.39/2.82 ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) ).
% 2.39/2.82
% 2.39/2.82 % abs_ge_self
% 2.39/2.82 thf(fact_4759_abs__mult,axiom,
% 2.39/2.82 ! [A: int,B: int] :
% 2.39/2.82 ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 2.39/2.82 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 2.39/2.82
% 2.39/2.82 % abs_mult
% 2.39/2.82 thf(fact_4760_abs__mult,axiom,
% 2.39/2.82 ! [A: code_integer,B: code_integer] :
% 2.39/2.82 ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 2.39/2.82 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_mult
% 2.52/2.82 thf(fact_4761_abs__one,axiom,
% 2.52/2.82 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 2.52/2.82 = one_one_Code_integer ) ).
% 2.52/2.82
% 2.52/2.82 % abs_one
% 2.52/2.82 thf(fact_4762_abs__one,axiom,
% 2.52/2.82 ( ( abs_abs_rat @ one_one_rat )
% 2.52/2.82 = one_one_rat ) ).
% 2.52/2.82
% 2.52/2.82 % abs_one
% 2.52/2.82 thf(fact_4763_abs__one,axiom,
% 2.52/2.82 ( ( abs_abs_int @ one_one_int )
% 2.52/2.82 = one_one_int ) ).
% 2.52/2.82
% 2.52/2.82 % abs_one
% 2.52/2.82 thf(fact_4764_abs__minus__commute,axiom,
% 2.52/2.82 ! [A: int,B: int] :
% 2.52/2.82 ( ( abs_abs_int @ ( minus_minus_int @ A @ B ) )
% 2.52/2.82 = ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_minus_commute
% 2.52/2.82 thf(fact_4765_abs__minus__commute,axiom,
% 2.52/2.82 ! [A: code_integer,B: code_integer] :
% 2.52/2.82 ( ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) )
% 2.52/2.82 = ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_minus_commute
% 2.52/2.82 thf(fact_4766_set__bit__nat__def,axiom,
% 2.52/2.82 ( bit_se7882103937844011126it_nat
% 2.52/2.82 = ( ^ [M3: nat,N3: nat] : ( bit_se1412395901928357646or_nat @ N3 @ ( bit_se547839408752420682it_nat @ M3 @ one_one_nat ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % set_bit_nat_def
% 2.52/2.82 thf(fact_4767_or__not__numerals_I4_J,axiom,
% 2.52/2.82 ! [M2: num] :
% 2.52/2.82 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 2.52/2.82 = ( bit_ri7919022796975470100ot_int @ one_one_int ) ) ).
% 2.52/2.82
% 2.52/2.82 % or_not_numerals(4)
% 2.52/2.82 thf(fact_4768_or__not__numerals_I2_J,axiom,
% 2.52/2.82 ! [N: num] :
% 2.52/2.82 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 2.52/2.82 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % or_not_numerals(2)
% 2.52/2.82 thf(fact_4769_or__not__numerals_I3_J,axiom,
% 2.52/2.82 ! [N: num] :
% 2.52/2.82 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 2.52/2.82 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % or_not_numerals(3)
% 2.52/2.82 thf(fact_4770_or__not__numerals_I7_J,axiom,
% 2.52/2.82 ! [M2: num] :
% 2.52/2.82 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 2.52/2.82 = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 2.52/2.82
% 2.52/2.82 % or_not_numerals(7)
% 2.52/2.82 thf(fact_4771_bit_Ocompl__unique,axiom,
% 2.52/2.82 ! [X: code_integer,Y: code_integer] :
% 2.52/2.82 ( ( ( bit_se3949692690581998587nteger @ X @ Y )
% 2.52/2.82 = zero_z3403309356797280102nteger )
% 2.52/2.82 => ( ( ( bit_se1080825931792720795nteger @ X @ Y )
% 2.52/2.82 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 2.52/2.82 => ( ( bit_ri7632146776885996613nteger @ X )
% 2.52/2.82 = Y ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % bit.compl_unique
% 2.52/2.82 thf(fact_4772_bit_Ocompl__unique,axiom,
% 2.52/2.82 ! [X: int,Y: int] :
% 2.52/2.82 ( ( ( bit_se725231765392027082nd_int @ X @ Y )
% 2.52/2.82 = zero_zero_int )
% 2.52/2.82 => ( ( ( bit_se1409905431419307370or_int @ X @ Y )
% 2.52/2.82 = ( uminus_uminus_int @ one_one_int ) )
% 2.52/2.82 => ( ( bit_ri7919022796975470100ot_int @ X )
% 2.52/2.82 = Y ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % bit.compl_unique
% 2.52/2.82 thf(fact_4773_abs__ge__zero,axiom,
% 2.52/2.82 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_ge_zero
% 2.52/2.82 thf(fact_4774_abs__ge__zero,axiom,
% 2.52/2.82 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_ge_zero
% 2.52/2.82 thf(fact_4775_abs__ge__zero,axiom,
% 2.52/2.82 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_ge_zero
% 2.52/2.82 thf(fact_4776_abs__not__less__zero,axiom,
% 2.52/2.82 ! [A: code_integer] :
% 2.52/2.82 ~ ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger ) ).
% 2.52/2.82
% 2.52/2.82 % abs_not_less_zero
% 2.52/2.82 thf(fact_4777_abs__not__less__zero,axiom,
% 2.52/2.82 ! [A: rat] :
% 2.52/2.82 ~ ( ord_less_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat ) ).
% 2.52/2.82
% 2.52/2.82 % abs_not_less_zero
% 2.52/2.82 thf(fact_4778_abs__not__less__zero,axiom,
% 2.52/2.82 ! [A: int] :
% 2.52/2.82 ~ ( ord_less_int @ ( abs_abs_int @ A ) @ zero_zero_int ) ).
% 2.52/2.82
% 2.52/2.82 % abs_not_less_zero
% 2.52/2.82 thf(fact_4779_abs__of__pos,axiom,
% 2.52/2.82 ! [A: code_integer] :
% 2.52/2.82 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 2.52/2.82 => ( ( abs_abs_Code_integer @ A )
% 2.52/2.82 = A ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_of_pos
% 2.52/2.82 thf(fact_4780_abs__of__pos,axiom,
% 2.52/2.82 ! [A: rat] :
% 2.52/2.82 ( ( ord_less_rat @ zero_zero_rat @ A )
% 2.52/2.82 => ( ( abs_abs_rat @ A )
% 2.52/2.82 = A ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_of_pos
% 2.52/2.82 thf(fact_4781_abs__of__pos,axiom,
% 2.52/2.82 ! [A: int] :
% 2.52/2.82 ( ( ord_less_int @ zero_zero_int @ A )
% 2.52/2.82 => ( ( abs_abs_int @ A )
% 2.52/2.82 = A ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_of_pos
% 2.52/2.82 thf(fact_4782_abs__triangle__ineq,axiom,
% 2.52/2.82 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_triangle_ineq
% 2.52/2.82 thf(fact_4783_abs__triangle__ineq,axiom,
% 2.52/2.82 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( plus_plus_rat @ A @ B ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_triangle_ineq
% 2.52/2.82 thf(fact_4784_abs__triangle__ineq,axiom,
% 2.52/2.82 ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( plus_plus_int @ A @ B ) ) @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_triangle_ineq
% 2.52/2.82 thf(fact_4785_abs__triangle__ineq2__sym,axiom,
% 2.52/2.82 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_triangle_ineq2_sym
% 2.52/2.82 thf(fact_4786_abs__triangle__ineq2__sym,axiom,
% 2.52/2.82 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_triangle_ineq2_sym
% 2.52/2.82 thf(fact_4787_abs__triangle__ineq2__sym,axiom,
% 2.52/2.82 ! [A: int,B: int] : ( ord_less_eq_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_triangle_ineq2_sym
% 2.52/2.82 thf(fact_4788_abs__triangle__ineq3,axiom,
% 2.52/2.82 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_triangle_ineq3
% 2.52/2.82 thf(fact_4789_abs__triangle__ineq3,axiom,
% 2.52/2.82 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_triangle_ineq3
% 2.52/2.82 thf(fact_4790_abs__triangle__ineq3,axiom,
% 2.52/2.82 ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_triangle_ineq3
% 2.52/2.82 thf(fact_4791_abs__triangle__ineq2,axiom,
% 2.52/2.82 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_triangle_ineq2
% 2.52/2.82 thf(fact_4792_abs__triangle__ineq2,axiom,
% 2.52/2.82 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_triangle_ineq2
% 2.52/2.82 thf(fact_4793_abs__triangle__ineq2,axiom,
% 2.52/2.82 ! [A: int,B: int] : ( ord_less_eq_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_triangle_ineq2
% 2.52/2.82 thf(fact_4794_abs__mult__less,axiom,
% 2.52/2.82 ! [A: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 2.52/2.82 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ C )
% 2.52/2.82 => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ B ) @ D2 )
% 2.52/2.82 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( times_3573771949741848930nteger @ C @ D2 ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_mult_less
% 2.52/2.82 thf(fact_4795_abs__mult__less,axiom,
% 2.52/2.82 ! [A: rat,C: rat,B: rat,D2: rat] :
% 2.52/2.82 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ C )
% 2.52/2.82 => ( ( ord_less_rat @ ( abs_abs_rat @ B ) @ D2 )
% 2.52/2.82 => ( ord_less_rat @ ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( times_times_rat @ C @ D2 ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_mult_less
% 2.52/2.82 thf(fact_4796_abs__mult__less,axiom,
% 2.52/2.82 ! [A: int,C: int,B: int,D2: int] :
% 2.52/2.82 ( ( ord_less_int @ ( abs_abs_int @ A ) @ C )
% 2.52/2.82 => ( ( ord_less_int @ ( abs_abs_int @ B ) @ D2 )
% 2.52/2.82 => ( ord_less_int @ ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( times_times_int @ C @ D2 ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_mult_less
% 2.52/2.82 thf(fact_4797_abs__leI,axiom,
% 2.52/2.82 ! [A: code_integer,B: code_integer] :
% 2.52/2.82 ( ( ord_le3102999989581377725nteger @ A @ B )
% 2.52/2.82 => ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 2.52/2.82 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_leI
% 2.52/2.82 thf(fact_4798_abs__leI,axiom,
% 2.52/2.82 ! [A: rat,B: rat] :
% 2.52/2.82 ( ( ord_less_eq_rat @ A @ B )
% 2.52/2.82 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 2.52/2.82 => ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_leI
% 2.52/2.82 thf(fact_4799_abs__leI,axiom,
% 2.52/2.82 ! [A: int,B: int] :
% 2.52/2.82 ( ( ord_less_eq_int @ A @ B )
% 2.52/2.82 => ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 2.52/2.82 => ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_leI
% 2.52/2.82 thf(fact_4800_abs__le__D2,axiom,
% 2.52/2.82 ! [A: code_integer,B: code_integer] :
% 2.52/2.82 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 2.52/2.82 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_le_D2
% 2.52/2.82 thf(fact_4801_abs__le__D2,axiom,
% 2.52/2.82 ! [A: rat,B: rat] :
% 2.52/2.82 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 2.52/2.82 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_le_D2
% 2.52/2.82 thf(fact_4802_abs__le__D2,axiom,
% 2.52/2.82 ! [A: int,B: int] :
% 2.52/2.82 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 2.52/2.82 => ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_le_D2
% 2.52/2.82 thf(fact_4803_abs__le__iff,axiom,
% 2.52/2.82 ! [A: code_integer,B: code_integer] :
% 2.52/2.82 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 2.52/2.82 = ( ( ord_le3102999989581377725nteger @ A @ B )
% 2.52/2.82 & ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_le_iff
% 2.52/2.82 thf(fact_4804_abs__le__iff,axiom,
% 2.52/2.82 ! [A: rat,B: rat] :
% 2.52/2.82 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 2.52/2.82 = ( ( ord_less_eq_rat @ A @ B )
% 2.52/2.82 & ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_le_iff
% 2.52/2.82 thf(fact_4805_abs__le__iff,axiom,
% 2.52/2.82 ! [A: int,B: int] :
% 2.52/2.82 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 2.52/2.82 = ( ( ord_less_eq_int @ A @ B )
% 2.52/2.82 & ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_le_iff
% 2.52/2.82 thf(fact_4806_abs__ge__minus__self,axiom,
% 2.52/2.82 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ ( abs_abs_Code_integer @ A ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_ge_minus_self
% 2.52/2.82 thf(fact_4807_abs__ge__minus__self,axiom,
% 2.52/2.82 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ ( abs_abs_rat @ A ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_ge_minus_self
% 2.52/2.82 thf(fact_4808_abs__ge__minus__self,axiom,
% 2.52/2.82 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( abs_abs_int @ A ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_ge_minus_self
% 2.52/2.82 thf(fact_4809_linordered__idom__class_Oabs__sgn,axiom,
% 2.52/2.82 ( abs_abs_rat
% 2.52/2.82 = ( ^ [K4: rat] : ( times_times_rat @ K4 @ ( sgn_sgn_rat @ K4 ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % linordered_idom_class.abs_sgn
% 2.52/2.82 thf(fact_4810_linordered__idom__class_Oabs__sgn,axiom,
% 2.52/2.82 ( abs_abs_int
% 2.52/2.82 = ( ^ [K4: int] : ( times_times_int @ K4 @ ( sgn_sgn_int @ K4 ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % linordered_idom_class.abs_sgn
% 2.52/2.82 thf(fact_4811_linordered__idom__class_Oabs__sgn,axiom,
% 2.52/2.82 ( abs_abs_Code_integer
% 2.52/2.82 = ( ^ [K4: code_integer] : ( times_3573771949741848930nteger @ K4 @ ( sgn_sgn_Code_integer @ K4 ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % linordered_idom_class.abs_sgn
% 2.52/2.82 thf(fact_4812_abs__mult__sgn,axiom,
% 2.52/2.82 ! [A: rat] :
% 2.52/2.82 ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( sgn_sgn_rat @ A ) )
% 2.52/2.82 = A ) ).
% 2.52/2.82
% 2.52/2.82 % abs_mult_sgn
% 2.52/2.82 thf(fact_4813_abs__mult__sgn,axiom,
% 2.52/2.82 ! [A: int] :
% 2.52/2.82 ( ( times_times_int @ ( abs_abs_int @ A ) @ ( sgn_sgn_int @ A ) )
% 2.52/2.82 = A ) ).
% 2.52/2.82
% 2.52/2.82 % abs_mult_sgn
% 2.52/2.82 thf(fact_4814_abs__mult__sgn,axiom,
% 2.52/2.82 ! [A: code_integer] :
% 2.52/2.82 ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ A ) )
% 2.52/2.82 = A ) ).
% 2.52/2.82
% 2.52/2.82 % abs_mult_sgn
% 2.52/2.82 thf(fact_4815_sgn__mult__abs,axiom,
% 2.52/2.82 ! [A: rat] :
% 2.52/2.82 ( ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( abs_abs_rat @ A ) )
% 2.52/2.82 = A ) ).
% 2.52/2.82
% 2.52/2.82 % sgn_mult_abs
% 2.52/2.82 thf(fact_4816_sgn__mult__abs,axiom,
% 2.52/2.82 ! [A: int] :
% 2.52/2.82 ( ( times_times_int @ ( sgn_sgn_int @ A ) @ ( abs_abs_int @ A ) )
% 2.52/2.82 = A ) ).
% 2.52/2.82
% 2.52/2.82 % sgn_mult_abs
% 2.52/2.82 thf(fact_4817_sgn__mult__abs,axiom,
% 2.52/2.82 ! [A: code_integer] :
% 2.52/2.82 ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 2.52/2.82 = A ) ).
% 2.52/2.82
% 2.52/2.82 % sgn_mult_abs
% 2.52/2.82 thf(fact_4818_mult__sgn__abs,axiom,
% 2.52/2.82 ! [X: rat] :
% 2.52/2.82 ( ( times_times_rat @ ( sgn_sgn_rat @ X ) @ ( abs_abs_rat @ X ) )
% 2.52/2.82 = X ) ).
% 2.52/2.82
% 2.52/2.82 % mult_sgn_abs
% 2.52/2.82 thf(fact_4819_mult__sgn__abs,axiom,
% 2.52/2.82 ! [X: int] :
% 2.52/2.82 ( ( times_times_int @ ( sgn_sgn_int @ X ) @ ( abs_abs_int @ X ) )
% 2.52/2.82 = X ) ).
% 2.52/2.82
% 2.52/2.82 % mult_sgn_abs
% 2.52/2.82 thf(fact_4820_mult__sgn__abs,axiom,
% 2.52/2.82 ! [X: code_integer] :
% 2.52/2.82 ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ X ) @ ( abs_abs_Code_integer @ X ) )
% 2.52/2.82 = X ) ).
% 2.52/2.82
% 2.52/2.82 % mult_sgn_abs
% 2.52/2.82 thf(fact_4821_abs__zmult__eq__1,axiom,
% 2.52/2.82 ! [M2: int,N: int] :
% 2.52/2.82 ( ( ( abs_abs_int @ ( times_times_int @ M2 @ N ) )
% 2.52/2.82 = one_one_int )
% 2.52/2.82 => ( ( abs_abs_int @ M2 )
% 2.52/2.82 = one_one_int ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_zmult_eq_1
% 2.52/2.82 thf(fact_4822_set__bit__int__def,axiom,
% 2.52/2.82 ( bit_se7879613467334960850it_int
% 2.52/2.82 = ( ^ [N3: nat,K4: int] : ( bit_se1409905431419307370or_int @ K4 @ ( bit_se545348938243370406it_int @ N3 @ one_one_int ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % set_bit_int_def
% 2.52/2.82 thf(fact_4823_bit_Oabstract__boolean__algebra__axioms,axiom,
% 2.52/2.82 boolea5643492148547655015nteger @ bit_se3949692690581998587nteger @ bit_se1080825931792720795nteger @ bit_ri7632146776885996613nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ).
% 2.52/2.82
% 2.52/2.82 % bit.abstract_boolean_algebra_axioms
% 2.52/2.82 thf(fact_4824_bit_Oabstract__boolean__algebra__axioms,axiom,
% 2.52/2.82 boolea5469654029284665142ra_int @ bit_se725231765392027082nd_int @ bit_se1409905431419307370or_int @ bit_ri7919022796975470100ot_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ).
% 2.52/2.82
% 2.52/2.82 % bit.abstract_boolean_algebra_axioms
% 2.52/2.82 thf(fact_4825_or__not__numerals_I5_J,axiom,
% 2.52/2.82 ! [M2: num,N: num] :
% 2.52/2.82 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 2.52/2.82 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % or_not_numerals(5)
% 2.52/2.82 thf(fact_4826_dense__eq0__I,axiom,
% 2.52/2.82 ! [X: rat] :
% 2.52/2.82 ( ! [E: rat] :
% 2.52/2.82 ( ( ord_less_rat @ zero_zero_rat @ E )
% 2.52/2.82 => ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ E ) )
% 2.52/2.82 => ( X = zero_zero_rat ) ) ).
% 2.52/2.82
% 2.52/2.82 % dense_eq0_I
% 2.52/2.82 thf(fact_4827_abs__mult__pos,axiom,
% 2.52/2.82 ! [X: code_integer,Y: code_integer] :
% 2.52/2.82 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 2.52/2.82 => ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ Y ) @ X )
% 2.52/2.82 = ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ Y @ X ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_mult_pos
% 2.52/2.82 thf(fact_4828_abs__mult__pos,axiom,
% 2.52/2.82 ! [X: rat,Y: rat] :
% 2.52/2.82 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 2.52/2.82 => ( ( times_times_rat @ ( abs_abs_rat @ Y ) @ X )
% 2.52/2.82 = ( abs_abs_rat @ ( times_times_rat @ Y @ X ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_mult_pos
% 2.52/2.82 thf(fact_4829_abs__mult__pos,axiom,
% 2.52/2.82 ! [X: int,Y: int] :
% 2.52/2.82 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 2.52/2.82 => ( ( times_times_int @ ( abs_abs_int @ Y ) @ X )
% 2.52/2.82 = ( abs_abs_int @ ( times_times_int @ Y @ X ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_mult_pos
% 2.52/2.82 thf(fact_4830_abs__eq__mult,axiom,
% 2.52/2.82 ! [A: code_integer,B: code_integer] :
% 2.52/2.82 ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 2.52/2.82 | ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 2.52/2.82 & ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 2.52/2.82 | ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 2.52/2.82 => ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 2.52/2.82 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_eq_mult
% 2.52/2.82 thf(fact_4831_abs__eq__mult,axiom,
% 2.52/2.82 ! [A: rat,B: rat] :
% 2.52/2.82 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 2.52/2.82 | ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 2.52/2.82 & ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 2.52/2.82 | ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 2.52/2.82 => ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 2.52/2.82 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_eq_mult
% 2.52/2.82 thf(fact_4832_abs__eq__mult,axiom,
% 2.52/2.82 ! [A: int,B: int] :
% 2.52/2.82 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 2.52/2.82 | ( ord_less_eq_int @ A @ zero_zero_int ) )
% 2.52/2.82 & ( ( ord_less_eq_int @ zero_zero_int @ B )
% 2.52/2.82 | ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 2.52/2.82 => ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 2.52/2.82 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_eq_mult
% 2.52/2.82 thf(fact_4833_abs__minus__le__zero,axiom,
% 2.52/2.82 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( abs_abs_Code_integer @ A ) ) @ zero_z3403309356797280102nteger ) ).
% 2.52/2.82
% 2.52/2.82 % abs_minus_le_zero
% 2.52/2.82 thf(fact_4834_abs__minus__le__zero,axiom,
% 2.52/2.82 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( abs_abs_rat @ A ) ) @ zero_zero_rat ) ).
% 2.52/2.82
% 2.52/2.82 % abs_minus_le_zero
% 2.52/2.82 thf(fact_4835_abs__minus__le__zero,axiom,
% 2.52/2.82 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A ) ) @ zero_zero_int ) ).
% 2.52/2.82
% 2.52/2.82 % abs_minus_le_zero
% 2.52/2.82 thf(fact_4836_abs__triangle__ineq4,axiom,
% 2.52/2.82 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_triangle_ineq4
% 2.52/2.82 thf(fact_4837_abs__triangle__ineq4,axiom,
% 2.52/2.82 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_triangle_ineq4
% 2.52/2.82 thf(fact_4838_abs__triangle__ineq4,axiom,
% 2.52/2.82 ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_triangle_ineq4
% 2.52/2.82 thf(fact_4839_abs__diff__triangle__ineq,axiom,
% 2.52/2.82 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ ( plus_p5714425477246183910nteger @ C @ D2 ) ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ C ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ D2 ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_diff_triangle_ineq
% 2.52/2.82 thf(fact_4840_abs__diff__triangle__ineq,axiom,
% 2.52/2.82 ! [A: rat,B: rat,C: rat,D2: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ C @ D2 ) ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ C ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ D2 ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_diff_triangle_ineq
% 2.52/2.82 thf(fact_4841_abs__diff__triangle__ineq,axiom,
% 2.52/2.82 ! [A: int,B: int,C: int,D2: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ D2 ) ) ) @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ A @ C ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ D2 ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_diff_triangle_ineq
% 2.52/2.82 thf(fact_4842_abs__of__neg,axiom,
% 2.52/2.82 ! [A: int] :
% 2.52/2.82 ( ( ord_less_int @ A @ zero_zero_int )
% 2.52/2.82 => ( ( abs_abs_int @ A )
% 2.52/2.82 = ( uminus_uminus_int @ A ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_of_neg
% 2.52/2.82 thf(fact_4843_abs__of__neg,axiom,
% 2.52/2.82 ! [A: rat] :
% 2.52/2.82 ( ( ord_less_rat @ A @ zero_zero_rat )
% 2.52/2.82 => ( ( abs_abs_rat @ A )
% 2.52/2.82 = ( uminus_uminus_rat @ A ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_of_neg
% 2.52/2.82 thf(fact_4844_abs__of__neg,axiom,
% 2.52/2.82 ! [A: code_integer] :
% 2.52/2.82 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 2.52/2.82 => ( ( abs_abs_Code_integer @ A )
% 2.52/2.82 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_of_neg
% 2.52/2.82 thf(fact_4845_abs__sgn__eq,axiom,
% 2.52/2.82 ! [A: int] :
% 2.52/2.82 ( ( ( A = zero_zero_int )
% 2.52/2.82 => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 2.52/2.82 = zero_zero_int ) )
% 2.52/2.82 & ( ( A != zero_zero_int )
% 2.52/2.82 => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 2.52/2.82 = one_one_int ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_sgn_eq
% 2.52/2.82 thf(fact_4846_abs__sgn__eq,axiom,
% 2.52/2.82 ! [A: rat] :
% 2.52/2.82 ( ( ( A = zero_zero_rat )
% 2.52/2.82 => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 2.52/2.82 = zero_zero_rat ) )
% 2.52/2.82 & ( ( A != zero_zero_rat )
% 2.52/2.82 => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 2.52/2.82 = one_one_rat ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_sgn_eq
% 2.52/2.82 thf(fact_4847_abs__sgn__eq,axiom,
% 2.52/2.82 ! [A: code_integer] :
% 2.52/2.82 ( ( ( A = zero_z3403309356797280102nteger )
% 2.52/2.82 => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 2.52/2.82 = zero_z3403309356797280102nteger ) )
% 2.52/2.82 & ( ( A != zero_z3403309356797280102nteger )
% 2.52/2.82 => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 2.52/2.82 = one_one_Code_integer ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_sgn_eq
% 2.52/2.82 thf(fact_4848_minus__eq__not__plus__1,axiom,
% 2.52/2.82 ( uminus1351360451143612070nteger
% 2.52/2.82 = ( ^ [A2: code_integer] : ( plus_p5714425477246183910nteger @ ( bit_ri7632146776885996613nteger @ A2 ) @ one_one_Code_integer ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % minus_eq_not_plus_1
% 2.52/2.82 thf(fact_4849_minus__eq__not__plus__1,axiom,
% 2.52/2.82 ( uminus_uminus_int
% 2.52/2.82 = ( ^ [A2: int] : ( plus_plus_int @ ( bit_ri7919022796975470100ot_int @ A2 ) @ one_one_int ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % minus_eq_not_plus_1
% 2.52/2.82 thf(fact_4850_minus__eq__not__minus__1,axiom,
% 2.52/2.82 ( uminus1351360451143612070nteger
% 2.52/2.82 = ( ^ [A2: code_integer] : ( bit_ri7632146776885996613nteger @ ( minus_8373710615458151222nteger @ A2 @ one_one_Code_integer ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % minus_eq_not_minus_1
% 2.52/2.82 thf(fact_4851_minus__eq__not__minus__1,axiom,
% 2.52/2.82 ( uminus_uminus_int
% 2.52/2.82 = ( ^ [A2: int] : ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ A2 @ one_one_int ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % minus_eq_not_minus_1
% 2.52/2.82 thf(fact_4852_not__eq__complement,axiom,
% 2.52/2.82 ( bit_ri7632146776885996613nteger
% 2.52/2.82 = ( ^ [A2: code_integer] : ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A2 ) @ one_one_Code_integer ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % not_eq_complement
% 2.52/2.82 thf(fact_4853_not__eq__complement,axiom,
% 2.52/2.82 ( bit_ri7919022796975470100ot_int
% 2.52/2.82 = ( ^ [A2: int] : ( minus_minus_int @ ( uminus_uminus_int @ A2 ) @ one_one_int ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % not_eq_complement
% 2.52/2.82 thf(fact_4854_not__int__def,axiom,
% 2.52/2.82 ( bit_ri7919022796975470100ot_int
% 2.52/2.82 = ( ^ [K4: int] : ( minus_minus_int @ ( uminus_uminus_int @ K4 ) @ one_one_int ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % not_int_def
% 2.52/2.82 thf(fact_4855_and__not__numerals_I1_J,axiom,
% 2.52/2.82 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 2.52/2.82 = zero_zero_int ) ).
% 2.52/2.82
% 2.52/2.82 % and_not_numerals(1)
% 2.52/2.82 thf(fact_4856_set__bit__eq__or,axiom,
% 2.52/2.82 ( bit_se2793503036327961859nteger
% 2.52/2.82 = ( ^ [N3: nat,A2: code_integer] : ( bit_se1080825931792720795nteger @ A2 @ ( bit_se7788150548672797655nteger @ N3 @ one_one_Code_integer ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % set_bit_eq_or
% 2.52/2.82 thf(fact_4857_set__bit__eq__or,axiom,
% 2.52/2.82 ( bit_se7879613467334960850it_int
% 2.52/2.82 = ( ^ [N3: nat,A2: int] : ( bit_se1409905431419307370or_int @ A2 @ ( bit_se545348938243370406it_int @ N3 @ one_one_int ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % set_bit_eq_or
% 2.52/2.82 thf(fact_4858_set__bit__eq__or,axiom,
% 2.52/2.82 ( bit_se7882103937844011126it_nat
% 2.52/2.82 = ( ^ [N3: nat,A2: nat] : ( bit_se1412395901928357646or_nat @ A2 @ ( bit_se547839408752420682it_nat @ N3 @ one_one_nat ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % set_bit_eq_or
% 2.52/2.82 thf(fact_4859_or__not__numerals_I8_J,axiom,
% 2.52/2.82 ! [M2: num,N: num] :
% 2.52/2.82 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 2.52/2.82 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % or_not_numerals(8)
% 2.52/2.82 thf(fact_4860_or__not__numerals_I9_J,axiom,
% 2.52/2.82 ! [M2: num,N: num] :
% 2.52/2.82 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 2.52/2.82 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % or_not_numerals(9)
% 2.52/2.82 thf(fact_4861_unset__bit__int__def,axiom,
% 2.52/2.82 ( bit_se4203085406695923979it_int
% 2.52/2.82 = ( ^ [N3: nat,K4: int] : ( bit_se725231765392027082nd_int @ K4 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N3 @ one_one_int ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % unset_bit_int_def
% 2.52/2.82 thf(fact_4862_abs__add__one__gt__zero,axiom,
% 2.52/2.82 ! [X: code_integer] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_add_one_gt_zero
% 2.52/2.82 thf(fact_4863_abs__add__one__gt__zero,axiom,
% 2.52/2.82 ! [X: rat] : ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ ( abs_abs_rat @ X ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_add_one_gt_zero
% 2.52/2.82 thf(fact_4864_abs__add__one__gt__zero,axiom,
% 2.52/2.82 ! [X: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_add_one_gt_zero
% 2.52/2.82 thf(fact_4865_bit_Ocomplement__unique,axiom,
% 2.52/2.82 ! [A: code_integer,X: code_integer,Y: code_integer] :
% 2.52/2.82 ( ( ( bit_se3949692690581998587nteger @ A @ X )
% 2.52/2.82 = zero_z3403309356797280102nteger )
% 2.52/2.82 => ( ( ( bit_se1080825931792720795nteger @ A @ X )
% 2.52/2.82 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 2.52/2.82 => ( ( ( bit_se3949692690581998587nteger @ A @ Y )
% 2.52/2.82 = zero_z3403309356797280102nteger )
% 2.52/2.82 => ( ( ( bit_se1080825931792720795nteger @ A @ Y )
% 2.52/2.82 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 2.52/2.82 => ( X = Y ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % bit.complement_unique
% 2.52/2.82 thf(fact_4866_bit_Ocomplement__unique,axiom,
% 2.52/2.82 ! [A: int,X: int,Y: int] :
% 2.52/2.82 ( ( ( bit_se725231765392027082nd_int @ A @ X )
% 2.52/2.82 = zero_zero_int )
% 2.52/2.82 => ( ( ( bit_se1409905431419307370or_int @ A @ X )
% 2.52/2.82 = ( uminus_uminus_int @ one_one_int ) )
% 2.52/2.82 => ( ( ( bit_se725231765392027082nd_int @ A @ Y )
% 2.52/2.82 = zero_zero_int )
% 2.52/2.82 => ( ( ( bit_se1409905431419307370or_int @ A @ Y )
% 2.52/2.82 = ( uminus_uminus_int @ one_one_int ) )
% 2.52/2.82 => ( X = Y ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % bit.complement_unique
% 2.52/2.82 thf(fact_4867_and__not__numerals_I4_J,axiom,
% 2.52/2.82 ! [M2: num] :
% 2.52/2.82 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 2.52/2.82 = ( numeral_numeral_int @ ( bit0 @ M2 ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % and_not_numerals(4)
% 2.52/2.82 thf(fact_4868_and__not__numerals_I2_J,axiom,
% 2.52/2.82 ! [N: num] :
% 2.52/2.82 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 2.52/2.82 = one_one_int ) ).
% 2.52/2.82
% 2.52/2.82 % and_not_numerals(2)
% 2.52/2.82 thf(fact_4869_zdvd__mult__cancel1,axiom,
% 2.52/2.82 ! [M2: int,N: int] :
% 2.52/2.82 ( ( M2 != zero_zero_int )
% 2.52/2.82 => ( ( dvd_dvd_int @ ( times_times_int @ M2 @ N ) @ M2 )
% 2.52/2.82 = ( ( abs_abs_int @ N )
% 2.52/2.82 = one_one_int ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % zdvd_mult_cancel1
% 2.52/2.82 thf(fact_4870_unset__bit__eq__and__not,axiom,
% 2.52/2.82 ( bit_se8260200283734997820nteger
% 2.52/2.82 = ( ^ [N3: nat,A2: code_integer] : ( bit_se3949692690581998587nteger @ A2 @ ( bit_ri7632146776885996613nteger @ ( bit_se7788150548672797655nteger @ N3 @ one_one_Code_integer ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % unset_bit_eq_and_not
% 2.52/2.82 thf(fact_4871_unset__bit__eq__and__not,axiom,
% 2.52/2.82 ( bit_se4203085406695923979it_int
% 2.52/2.82 = ( ^ [N3: nat,A2: int] : ( bit_se725231765392027082nd_int @ A2 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N3 @ one_one_int ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % unset_bit_eq_and_not
% 2.52/2.82 thf(fact_4872_abs__square__eq__1,axiom,
% 2.52/2.82 ! [X: code_integer] :
% 2.52/2.82 ( ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.52/2.82 = one_one_Code_integer )
% 2.52/2.82 = ( ( abs_abs_Code_integer @ X )
% 2.52/2.82 = one_one_Code_integer ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_square_eq_1
% 2.52/2.82 thf(fact_4873_abs__square__eq__1,axiom,
% 2.52/2.82 ! [X: rat] :
% 2.52/2.82 ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.52/2.82 = one_one_rat )
% 2.52/2.82 = ( ( abs_abs_rat @ X )
% 2.52/2.82 = one_one_rat ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_square_eq_1
% 2.52/2.82 thf(fact_4874_abs__square__eq__1,axiom,
% 2.52/2.82 ! [X: int] :
% 2.52/2.82 ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.52/2.82 = one_one_int )
% 2.52/2.82 = ( ( abs_abs_int @ X )
% 2.52/2.82 = one_one_int ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_square_eq_1
% 2.52/2.82 thf(fact_4875_and__not__numerals_I7_J,axiom,
% 2.52/2.82 ! [M2: num] :
% 2.52/2.82 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 2.52/2.82 = ( numeral_numeral_int @ ( bit0 @ M2 ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % and_not_numerals(7)
% 2.52/2.82 thf(fact_4876_and__not__numerals_I3_J,axiom,
% 2.52/2.82 ! [N: num] :
% 2.52/2.82 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 2.52/2.82 = zero_zero_int ) ).
% 2.52/2.82
% 2.52/2.82 % and_not_numerals(3)
% 2.52/2.82 thf(fact_4877_xor__int__unfold,axiom,
% 2.52/2.82 ( bit_se6526347334894502574or_int
% 2.52/2.82 = ( ^ [K4: int,L3: int] :
% 2.52/2.82 ( if_int
% 2.52/2.82 @ ( K4
% 2.52/2.82 = ( uminus_uminus_int @ one_one_int ) )
% 2.52/2.82 @ ( bit_ri7919022796975470100ot_int @ L3 )
% 2.52/2.82 @ ( if_int
% 2.52/2.82 @ ( L3
% 2.52/2.82 = ( uminus_uminus_int @ one_one_int ) )
% 2.52/2.82 @ ( bit_ri7919022796975470100ot_int @ K4 )
% 2.52/2.82 @ ( if_int @ ( K4 = zero_zero_int ) @ L3 @ ( if_int @ ( L3 = zero_zero_int ) @ K4 @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ ( modulo_modulo_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % xor_int_unfold
% 2.52/2.82 thf(fact_4878_abs__square__le__1,axiom,
% 2.52/2.82 ! [X: code_integer] :
% 2.52/2.82 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 2.52/2.82 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_square_le_1
% 2.52/2.82 thf(fact_4879_abs__square__le__1,axiom,
% 2.52/2.82 ! [X: rat] :
% 2.52/2.82 ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 2.52/2.82 = ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_square_le_1
% 2.52/2.82 thf(fact_4880_abs__square__le__1,axiom,
% 2.52/2.82 ! [X: int] :
% 2.52/2.82 ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 2.52/2.82 = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_square_le_1
% 2.52/2.82 thf(fact_4881_abs__square__less__1,axiom,
% 2.52/2.82 ! [X: code_integer] :
% 2.52/2.82 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 2.52/2.82 = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_square_less_1
% 2.52/2.82 thf(fact_4882_abs__square__less__1,axiom,
% 2.52/2.82 ! [X: rat] :
% 2.52/2.82 ( ( ord_less_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 2.52/2.82 = ( ord_less_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_square_less_1
% 2.52/2.82 thf(fact_4883_abs__square__less__1,axiom,
% 2.52/2.82 ! [X: int] :
% 2.52/2.82 ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 2.52/2.82 = ( ord_less_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 2.52/2.82
% 2.52/2.82 % abs_square_less_1
% 2.52/2.82 thf(fact_4884_nat__intermed__int__val,axiom,
% 2.52/2.82 ! [M2: nat,N: nat,F2: nat > int,K: int] :
% 2.52/2.82 ( ! [I3: nat] :
% 2.52/2.82 ( ( ( ord_less_eq_nat @ M2 @ I3 )
% 2.52/2.82 & ( ord_less_nat @ I3 @ N ) )
% 2.52/2.82 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F2 @ ( suc @ I3 ) ) @ ( F2 @ I3 ) ) ) @ one_one_int ) )
% 2.52/2.82 => ( ( ord_less_eq_nat @ M2 @ N )
% 2.52/2.82 => ( ( ord_less_eq_int @ ( F2 @ M2 ) @ K )
% 2.52/2.82 => ( ( ord_less_eq_int @ K @ ( F2 @ N ) )
% 2.52/2.82 => ? [I3: nat] :
% 2.52/2.82 ( ( ord_less_eq_nat @ M2 @ I3 )
% 2.52/2.82 & ( ord_less_eq_nat @ I3 @ N )
% 2.52/2.82 & ( ( F2 @ I3 )
% 2.52/2.82 = K ) ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % nat_intermed_int_val
% 2.52/2.82 thf(fact_4885_decr__lemma,axiom,
% 2.52/2.82 ! [D2: int,X: int,Z: int] :
% 2.52/2.82 ( ( ord_less_int @ zero_zero_int @ D2 )
% 2.52/2.82 => ( ord_less_int @ ( minus_minus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z ) ) @ one_one_int ) @ D2 ) ) @ Z ) ) ).
% 2.52/2.82
% 2.52/2.82 % decr_lemma
% 2.52/2.82 thf(fact_4886_incr__lemma,axiom,
% 2.52/2.82 ! [D2: int,Z: int,X: int] :
% 2.52/2.82 ( ( ord_less_int @ zero_zero_int @ D2 )
% 2.52/2.82 => ( ord_less_int @ Z @ ( plus_plus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z ) ) @ one_one_int ) @ D2 ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % incr_lemma
% 2.52/2.82 thf(fact_4887_or__one__eq,axiom,
% 2.52/2.82 ! [A: code_integer] :
% 2.52/2.82 ( ( bit_se1080825931792720795nteger @ A @ one_one_Code_integer )
% 2.52/2.82 = ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % or_one_eq
% 2.52/2.82 thf(fact_4888_or__one__eq,axiom,
% 2.52/2.82 ! [A: code_natural] :
% 2.52/2.82 ( ( bit_se9127793120404214118atural @ A @ one_one_Code_natural )
% 2.52/2.82 = ( plus_p4538020629002901425atural @ A @ ( zero_n8403883297036319079atural @ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % or_one_eq
% 2.52/2.82 thf(fact_4889_or__one__eq,axiom,
% 2.52/2.82 ! [A: int] :
% 2.52/2.82 ( ( bit_se1409905431419307370or_int @ A @ one_one_int )
% 2.52/2.82 = ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % or_one_eq
% 2.52/2.82 thf(fact_4890_or__one__eq,axiom,
% 2.52/2.82 ! [A: nat] :
% 2.52/2.82 ( ( bit_se1412395901928357646or_nat @ A @ one_one_nat )
% 2.52/2.82 = ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % or_one_eq
% 2.52/2.82 thf(fact_4891_one__or__eq,axiom,
% 2.52/2.82 ! [A: code_integer] :
% 2.52/2.82 ( ( bit_se1080825931792720795nteger @ one_one_Code_integer @ A )
% 2.52/2.82 = ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % one_or_eq
% 2.52/2.82 thf(fact_4892_one__or__eq,axiom,
% 2.52/2.82 ! [A: code_natural] :
% 2.52/2.82 ( ( bit_se9127793120404214118atural @ one_one_Code_natural @ A )
% 2.52/2.82 = ( plus_p4538020629002901425atural @ A @ ( zero_n8403883297036319079atural @ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % one_or_eq
% 2.52/2.82 thf(fact_4893_one__or__eq,axiom,
% 2.52/2.82 ! [A: int] :
% 2.52/2.82 ( ( bit_se1409905431419307370or_int @ one_one_int @ A )
% 2.52/2.82 = ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % one_or_eq
% 2.52/2.82 thf(fact_4894_one__or__eq,axiom,
% 2.52/2.82 ! [A: nat] :
% 2.52/2.82 ( ( bit_se1412395901928357646or_nat @ one_one_nat @ A )
% 2.52/2.82 = ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % one_or_eq
% 2.52/2.82 thf(fact_4895_mask__Suc__double,axiom,
% 2.52/2.82 ! [N: nat] :
% 2.52/2.82 ( ( bit_se2119862282449309892nteger @ ( suc @ N ) )
% 2.52/2.82 = ( bit_se1080825931792720795nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2119862282449309892nteger @ N ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % mask_Suc_double
% 2.52/2.82 thf(fact_4896_mask__Suc__double,axiom,
% 2.52/2.82 ! [N: nat] :
% 2.52/2.82 ( ( bit_se943457434206027407atural @ ( suc @ N ) )
% 2.52/2.82 = ( bit_se9127793120404214118atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se943457434206027407atural @ N ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % mask_Suc_double
% 2.52/2.82 thf(fact_4897_mask__Suc__double,axiom,
% 2.52/2.82 ! [N: nat] :
% 2.52/2.82 ( ( bit_se2000444600071755411sk_int @ ( suc @ N ) )
% 2.52/2.82 = ( bit_se1409905431419307370or_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ N ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % mask_Suc_double
% 2.52/2.82 thf(fact_4898_mask__Suc__double,axiom,
% 2.52/2.82 ! [N: nat] :
% 2.52/2.82 ( ( bit_se2002935070580805687sk_nat @ ( suc @ N ) )
% 2.52/2.82 = ( bit_se1412395901928357646or_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % mask_Suc_double
% 2.52/2.82 thf(fact_4899_nat__ivt__aux,axiom,
% 2.52/2.82 ! [N: nat,F2: nat > int,K: int] :
% 2.52/2.82 ( ! [I3: nat] :
% 2.52/2.82 ( ( ord_less_nat @ I3 @ N )
% 2.52/2.82 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F2 @ ( suc @ I3 ) ) @ ( F2 @ I3 ) ) ) @ one_one_int ) )
% 2.52/2.82 => ( ( ord_less_eq_int @ ( F2 @ zero_zero_nat ) @ K )
% 2.52/2.82 => ( ( ord_less_eq_int @ K @ ( F2 @ N ) )
% 2.52/2.82 => ? [I3: nat] :
% 2.52/2.82 ( ( ord_less_eq_nat @ I3 @ N )
% 2.52/2.82 & ( ( F2 @ I3 )
% 2.52/2.82 = K ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % nat_ivt_aux
% 2.52/2.82 thf(fact_4900_bit_Oabstract__boolean__algebra__sym__diff__axioms,axiom,
% 2.52/2.82 boolea2445317508997433345nteger @ bit_se3949692690581998587nteger @ bit_se1080825931792720795nteger @ bit_ri7632146776885996613nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ bit_se3222712562003087583nteger ).
% 2.52/2.82
% 2.52/2.82 % bit.abstract_boolean_algebra_sym_diff_axioms
% 2.52/2.82 thf(fact_4901_bit_Oabstract__boolean__algebra__sym__diff__axioms,axiom,
% 2.52/2.82 boolea8527374999097803216ff_int @ bit_se725231765392027082nd_int @ bit_se1409905431419307370or_int @ bit_ri7919022796975470100ot_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) @ bit_se6526347334894502574or_int ).
% 2.52/2.82
% 2.52/2.82 % bit.abstract_boolean_algebra_sym_diff_axioms
% 2.52/2.82 thf(fact_4902_or__int__unfold,axiom,
% 2.52/2.82 ( bit_se1409905431419307370or_int
% 2.52/2.82 = ( ^ [K4: int,L3: int] :
% 2.52/2.82 ( if_int
% 2.52/2.82 @ ( ( K4
% 2.52/2.82 = ( uminus_uminus_int @ one_one_int ) )
% 2.52/2.82 | ( L3
% 2.52/2.82 = ( uminus_uminus_int @ one_one_int ) ) )
% 2.52/2.82 @ ( uminus_uminus_int @ one_one_int )
% 2.52/2.82 @ ( if_int @ ( K4 = zero_zero_int ) @ L3 @ ( if_int @ ( L3 = zero_zero_int ) @ K4 @ ( plus_plus_int @ ( ord_max_int @ ( modulo_modulo_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % or_int_unfold
% 2.52/2.82 thf(fact_4903_or__minus__numerals_I5_J,axiom,
% 2.52/2.82 ! [N: num] :
% 2.52/2.82 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 2.52/2.82 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % or_minus_numerals(5)
% 2.52/2.82 thf(fact_4904_or__minus__numerals_I1_J,axiom,
% 2.52/2.82 ! [N: num] :
% 2.52/2.82 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 2.52/2.82 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % or_minus_numerals(1)
% 2.52/2.82 thf(fact_4905_product__nth,axiom,
% 2.52/2.82 ! [N: nat,Xs: list_h2745205591237434579t_unit,Ys: list_set_nat] :
% 2.52/2.82 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s7011499401410611007t_unit @ Xs ) @ ( size_s3254054031482475050et_nat @ Ys ) ) )
% 2.52/2.82 => ( ( nth_Pr7683458668995092411et_nat @ ( produc7481864959766642638et_nat @ Xs @ Ys ) @ N )
% 2.52/2.82 = ( produc7507926704131184380et_nat @ ( nth_he7452997726511547988t_unit @ Xs @ ( divide_divide_nat @ N @ ( size_s3254054031482475050et_nat @ Ys ) ) ) @ ( nth_set_nat @ Ys @ ( modulo_modulo_nat @ N @ ( size_s3254054031482475050et_nat @ Ys ) ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % product_nth
% 2.52/2.82 thf(fact_4906_product__nth,axiom,
% 2.52/2.82 ! [N: nat,Xs: list_P7985473006766602707_nat_o,Ys: list_P9062070895058802706et_nat] :
% 2.52/2.82 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s8908918004648414271_nat_o @ Xs ) @ ( size_s2864271983995610790et_nat @ Ys ) ) )
% 2.52/2.82 => ( ( nth_Pr3610913089060847927et_nat @ ( produc2866688925348378442et_nat @ Xs @ Ys ) @ N )
% 2.52/2.82 = ( produc5001842942810119800et_nat @ ( nth_Pr6840583978799713108_nat_o @ Xs @ ( divide_divide_nat @ N @ ( size_s2864271983995610790et_nat @ Ys ) ) ) @ ( nth_Pr7683458668995092411et_nat @ Ys @ ( modulo_modulo_nat @ N @ ( size_s2864271983995610790et_nat @ Ys ) ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % product_nth
% 2.52/2.82 thf(fact_4907_product__nth,axiom,
% 2.52/2.82 ! [N: nat,Xs: list_P7985473006766602707_nat_o,Ys: list_P2321686559999237006et_nat] :
% 2.52/2.82 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s8908918004648414271_nat_o @ Xs ) @ ( size_s6841928198497307170et_nat @ Ys ) ) )
% 2.52/2.82 => ( ( nth_Pr7590663101126261939et_nat @ ( produc7119410244218060998et_nat @ Xs @ Ys ) @ N )
% 2.52/2.82 = ( produc2245416461498447860et_nat @ ( nth_Pr6840583978799713108_nat_o @ Xs @ ( divide_divide_nat @ N @ ( size_s6841928198497307170et_nat @ Ys ) ) ) @ ( nth_Pr3610913089060847927et_nat @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6841928198497307170et_nat @ Ys ) ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % product_nth
% 2.52/2.82 thf(fact_4908_product__nth,axiom,
% 2.52/2.82 ! [N: nat,Xs: list_int,Ys: list_int] :
% 2.52/2.82 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_int @ Xs ) @ ( size_size_list_int @ Ys ) ) )
% 2.52/2.82 => ( ( nth_Pr4439495888332055232nt_int @ ( product_int_int @ Xs @ Ys ) @ N )
% 2.52/2.82 = ( product_Pair_int_int @ ( nth_int @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % product_nth
% 2.52/2.82 thf(fact_4909_product__nth,axiom,
% 2.52/2.82 ! [N: nat,Xs: list_int,Ys: list_nat] :
% 2.52/2.82 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_int @ Xs ) @ ( size_size_list_nat @ Ys ) ) )
% 2.52/2.82 => ( ( nth_Pr8617346907841251940nt_nat @ ( product_int_nat @ Xs @ Ys ) @ N )
% 2.52/2.82 = ( product_Pair_int_nat @ ( nth_int @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % product_nth
% 2.52/2.82 thf(fact_4910_product__nth,axiom,
% 2.52/2.82 ! [N: nat,Xs: list_nat,Ys: list_int] :
% 2.52/2.82 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_int @ Ys ) ) )
% 2.52/2.82 => ( ( nth_Pr3440142176431000676at_int @ ( product_nat_int @ Xs @ Ys ) @ N )
% 2.52/2.82 = ( product_Pair_nat_int @ ( nth_nat @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % product_nth
% 2.52/2.82 thf(fact_4911_product__nth,axiom,
% 2.52/2.82 ! [N: nat,Xs: list_nat,Ys: list_nat] :
% 2.52/2.82 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_nat @ Ys ) ) )
% 2.52/2.82 => ( ( nth_Pr7617993195940197384at_nat @ ( product_nat_nat @ Xs @ Ys ) @ N )
% 2.52/2.82 = ( product_Pair_nat_nat @ ( nth_nat @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % product_nth
% 2.52/2.82 thf(fact_4912_drop__bit__rec,axiom,
% 2.52/2.82 ( bit_se3928097537394005634nteger
% 2.52/2.82 = ( ^ [N3: nat,A2: code_integer] : ( if_Code_integer @ ( N3 = zero_zero_nat ) @ A2 @ ( bit_se3928097537394005634nteger @ ( minus_minus_nat @ N3 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % drop_bit_rec
% 2.52/2.82 thf(fact_4913_drop__bit__rec,axiom,
% 2.52/2.82 ( bit_se8570568707652914677it_nat
% 2.52/2.82 = ( ^ [N3: nat,A2: nat] : ( if_nat @ ( N3 = zero_zero_nat ) @ A2 @ ( bit_se8570568707652914677it_nat @ ( minus_minus_nat @ N3 @ one_one_nat ) @ ( divide_divide_nat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % drop_bit_rec
% 2.52/2.82 thf(fact_4914_drop__bit__rec,axiom,
% 2.52/2.82 ( bit_se2751692689150723149atural
% 2.52/2.82 = ( ^ [N3: nat,A2: code_natural] : ( if_Code_natural @ ( N3 = zero_zero_nat ) @ A2 @ ( bit_se2751692689150723149atural @ ( minus_minus_nat @ N3 @ one_one_nat ) @ ( divide5121882707175180666atural @ A2 @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % drop_bit_rec
% 2.52/2.82 thf(fact_4915_drop__bit__rec,axiom,
% 2.52/2.82 ( bit_se8568078237143864401it_int
% 2.52/2.82 = ( ^ [N3: nat,A2: int] : ( if_int @ ( N3 = zero_zero_nat ) @ A2 @ ( bit_se8568078237143864401it_int @ ( minus_minus_nat @ N3 @ one_one_nat ) @ ( divide_divide_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % drop_bit_rec
% 2.52/2.82 thf(fact_4916_bit__rec,axiom,
% 2.52/2.82 ( bit_se9216721137139052372nteger
% 2.52/2.82 = ( ^ [A2: code_integer,N3: nat] :
% 2.52/2.82 ( ( ( N3 = zero_zero_nat )
% 2.52/2.82 => ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A2 ) )
% 2.52/2.82 & ( ( N3 != zero_zero_nat )
% 2.52/2.82 => ( bit_se9216721137139052372nteger @ ( divide6298287555418463151nteger @ A2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % bit_rec
% 2.52/2.82 thf(fact_4917_bit__rec,axiom,
% 2.52/2.82 ( bit_se1148574629649215175it_nat
% 2.52/2.82 = ( ^ [A2: nat,N3: nat] :
% 2.52/2.82 ( ( ( N3 = zero_zero_nat )
% 2.52/2.82 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A2 ) )
% 2.52/2.82 & ( ( N3 != zero_zero_nat )
% 2.52/2.82 => ( bit_se1148574629649215175it_nat @ ( divide_divide_nat @ A2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % bit_rec
% 2.52/2.82 thf(fact_4918_bit__rec,axiom,
% 2.52/2.82 ( bit_se8040316288895769887atural
% 2.52/2.82 = ( ^ [A2: code_natural,N3: nat] :
% 2.52/2.82 ( ( ( N3 = zero_zero_nat )
% 2.52/2.82 => ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A2 ) )
% 2.52/2.82 & ( ( N3 != zero_zero_nat )
% 2.52/2.82 => ( bit_se8040316288895769887atural @ ( divide5121882707175180666atural @ A2 @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % bit_rec
% 2.52/2.82 thf(fact_4919_bit__rec,axiom,
% 2.52/2.82 ( bit_se1146084159140164899it_int
% 2.52/2.82 = ( ^ [A2: int,N3: nat] :
% 2.52/2.82 ( ( ( N3 = zero_zero_nat )
% 2.52/2.82 => ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 ) )
% 2.52/2.82 & ( ( N3 != zero_zero_nat )
% 2.52/2.82 => ( bit_se1146084159140164899it_int @ ( divide_divide_int @ A2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % bit_rec
% 2.52/2.82 thf(fact_4920_bit__sum__mult__2__cases,axiom,
% 2.52/2.82 ! [A: nat,B: nat,N: nat] :
% 2.52/2.82 ( ! [J3: nat] :
% 2.52/2.82 ~ ( bit_se1148574629649215175it_nat @ A @ ( suc @ J3 ) )
% 2.52/2.82 => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ N )
% 2.52/2.82 = ( ( ( N = zero_zero_nat )
% 2.52/2.82 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 2.52/2.82 & ( ( N != zero_zero_nat )
% 2.52/2.82 => ( bit_se1148574629649215175it_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) @ N ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % bit_sum_mult_2_cases
% 2.52/2.82 thf(fact_4921_bit__sum__mult__2__cases,axiom,
% 2.52/2.82 ! [A: code_integer,B: code_integer,N: nat] :
% 2.52/2.82 ( ! [J3: nat] :
% 2.52/2.82 ~ ( bit_se9216721137139052372nteger @ A @ ( suc @ J3 ) )
% 2.52/2.82 => ( ( bit_se9216721137139052372nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ N )
% 2.52/2.82 = ( ( ( N = zero_zero_nat )
% 2.52/2.82 => ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 2.52/2.82 & ( ( N != zero_zero_nat )
% 2.52/2.82 => ( bit_se9216721137139052372nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) @ N ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % bit_sum_mult_2_cases
% 2.52/2.82 thf(fact_4922_bit__sum__mult__2__cases,axiom,
% 2.52/2.82 ! [A: code_natural,B: code_natural,N: nat] :
% 2.52/2.82 ( ! [J3: nat] :
% 2.52/2.82 ~ ( bit_se8040316288895769887atural @ A @ ( suc @ J3 ) )
% 2.52/2.82 => ( ( bit_se8040316288895769887atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ B ) ) @ N )
% 2.52/2.82 = ( ( ( N = zero_zero_nat )
% 2.52/2.82 => ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) )
% 2.52/2.82 & ( ( N != zero_zero_nat )
% 2.52/2.82 => ( bit_se8040316288895769887atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ B ) @ N ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % bit_sum_mult_2_cases
% 2.52/2.82 thf(fact_4923_bit__sum__mult__2__cases,axiom,
% 2.52/2.82 ! [A: int,B: int,N: nat] :
% 2.52/2.82 ( ! [J3: nat] :
% 2.52/2.82 ~ ( bit_se1146084159140164899it_int @ A @ ( suc @ J3 ) )
% 2.52/2.82 => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ N )
% 2.52/2.82 = ( ( ( N = zero_zero_nat )
% 2.52/2.82 => ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 2.52/2.82 & ( ( N != zero_zero_nat )
% 2.52/2.82 => ( bit_se1146084159140164899it_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ N ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % bit_sum_mult_2_cases
% 2.52/2.82 thf(fact_4924_max_Oright__idem,axiom,
% 2.52/2.82 ! [A: int,B: int] :
% 2.52/2.82 ( ( ord_max_int @ ( ord_max_int @ A @ B ) @ B )
% 2.52/2.82 = ( ord_max_int @ A @ B ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.right_idem
% 2.52/2.82 thf(fact_4925_max_Oleft__idem,axiom,
% 2.52/2.82 ! [A: int,B: int] :
% 2.52/2.82 ( ( ord_max_int @ A @ ( ord_max_int @ A @ B ) )
% 2.52/2.82 = ( ord_max_int @ A @ B ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.left_idem
% 2.52/2.82 thf(fact_4926_max_Oidem,axiom,
% 2.52/2.82 ! [A: int] :
% 2.52/2.82 ( ( ord_max_int @ A @ A )
% 2.52/2.82 = A ) ).
% 2.52/2.82
% 2.52/2.82 % max.idem
% 2.52/2.82 thf(fact_4927_max_Obounded__iff,axiom,
% 2.52/2.82 ! [B: rat,C: rat,A: rat] :
% 2.52/2.82 ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A )
% 2.52/2.82 = ( ( ord_less_eq_rat @ B @ A )
% 2.52/2.82 & ( ord_less_eq_rat @ C @ A ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.bounded_iff
% 2.52/2.82 thf(fact_4928_max_Obounded__iff,axiom,
% 2.52/2.82 ! [B: nat,C: nat,A: nat] :
% 2.52/2.82 ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 2.52/2.82 = ( ( ord_less_eq_nat @ B @ A )
% 2.52/2.82 & ( ord_less_eq_nat @ C @ A ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.bounded_iff
% 2.52/2.82 thf(fact_4929_max_Obounded__iff,axiom,
% 2.52/2.82 ! [B: int,C: int,A: int] :
% 2.52/2.82 ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 2.52/2.82 = ( ( ord_less_eq_int @ B @ A )
% 2.52/2.82 & ( ord_less_eq_int @ C @ A ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.bounded_iff
% 2.52/2.82 thf(fact_4930_max_Oabsorb2,axiom,
% 2.52/2.82 ! [A: rat,B: rat] :
% 2.52/2.82 ( ( ord_less_eq_rat @ A @ B )
% 2.52/2.82 => ( ( ord_max_rat @ A @ B )
% 2.52/2.82 = B ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.absorb2
% 2.52/2.82 thf(fact_4931_max_Oabsorb2,axiom,
% 2.52/2.82 ! [A: nat,B: nat] :
% 2.52/2.82 ( ( ord_less_eq_nat @ A @ B )
% 2.52/2.82 => ( ( ord_max_nat @ A @ B )
% 2.52/2.82 = B ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.absorb2
% 2.52/2.82 thf(fact_4932_max_Oabsorb2,axiom,
% 2.52/2.82 ! [A: int,B: int] :
% 2.52/2.82 ( ( ord_less_eq_int @ A @ B )
% 2.52/2.82 => ( ( ord_max_int @ A @ B )
% 2.52/2.82 = B ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.absorb2
% 2.52/2.82 thf(fact_4933_max_Oabsorb1,axiom,
% 2.52/2.82 ! [B: rat,A: rat] :
% 2.52/2.82 ( ( ord_less_eq_rat @ B @ A )
% 2.52/2.82 => ( ( ord_max_rat @ A @ B )
% 2.52/2.82 = A ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.absorb1
% 2.52/2.82 thf(fact_4934_max_Oabsorb1,axiom,
% 2.52/2.82 ! [B: nat,A: nat] :
% 2.52/2.82 ( ( ord_less_eq_nat @ B @ A )
% 2.52/2.82 => ( ( ord_max_nat @ A @ B )
% 2.52/2.82 = A ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.absorb1
% 2.52/2.82 thf(fact_4935_max_Oabsorb1,axiom,
% 2.52/2.82 ! [B: int,A: int] :
% 2.52/2.82 ( ( ord_less_eq_int @ B @ A )
% 2.52/2.82 => ( ( ord_max_int @ A @ B )
% 2.52/2.82 = A ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.absorb1
% 2.52/2.82 thf(fact_4936_length__map,axiom,
% 2.52/2.82 ! [F2: produc6575502325842934193n_assn > assn,Xs: list_P8527749157015355191n_assn] :
% 2.52/2.82 ( ( size_size_list_assn @ ( map_Pr8991440229025900053n_assn @ F2 @ Xs ) )
% 2.52/2.82 = ( size_s6829681357464350627n_assn @ Xs ) ) ).
% 2.52/2.82
% 2.52/2.82 % length_map
% 2.52/2.82 thf(fact_4937_length__map,axiom,
% 2.52/2.82 ! [F2: int > int,Xs: list_int] :
% 2.52/2.82 ( ( size_size_list_int @ ( map_int_int @ F2 @ Xs ) )
% 2.52/2.82 = ( size_size_list_int @ Xs ) ) ).
% 2.52/2.82
% 2.52/2.82 % length_map
% 2.52/2.82 thf(fact_4938_length__map,axiom,
% 2.52/2.82 ! [F2: nat > int,Xs: list_nat] :
% 2.52/2.82 ( ( size_size_list_int @ ( map_nat_int @ F2 @ Xs ) )
% 2.52/2.82 = ( size_size_list_nat @ Xs ) ) ).
% 2.52/2.82
% 2.52/2.82 % length_map
% 2.52/2.82 thf(fact_4939_length__map,axiom,
% 2.52/2.82 ! [F2: int > nat,Xs: list_int] :
% 2.52/2.82 ( ( size_size_list_nat @ ( map_int_nat @ F2 @ Xs ) )
% 2.52/2.82 = ( size_size_list_int @ Xs ) ) ).
% 2.52/2.82
% 2.52/2.82 % length_map
% 2.52/2.82 thf(fact_4940_length__map,axiom,
% 2.52/2.82 ! [F2: nat > nat,Xs: list_nat] :
% 2.52/2.82 ( ( size_size_list_nat @ ( map_nat_nat @ F2 @ Xs ) )
% 2.52/2.82 = ( size_size_list_nat @ Xs ) ) ).
% 2.52/2.82
% 2.52/2.82 % length_map
% 2.52/2.82 thf(fact_4941_max__less__iff__conj,axiom,
% 2.52/2.82 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 2.52/2.82 ( ( ord_le6747313008572928689nteger @ ( ord_max_Code_integer @ X @ Y ) @ Z )
% 2.52/2.82 = ( ( ord_le6747313008572928689nteger @ X @ Z )
% 2.52/2.82 & ( ord_le6747313008572928689nteger @ Y @ Z ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % max_less_iff_conj
% 2.52/2.82 thf(fact_4942_max__less__iff__conj,axiom,
% 2.52/2.82 ! [X: rat,Y: rat,Z: rat] :
% 2.52/2.82 ( ( ord_less_rat @ ( ord_max_rat @ X @ Y ) @ Z )
% 2.52/2.82 = ( ( ord_less_rat @ X @ Z )
% 2.52/2.82 & ( ord_less_rat @ Y @ Z ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % max_less_iff_conj
% 2.52/2.82 thf(fact_4943_max__less__iff__conj,axiom,
% 2.52/2.82 ! [X: nat,Y: nat,Z: nat] :
% 2.52/2.82 ( ( ord_less_nat @ ( ord_max_nat @ X @ Y ) @ Z )
% 2.52/2.82 = ( ( ord_less_nat @ X @ Z )
% 2.52/2.82 & ( ord_less_nat @ Y @ Z ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % max_less_iff_conj
% 2.52/2.82 thf(fact_4944_max__less__iff__conj,axiom,
% 2.52/2.82 ! [X: int,Y: int,Z: int] :
% 2.52/2.82 ( ( ord_less_int @ ( ord_max_int @ X @ Y ) @ Z )
% 2.52/2.82 = ( ( ord_less_int @ X @ Z )
% 2.52/2.82 & ( ord_less_int @ Y @ Z ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % max_less_iff_conj
% 2.52/2.82 thf(fact_4945_max_Oabsorb4,axiom,
% 2.52/2.82 ! [A: code_integer,B: code_integer] :
% 2.52/2.82 ( ( ord_le6747313008572928689nteger @ A @ B )
% 2.52/2.82 => ( ( ord_max_Code_integer @ A @ B )
% 2.52/2.82 = B ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.absorb4
% 2.52/2.82 thf(fact_4946_max_Oabsorb4,axiom,
% 2.52/2.82 ! [A: rat,B: rat] :
% 2.52/2.82 ( ( ord_less_rat @ A @ B )
% 2.52/2.82 => ( ( ord_max_rat @ A @ B )
% 2.52/2.82 = B ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.absorb4
% 2.52/2.82 thf(fact_4947_max_Oabsorb4,axiom,
% 2.52/2.82 ! [A: nat,B: nat] :
% 2.52/2.82 ( ( ord_less_nat @ A @ B )
% 2.52/2.82 => ( ( ord_max_nat @ A @ B )
% 2.52/2.82 = B ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.absorb4
% 2.52/2.82 thf(fact_4948_max_Oabsorb4,axiom,
% 2.52/2.82 ! [A: int,B: int] :
% 2.52/2.82 ( ( ord_less_int @ A @ B )
% 2.52/2.82 => ( ( ord_max_int @ A @ B )
% 2.52/2.82 = B ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.absorb4
% 2.52/2.82 thf(fact_4949_max_Oabsorb3,axiom,
% 2.52/2.82 ! [B: code_integer,A: code_integer] :
% 2.52/2.82 ( ( ord_le6747313008572928689nteger @ B @ A )
% 2.52/2.82 => ( ( ord_max_Code_integer @ A @ B )
% 2.52/2.82 = A ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.absorb3
% 2.52/2.82 thf(fact_4950_max_Oabsorb3,axiom,
% 2.52/2.82 ! [B: rat,A: rat] :
% 2.52/2.82 ( ( ord_less_rat @ B @ A )
% 2.52/2.82 => ( ( ord_max_rat @ A @ B )
% 2.52/2.82 = A ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.absorb3
% 2.52/2.82 thf(fact_4951_max_Oabsorb3,axiom,
% 2.52/2.82 ! [B: nat,A: nat] :
% 2.52/2.82 ( ( ord_less_nat @ B @ A )
% 2.52/2.82 => ( ( ord_max_nat @ A @ B )
% 2.52/2.82 = A ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.absorb3
% 2.52/2.82 thf(fact_4952_max_Oabsorb3,axiom,
% 2.52/2.82 ! [B: int,A: int] :
% 2.52/2.82 ( ( ord_less_int @ B @ A )
% 2.52/2.82 => ( ( ord_max_int @ A @ B )
% 2.52/2.82 = A ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.absorb3
% 2.52/2.82 thf(fact_4953_drop__bit__minus__one,axiom,
% 2.52/2.82 ! [N: nat] :
% 2.52/2.82 ( ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 2.52/2.82 = ( uminus_uminus_int @ one_one_int ) ) ).
% 2.52/2.82
% 2.52/2.82 % drop_bit_minus_one
% 2.52/2.82 thf(fact_4954_zip__eq__zip__same__len,axiom,
% 2.52/2.82 ! [A: list_int,B: list_int,A5: list_int,B6: list_int] :
% 2.52/2.82 ( ( ( size_size_list_int @ A )
% 2.52/2.82 = ( size_size_list_int @ B ) )
% 2.52/2.82 => ( ( ( size_size_list_int @ A5 )
% 2.52/2.82 = ( size_size_list_int @ B6 ) )
% 2.52/2.82 => ( ( ( zip_int_int @ A @ B )
% 2.52/2.82 = ( zip_int_int @ A5 @ B6 ) )
% 2.52/2.82 = ( ( A = A5 )
% 2.52/2.82 & ( B = B6 ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % zip_eq_zip_same_len
% 2.52/2.82 thf(fact_4955_zip__eq__zip__same__len,axiom,
% 2.52/2.82 ! [A: list_int,B: list_nat,A5: list_int,B6: list_nat] :
% 2.52/2.82 ( ( ( size_size_list_int @ A )
% 2.52/2.82 = ( size_size_list_nat @ B ) )
% 2.52/2.82 => ( ( ( size_size_list_int @ A5 )
% 2.52/2.82 = ( size_size_list_nat @ B6 ) )
% 2.52/2.82 => ( ( ( zip_int_nat @ A @ B )
% 2.52/2.82 = ( zip_int_nat @ A5 @ B6 ) )
% 2.52/2.82 = ( ( A = A5 )
% 2.52/2.82 & ( B = B6 ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % zip_eq_zip_same_len
% 2.52/2.82 thf(fact_4956_zip__eq__zip__same__len,axiom,
% 2.52/2.82 ! [A: list_nat,B: list_int,A5: list_nat,B6: list_int] :
% 2.52/2.82 ( ( ( size_size_list_nat @ A )
% 2.52/2.82 = ( size_size_list_int @ B ) )
% 2.52/2.82 => ( ( ( size_size_list_nat @ A5 )
% 2.52/2.82 = ( size_size_list_int @ B6 ) )
% 2.52/2.82 => ( ( ( zip_nat_int @ A @ B )
% 2.52/2.82 = ( zip_nat_int @ A5 @ B6 ) )
% 2.52/2.82 = ( ( A = A5 )
% 2.52/2.82 & ( B = B6 ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % zip_eq_zip_same_len
% 2.52/2.82 thf(fact_4957_zip__eq__zip__same__len,axiom,
% 2.52/2.82 ! [A: list_nat,B: list_nat,A5: list_nat,B6: list_nat] :
% 2.52/2.82 ( ( ( size_size_list_nat @ A )
% 2.52/2.82 = ( size_size_list_nat @ B ) )
% 2.52/2.82 => ( ( ( size_size_list_nat @ A5 )
% 2.52/2.82 = ( size_size_list_nat @ B6 ) )
% 2.52/2.82 => ( ( ( zip_nat_nat @ A @ B )
% 2.52/2.82 = ( zip_nat_nat @ A5 @ B6 ) )
% 2.52/2.82 = ( ( A = A5 )
% 2.52/2.82 & ( B = B6 ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % zip_eq_zip_same_len
% 2.52/2.82 thf(fact_4958_length__enumerate,axiom,
% 2.52/2.82 ! [N: nat,Xs: list_int] :
% 2.52/2.82 ( ( size_s2970893825323803983at_int @ ( enumerate_int @ N @ Xs ) )
% 2.52/2.82 = ( size_size_list_int @ Xs ) ) ).
% 2.52/2.82
% 2.52/2.82 % length_enumerate
% 2.52/2.82 thf(fact_4959_length__enumerate,axiom,
% 2.52/2.82 ! [N: nat,Xs: list_nat] :
% 2.52/2.82 ( ( size_s5460976970255530739at_nat @ ( enumerate_nat @ N @ Xs ) )
% 2.52/2.82 = ( size_size_list_nat @ Xs ) ) ).
% 2.52/2.82
% 2.52/2.82 % length_enumerate
% 2.52/2.82 thf(fact_4960_length__rotate1,axiom,
% 2.52/2.82 ! [Xs: list_int] :
% 2.52/2.82 ( ( size_size_list_int @ ( rotate1_int @ Xs ) )
% 2.52/2.82 = ( size_size_list_int @ Xs ) ) ).
% 2.52/2.82
% 2.52/2.82 % length_rotate1
% 2.52/2.82 thf(fact_4961_length__rotate1,axiom,
% 2.52/2.82 ! [Xs: list_nat] :
% 2.52/2.82 ( ( size_size_list_nat @ ( rotate1_nat @ Xs ) )
% 2.52/2.82 = ( size_size_list_nat @ Xs ) ) ).
% 2.52/2.82
% 2.52/2.82 % length_rotate1
% 2.52/2.82 thf(fact_4962_length__0__conv,axiom,
% 2.52/2.82 ! [Xs: list_P8527749157015355191n_assn] :
% 2.52/2.82 ( ( ( size_s6829681357464350627n_assn @ Xs )
% 2.52/2.82 = zero_zero_nat )
% 2.52/2.82 = ( Xs = nil_Pr5671120429643327159n_assn ) ) ).
% 2.52/2.82
% 2.52/2.82 % length_0_conv
% 2.52/2.82 thf(fact_4963_length__0__conv,axiom,
% 2.52/2.82 ! [Xs: list_int] :
% 2.52/2.82 ( ( ( size_size_list_int @ Xs )
% 2.52/2.82 = zero_zero_nat )
% 2.52/2.82 = ( Xs = nil_int ) ) ).
% 2.52/2.82
% 2.52/2.82 % length_0_conv
% 2.52/2.82 thf(fact_4964_length__0__conv,axiom,
% 2.52/2.82 ! [Xs: list_nat] :
% 2.52/2.82 ( ( ( size_size_list_nat @ Xs )
% 2.52/2.82 = zero_zero_nat )
% 2.52/2.82 = ( Xs = nil_nat ) ) ).
% 2.52/2.82
% 2.52/2.82 % length_0_conv
% 2.52/2.82 thf(fact_4965_max__0__1_I2_J,axiom,
% 2.52/2.82 ( ( ord_max_nat @ one_one_nat @ zero_zero_nat )
% 2.52/2.82 = one_one_nat ) ).
% 2.52/2.82
% 2.52/2.82 % max_0_1(2)
% 2.52/2.82 thf(fact_4966_max__0__1_I2_J,axiom,
% 2.52/2.82 ( ( ord_max_rat @ one_one_rat @ zero_zero_rat )
% 2.52/2.82 = one_one_rat ) ).
% 2.52/2.82
% 2.52/2.82 % max_0_1(2)
% 2.52/2.82 thf(fact_4967_max__0__1_I2_J,axiom,
% 2.52/2.82 ( ( ord_max_Code_integer @ one_one_Code_integer @ zero_z3403309356797280102nteger )
% 2.52/2.82 = one_one_Code_integer ) ).
% 2.52/2.82
% 2.52/2.82 % max_0_1(2)
% 2.52/2.82 thf(fact_4968_max__0__1_I2_J,axiom,
% 2.52/2.82 ( ( ord_max_Code_natural @ one_one_Code_natural @ zero_z2226904508553997617atural )
% 2.52/2.82 = one_one_Code_natural ) ).
% 2.52/2.82
% 2.52/2.82 % max_0_1(2)
% 2.52/2.82 thf(fact_4969_max__0__1_I2_J,axiom,
% 2.52/2.82 ( ( ord_max_int @ one_one_int @ zero_zero_int )
% 2.52/2.82 = one_one_int ) ).
% 2.52/2.82
% 2.52/2.82 % max_0_1(2)
% 2.52/2.82 thf(fact_4970_max__0__1_I1_J,axiom,
% 2.52/2.82 ( ( ord_max_nat @ zero_zero_nat @ one_one_nat )
% 2.52/2.82 = one_one_nat ) ).
% 2.52/2.82
% 2.52/2.82 % max_0_1(1)
% 2.52/2.82 thf(fact_4971_max__0__1_I1_J,axiom,
% 2.52/2.82 ( ( ord_max_rat @ zero_zero_rat @ one_one_rat )
% 2.52/2.82 = one_one_rat ) ).
% 2.52/2.82
% 2.52/2.82 % max_0_1(1)
% 2.52/2.82 thf(fact_4972_max__0__1_I1_J,axiom,
% 2.52/2.82 ( ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer )
% 2.52/2.82 = one_one_Code_integer ) ).
% 2.52/2.82
% 2.52/2.82 % max_0_1(1)
% 2.52/2.82 thf(fact_4973_max__0__1_I1_J,axiom,
% 2.52/2.82 ( ( ord_max_Code_natural @ zero_z2226904508553997617atural @ one_one_Code_natural )
% 2.52/2.82 = one_one_Code_natural ) ).
% 2.52/2.82
% 2.52/2.82 % max_0_1(1)
% 2.52/2.82 thf(fact_4974_max__0__1_I1_J,axiom,
% 2.52/2.82 ( ( ord_max_int @ zero_zero_int @ one_one_int )
% 2.52/2.82 = one_one_int ) ).
% 2.52/2.82
% 2.52/2.82 % max_0_1(1)
% 2.52/2.82 thf(fact_4975_max__0__1_I6_J,axiom,
% 2.52/2.82 ! [X: num] :
% 2.52/2.82 ( ( ord_max_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat )
% 2.52/2.82 = ( numeral_numeral_nat @ X ) ) ).
% 2.52/2.82
% 2.52/2.82 % max_0_1(6)
% 2.52/2.82 thf(fact_4976_max__0__1_I6_J,axiom,
% 2.52/2.82 ! [X: num] :
% 2.52/2.82 ( ( ord_max_int @ ( numeral_numeral_int @ X ) @ one_one_int )
% 2.52/2.82 = ( numeral_numeral_int @ X ) ) ).
% 2.52/2.82
% 2.52/2.82 % max_0_1(6)
% 2.52/2.82 thf(fact_4977_max__0__1_I6_J,axiom,
% 2.52/2.82 ! [X: num] :
% 2.52/2.82 ( ( ord_max_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat )
% 2.52/2.82 = ( numeral_numeral_rat @ X ) ) ).
% 2.52/2.82
% 2.52/2.82 % max_0_1(6)
% 2.52/2.82 thf(fact_4978_max__0__1_I6_J,axiom,
% 2.52/2.82 ! [X: num] :
% 2.52/2.82 ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ X ) @ one_one_Code_integer )
% 2.52/2.82 = ( numera6620942414471956472nteger @ X ) ) ).
% 2.52/2.82
% 2.52/2.82 % max_0_1(6)
% 2.52/2.82 thf(fact_4979_max__0__1_I6_J,axiom,
% 2.52/2.82 ! [X: num] :
% 2.52/2.82 ( ( ord_max_Code_natural @ ( numera5444537566228673987atural @ X ) @ one_one_Code_natural )
% 2.52/2.82 = ( numera5444537566228673987atural @ X ) ) ).
% 2.52/2.82
% 2.52/2.82 % max_0_1(6)
% 2.52/2.82 thf(fact_4980_max__0__1_I5_J,axiom,
% 2.52/2.82 ! [X: num] :
% 2.52/2.82 ( ( ord_max_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 2.52/2.82 = ( numeral_numeral_nat @ X ) ) ).
% 2.52/2.82
% 2.52/2.82 % max_0_1(5)
% 2.52/2.82 thf(fact_4981_max__0__1_I5_J,axiom,
% 2.52/2.82 ! [X: num] :
% 2.52/2.82 ( ( ord_max_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 2.52/2.82 = ( numeral_numeral_int @ X ) ) ).
% 2.52/2.82
% 2.52/2.82 % max_0_1(5)
% 2.52/2.82 thf(fact_4982_max__0__1_I5_J,axiom,
% 2.52/2.82 ! [X: num] :
% 2.52/2.82 ( ( ord_max_rat @ one_one_rat @ ( numeral_numeral_rat @ X ) )
% 2.52/2.82 = ( numeral_numeral_rat @ X ) ) ).
% 2.52/2.82
% 2.52/2.82 % max_0_1(5)
% 2.52/2.82 thf(fact_4983_max__0__1_I5_J,axiom,
% 2.52/2.82 ! [X: num] :
% 2.52/2.82 ( ( ord_max_Code_integer @ one_one_Code_integer @ ( numera6620942414471956472nteger @ X ) )
% 2.52/2.82 = ( numera6620942414471956472nteger @ X ) ) ).
% 2.52/2.82
% 2.52/2.82 % max_0_1(5)
% 2.52/2.82 thf(fact_4984_max__0__1_I5_J,axiom,
% 2.52/2.82 ! [X: num] :
% 2.52/2.82 ( ( ord_max_Code_natural @ one_one_Code_natural @ ( numera5444537566228673987atural @ X ) )
% 2.52/2.82 = ( numera5444537566228673987atural @ X ) ) ).
% 2.52/2.82
% 2.52/2.82 % max_0_1(5)
% 2.52/2.82 thf(fact_4985_length__splice,axiom,
% 2.52/2.82 ! [Xs: list_int,Ys: list_int] :
% 2.52/2.82 ( ( size_size_list_int @ ( splice_int @ Xs @ Ys ) )
% 2.52/2.82 = ( plus_plus_nat @ ( size_size_list_int @ Xs ) @ ( size_size_list_int @ Ys ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % length_splice
% 2.52/2.82 thf(fact_4986_length__splice,axiom,
% 2.52/2.82 ! [Xs: list_nat,Ys: list_nat] :
% 2.52/2.82 ( ( size_size_list_nat @ ( splice_nat @ Xs @ Ys ) )
% 2.52/2.82 = ( plus_plus_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % length_splice
% 2.52/2.82 thf(fact_4987_length__product,axiom,
% 2.52/2.82 ! [Xs: list_int,Ys: list_int] :
% 2.52/2.82 ( ( size_s5157815400016825771nt_int @ ( product_int_int @ Xs @ Ys ) )
% 2.52/2.82 = ( times_times_nat @ ( size_size_list_int @ Xs ) @ ( size_size_list_int @ Ys ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % length_product
% 2.52/2.82 thf(fact_4988_length__product,axiom,
% 2.52/2.82 ! [Xs: list_int,Ys: list_nat] :
% 2.52/2.82 ( ( size_s7647898544948552527nt_nat @ ( product_int_nat @ Xs @ Ys ) )
% 2.52/2.82 = ( times_times_nat @ ( size_size_list_int @ Xs ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % length_product
% 2.52/2.82 thf(fact_4989_length__product,axiom,
% 2.52/2.82 ! [Xs: list_nat,Ys: list_int] :
% 2.52/2.82 ( ( size_s2970893825323803983at_int @ ( product_nat_int @ Xs @ Ys ) )
% 2.52/2.82 = ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_int @ Ys ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % length_product
% 2.52/2.82 thf(fact_4990_length__product,axiom,
% 2.52/2.82 ! [Xs: list_nat,Ys: list_nat] :
% 2.52/2.82 ( ( size_s5460976970255530739at_nat @ ( product_nat_nat @ Xs @ Ys ) )
% 2.52/2.82 = ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % length_product
% 2.52/2.82 thf(fact_4991_length__greater__0__conv,axiom,
% 2.52/2.82 ! [Xs: list_P8527749157015355191n_assn] :
% 2.52/2.82 ( ( ord_less_nat @ zero_zero_nat @ ( size_s6829681357464350627n_assn @ Xs ) )
% 2.52/2.82 = ( Xs != nil_Pr5671120429643327159n_assn ) ) ).
% 2.52/2.82
% 2.52/2.82 % length_greater_0_conv
% 2.52/2.82 thf(fact_4992_length__greater__0__conv,axiom,
% 2.52/2.82 ! [Xs: list_int] :
% 2.52/2.82 ( ( ord_less_nat @ zero_zero_nat @ ( size_size_list_int @ Xs ) )
% 2.52/2.82 = ( Xs != nil_int ) ) ).
% 2.52/2.82
% 2.52/2.82 % length_greater_0_conv
% 2.52/2.82 thf(fact_4993_length__greater__0__conv,axiom,
% 2.52/2.82 ! [Xs: list_nat] :
% 2.52/2.82 ( ( ord_less_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs ) )
% 2.52/2.82 = ( Xs != nil_nat ) ) ).
% 2.52/2.82
% 2.52/2.82 % length_greater_0_conv
% 2.52/2.82 thf(fact_4994_nth__map,axiom,
% 2.52/2.82 ! [N: nat,Xs: list_P8527749157015355191n_assn,F2: produc6575502325842934193n_assn > assn] :
% 2.52/2.82 ( ( ord_less_nat @ N @ ( size_s6829681357464350627n_assn @ Xs ) )
% 2.52/2.82 => ( ( nth_assn @ ( map_Pr8991440229025900053n_assn @ F2 @ Xs ) @ N )
% 2.52/2.82 = ( F2 @ ( nth_Pr1769885009046257848n_assn @ Xs @ N ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % nth_map
% 2.52/2.82 thf(fact_4995_nth__map,axiom,
% 2.52/2.82 ! [N: nat,Xs: list_int,F2: int > nat] :
% 2.52/2.82 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 2.52/2.82 => ( ( nth_nat @ ( map_int_nat @ F2 @ Xs ) @ N )
% 2.52/2.82 = ( F2 @ ( nth_int @ Xs @ N ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % nth_map
% 2.52/2.82 thf(fact_4996_nth__map,axiom,
% 2.52/2.82 ! [N: nat,Xs: list_int,F2: int > int] :
% 2.52/2.82 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 2.52/2.82 => ( ( nth_int @ ( map_int_int @ F2 @ Xs ) @ N )
% 2.52/2.82 = ( F2 @ ( nth_int @ Xs @ N ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % nth_map
% 2.52/2.82 thf(fact_4997_nth__map,axiom,
% 2.52/2.82 ! [N: nat,Xs: list_nat,F2: nat > int] :
% 2.52/2.82 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 2.52/2.82 => ( ( nth_int @ ( map_nat_int @ F2 @ Xs ) @ N )
% 2.52/2.82 = ( F2 @ ( nth_nat @ Xs @ N ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % nth_map
% 2.52/2.82 thf(fact_4998_nth__map,axiom,
% 2.52/2.82 ! [N: nat,Xs: list_nat,F2: nat > nat] :
% 2.52/2.82 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 2.52/2.82 => ( ( nth_nat @ ( map_nat_nat @ F2 @ Xs ) @ N )
% 2.52/2.82 = ( F2 @ ( nth_nat @ Xs @ N ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % nth_map
% 2.52/2.82 thf(fact_4999_drop__bit__of__1,axiom,
% 2.52/2.82 ! [N: nat] :
% 2.52/2.82 ( ( bit_se3928097537394005634nteger @ N @ one_one_Code_integer )
% 2.52/2.82 = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % drop_bit_of_1
% 2.52/2.82 thf(fact_5000_drop__bit__of__1,axiom,
% 2.52/2.82 ! [N: nat] :
% 2.52/2.82 ( ( bit_se8570568707652914677it_nat @ N @ one_one_nat )
% 2.52/2.82 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % drop_bit_of_1
% 2.52/2.82 thf(fact_5001_drop__bit__of__1,axiom,
% 2.52/2.82 ! [N: nat] :
% 2.52/2.82 ( ( bit_se8568078237143864401it_int @ N @ one_one_int )
% 2.52/2.82 = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % drop_bit_of_1
% 2.52/2.82 thf(fact_5002_map__fst__zip,axiom,
% 2.52/2.82 ! [Xs: list_int,Ys: list_nat] :
% 2.52/2.82 ( ( ( size_size_list_int @ Xs )
% 2.52/2.82 = ( size_size_list_nat @ Ys ) )
% 2.52/2.82 => ( ( map_Pr4307537318738222789at_int @ product_fst_int_nat @ ( zip_int_nat @ Xs @ Ys ) )
% 2.52/2.82 = Xs ) ) ).
% 2.52/2.82
% 2.52/2.82 % map_fst_zip
% 2.52/2.82 thf(fact_5003_map__fst__zip,axiom,
% 2.52/2.82 ! [Xs: list_nat,Ys: list_int] :
% 2.52/2.82 ( ( ( size_size_list_nat @ Xs )
% 2.52/2.82 = ( size_size_list_int @ Ys ) )
% 2.52/2.82 => ( ( map_Pr6125295803703450217nt_nat @ product_fst_nat_int @ ( zip_nat_int @ Xs @ Ys ) )
% 2.52/2.82 = Xs ) ) ).
% 2.52/2.82
% 2.52/2.82 % map_fst_zip
% 2.52/2.82 thf(fact_5004_map__fst__zip,axiom,
% 2.52/2.82 ! [Xs: list_nat,Ys: list_nat] :
% 2.52/2.82 ( ( ( size_size_list_nat @ Xs )
% 2.52/2.82 = ( size_size_list_nat @ Ys ) )
% 2.52/2.82 => ( ( map_Pr3938374229010428429at_nat @ product_fst_nat_nat @ ( zip_nat_nat @ Xs @ Ys ) )
% 2.52/2.82 = Xs ) ) ).
% 2.52/2.82
% 2.52/2.82 % map_fst_zip
% 2.52/2.82 thf(fact_5005_map__fst__zip,axiom,
% 2.52/2.82 ! [Xs: list_h2745205591237434579t_unit,Ys: list_set_nat] :
% 2.52/2.82 ( ( ( size_s7011499401410611007t_unit @ Xs )
% 2.52/2.82 = ( size_s3254054031482475050et_nat @ Ys ) )
% 2.52/2.82 => ( ( map_Pr7042224834074979589t_unit @ produc1824681642469235216et_nat @ ( zip_he6711929980790699996et_nat @ Xs @ Ys ) )
% 2.52/2.82 = Xs ) ) ).
% 2.52/2.82
% 2.52/2.82 % map_fst_zip
% 2.52/2.82 thf(fact_5006_map__fst__zip,axiom,
% 2.52/2.82 ! [Xs: list_int,Ys: list_int] :
% 2.52/2.82 ( ( ( size_size_list_int @ Xs )
% 2.52/2.82 = ( size_size_list_int @ Ys ) )
% 2.52/2.82 => ( ( map_Pr6494458893431244577nt_int @ product_fst_int_int @ ( zip_int_int @ Xs @ Ys ) )
% 2.52/2.82 = Xs ) ) ).
% 2.52/2.82
% 2.52/2.82 % map_fst_zip
% 2.52/2.82 thf(fact_5007_map__fst__zip,axiom,
% 2.52/2.82 ! [Xs: list_assn,Ys: list_assn] :
% 2.52/2.82 ( ( ( size_size_list_assn @ Xs )
% 2.52/2.82 = ( size_size_list_assn @ Ys ) )
% 2.52/2.82 => ( ( map_Pr8991440229025900053n_assn @ produc9167289414957590229n_assn @ ( zip_assn_assn @ Xs @ Ys ) )
% 2.52/2.82 = Xs ) ) ).
% 2.52/2.82
% 2.52/2.82 % map_fst_zip
% 2.52/2.82 thf(fact_5008_map__snd__zip,axiom,
% 2.52/2.82 ! [Xs: list_int,Ys: list_nat] :
% 2.52/2.82 ( ( ( size_size_list_int @ Xs )
% 2.52/2.82 = ( size_size_list_nat @ Ys ) )
% 2.52/2.82 => ( ( map_Pr4310027789247273065at_nat @ product_snd_int_nat @ ( zip_int_nat @ Xs @ Ys ) )
% 2.52/2.82 = Ys ) ) ).
% 2.52/2.82
% 2.52/2.82 % map_snd_zip
% 2.52/2.82 thf(fact_5009_map__snd__zip,axiom,
% 2.52/2.82 ! [Xs: list_nat,Ys: list_int] :
% 2.52/2.82 ( ( ( size_size_list_nat @ Xs )
% 2.52/2.82 = ( size_size_list_int @ Ys ) )
% 2.52/2.82 => ( ( map_Pr6122805333194399941nt_int @ product_snd_nat_int @ ( zip_nat_int @ Xs @ Ys ) )
% 2.52/2.82 = Ys ) ) ).
% 2.52/2.82
% 2.52/2.82 % map_snd_zip
% 2.52/2.82 thf(fact_5010_map__snd__zip,axiom,
% 2.52/2.82 ! [Xs: list_nat,Ys: list_nat] :
% 2.52/2.82 ( ( ( size_size_list_nat @ Xs )
% 2.52/2.82 = ( size_size_list_nat @ Ys ) )
% 2.52/2.82 => ( ( map_Pr3938374229010428429at_nat @ product_snd_nat_nat @ ( zip_nat_nat @ Xs @ Ys ) )
% 2.52/2.82 = Ys ) ) ).
% 2.52/2.82
% 2.52/2.82 % map_snd_zip
% 2.52/2.82 thf(fact_5011_map__snd__zip,axiom,
% 2.52/2.82 ! [Xs: list_h2745205591237434579t_unit,Ys: list_set_nat] :
% 2.52/2.82 ( ( ( size_s7011499401410611007t_unit @ Xs )
% 2.52/2.82 = ( size_s3254054031482475050et_nat @ Ys ) )
% 2.52/2.82 => ( ( map_Pr4871828589360411470et_nat @ produc8586169260539613262et_nat @ ( zip_he6711929980790699996et_nat @ Xs @ Ys ) )
% 2.52/2.82 = Ys ) ) ).
% 2.52/2.82
% 2.52/2.82 % map_snd_zip
% 2.52/2.82 thf(fact_5012_map__snd__zip,axiom,
% 2.52/2.82 ! [Xs: list_int,Ys: list_int] :
% 2.52/2.82 ( ( ( size_size_list_int @ Xs )
% 2.52/2.82 = ( size_size_list_int @ Ys ) )
% 2.52/2.82 => ( ( map_Pr6494458893431244577nt_int @ product_snd_int_int @ ( zip_int_int @ Xs @ Ys ) )
% 2.52/2.82 = Ys ) ) ).
% 2.52/2.82
% 2.52/2.82 % map_snd_zip
% 2.52/2.82 thf(fact_5013_map__snd__zip,axiom,
% 2.52/2.82 ! [Xs: list_assn,Ys: list_assn] :
% 2.52/2.82 ( ( ( size_size_list_assn @ Xs )
% 2.52/2.82 = ( size_size_list_assn @ Ys ) )
% 2.52/2.82 => ( ( map_Pr8991440229025900053n_assn @ produc2051961928117032727n_assn @ ( zip_assn_assn @ Xs @ Ys ) )
% 2.52/2.82 = Ys ) ) ).
% 2.52/2.82
% 2.52/2.82 % map_snd_zip
% 2.52/2.82 thf(fact_5014_rotate1__length01,axiom,
% 2.52/2.82 ! [Xs: list_int] :
% 2.52/2.82 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ one_one_nat )
% 2.52/2.82 => ( ( rotate1_int @ Xs )
% 2.52/2.82 = Xs ) ) ).
% 2.52/2.82
% 2.52/2.82 % rotate1_length01
% 2.52/2.82 thf(fact_5015_rotate1__length01,axiom,
% 2.52/2.82 ! [Xs: list_nat] :
% 2.52/2.82 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ one_one_nat )
% 2.52/2.82 => ( ( rotate1_nat @ Xs )
% 2.52/2.82 = Xs ) ) ).
% 2.52/2.82
% 2.52/2.82 % rotate1_length01
% 2.52/2.82 thf(fact_5016_length__ge__1__conv,axiom,
% 2.52/2.82 ! [L: list_P8527749157015355191n_assn] :
% 2.52/2.82 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( size_s6829681357464350627n_assn @ L ) )
% 2.52/2.82 = ( L != nil_Pr5671120429643327159n_assn ) ) ).
% 2.52/2.82
% 2.52/2.82 % length_ge_1_conv
% 2.52/2.82 thf(fact_5017_length__ge__1__conv,axiom,
% 2.52/2.82 ! [L: list_int] :
% 2.52/2.82 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( size_size_list_int @ L ) )
% 2.52/2.82 = ( L != nil_int ) ) ).
% 2.52/2.82
% 2.52/2.82 % length_ge_1_conv
% 2.52/2.82 thf(fact_5018_length__ge__1__conv,axiom,
% 2.52/2.82 ! [L: list_nat] :
% 2.52/2.82 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( size_size_list_nat @ L ) )
% 2.52/2.82 = ( L != nil_nat ) ) ).
% 2.52/2.82
% 2.52/2.82 % length_ge_1_conv
% 2.52/2.82 thf(fact_5019_nth__zip,axiom,
% 2.52/2.82 ! [I2: nat,Xs: list_h2745205591237434579t_unit,Ys: list_set_nat] :
% 2.52/2.82 ( ( ord_less_nat @ I2 @ ( size_s7011499401410611007t_unit @ Xs ) )
% 2.52/2.82 => ( ( ord_less_nat @ I2 @ ( size_s3254054031482475050et_nat @ Ys ) )
% 2.52/2.82 => ( ( nth_Pr7683458668995092411et_nat @ ( zip_he6711929980790699996et_nat @ Xs @ Ys ) @ I2 )
% 2.52/2.82 = ( produc7507926704131184380et_nat @ ( nth_he7452997726511547988t_unit @ Xs @ I2 ) @ ( nth_set_nat @ Ys @ I2 ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % nth_zip
% 2.52/2.82 thf(fact_5020_nth__zip,axiom,
% 2.52/2.82 ! [I2: nat,Xs: list_P7985473006766602707_nat_o,Ys: list_P9062070895058802706et_nat] :
% 2.52/2.82 ( ( ord_less_nat @ I2 @ ( size_s8908918004648414271_nat_o @ Xs ) )
% 2.52/2.82 => ( ( ord_less_nat @ I2 @ ( size_s2864271983995610790et_nat @ Ys ) )
% 2.52/2.82 => ( ( nth_Pr3610913089060847927et_nat @ ( zip_Pr7134870689397686104et_nat @ Xs @ Ys ) @ I2 )
% 2.52/2.82 = ( produc5001842942810119800et_nat @ ( nth_Pr6840583978799713108_nat_o @ Xs @ I2 ) @ ( nth_Pr7683458668995092411et_nat @ Ys @ I2 ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % nth_zip
% 2.52/2.82 thf(fact_5021_nth__zip,axiom,
% 2.52/2.82 ! [I2: nat,Xs: list_P7985473006766602707_nat_o,Ys: list_P2321686559999237006et_nat] :
% 2.52/2.82 ( ( ord_less_nat @ I2 @ ( size_s8908918004648414271_nat_o @ Xs ) )
% 2.52/2.82 => ( ( ord_less_nat @ I2 @ ( size_s6841928198497307170et_nat @ Ys ) )
% 2.52/2.82 => ( ( nth_Pr7590663101126261939et_nat @ ( zip_Pr8136144321567152340et_nat @ Xs @ Ys ) @ I2 )
% 2.52/2.82 = ( produc2245416461498447860et_nat @ ( nth_Pr6840583978799713108_nat_o @ Xs @ I2 ) @ ( nth_Pr3610913089060847927et_nat @ Ys @ I2 ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % nth_zip
% 2.52/2.82 thf(fact_5022_nth__zip,axiom,
% 2.52/2.82 ! [I2: nat,Xs: list_int,Ys: list_int] :
% 2.52/2.82 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 2.52/2.82 => ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Ys ) )
% 2.52/2.82 => ( ( nth_Pr4439495888332055232nt_int @ ( zip_int_int @ Xs @ Ys ) @ I2 )
% 2.52/2.82 = ( product_Pair_int_int @ ( nth_int @ Xs @ I2 ) @ ( nth_int @ Ys @ I2 ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % nth_zip
% 2.52/2.82 thf(fact_5023_nth__zip,axiom,
% 2.52/2.82 ! [I2: nat,Xs: list_int,Ys: list_nat] :
% 2.52/2.82 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 2.52/2.82 => ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Ys ) )
% 2.52/2.82 => ( ( nth_Pr8617346907841251940nt_nat @ ( zip_int_nat @ Xs @ Ys ) @ I2 )
% 2.52/2.82 = ( product_Pair_int_nat @ ( nth_int @ Xs @ I2 ) @ ( nth_nat @ Ys @ I2 ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % nth_zip
% 2.52/2.82 thf(fact_5024_nth__zip,axiom,
% 2.52/2.82 ! [I2: nat,Xs: list_nat,Ys: list_int] :
% 2.52/2.82 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs ) )
% 2.52/2.82 => ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Ys ) )
% 2.52/2.82 => ( ( nth_Pr3440142176431000676at_int @ ( zip_nat_int @ Xs @ Ys ) @ I2 )
% 2.52/2.82 = ( product_Pair_nat_int @ ( nth_nat @ Xs @ I2 ) @ ( nth_int @ Ys @ I2 ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % nth_zip
% 2.52/2.82 thf(fact_5025_nth__zip,axiom,
% 2.52/2.82 ! [I2: nat,Xs: list_nat,Ys: list_nat] :
% 2.52/2.82 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs ) )
% 2.52/2.82 => ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Ys ) )
% 2.52/2.82 => ( ( nth_Pr7617993195940197384at_nat @ ( zip_nat_nat @ Xs @ Ys ) @ I2 )
% 2.52/2.82 = ( product_Pair_nat_nat @ ( nth_nat @ Xs @ I2 ) @ ( nth_nat @ Ys @ I2 ) ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % nth_zip
% 2.52/2.82 thf(fact_5026_neq__if__length__neq,axiom,
% 2.52/2.82 ! [Xs: list_int,Ys: list_int] :
% 2.52/2.82 ( ( ( size_size_list_int @ Xs )
% 2.52/2.82 != ( size_size_list_int @ Ys ) )
% 2.52/2.82 => ( Xs != Ys ) ) ).
% 2.52/2.82
% 2.52/2.82 % neq_if_length_neq
% 2.52/2.82 thf(fact_5027_neq__if__length__neq,axiom,
% 2.52/2.82 ! [Xs: list_nat,Ys: list_nat] :
% 2.52/2.82 ( ( ( size_size_list_nat @ Xs )
% 2.52/2.82 != ( size_size_list_nat @ Ys ) )
% 2.52/2.82 => ( Xs != Ys ) ) ).
% 2.52/2.82
% 2.52/2.82 % neq_if_length_neq
% 2.52/2.82 thf(fact_5028_Ex__list__of__length,axiom,
% 2.52/2.82 ! [N: nat] :
% 2.52/2.82 ? [Xs2: list_int] :
% 2.52/2.82 ( ( size_size_list_int @ Xs2 )
% 2.52/2.82 = N ) ).
% 2.52/2.82
% 2.52/2.82 % Ex_list_of_length
% 2.52/2.82 thf(fact_5029_Ex__list__of__length,axiom,
% 2.52/2.82 ! [N: nat] :
% 2.52/2.82 ? [Xs2: list_nat] :
% 2.52/2.82 ( ( size_size_list_nat @ Xs2 )
% 2.52/2.82 = N ) ).
% 2.52/2.82
% 2.52/2.82 % Ex_list_of_length
% 2.52/2.82 thf(fact_5030_max_Oleft__commute,axiom,
% 2.52/2.82 ! [B: int,A: int,C: int] :
% 2.52/2.82 ( ( ord_max_int @ B @ ( ord_max_int @ A @ C ) )
% 2.52/2.82 = ( ord_max_int @ A @ ( ord_max_int @ B @ C ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.left_commute
% 2.52/2.82 thf(fact_5031_max_Ocommute,axiom,
% 2.52/2.82 ( ord_max_int
% 2.52/2.82 = ( ^ [A2: int,B2: int] : ( ord_max_int @ B2 @ A2 ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.commute
% 2.52/2.82 thf(fact_5032_max_Oassoc,axiom,
% 2.52/2.82 ! [A: int,B: int,C: int] :
% 2.52/2.82 ( ( ord_max_int @ ( ord_max_int @ A @ B ) @ C )
% 2.52/2.82 = ( ord_max_int @ A @ ( ord_max_int @ B @ C ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.assoc
% 2.52/2.82 thf(fact_5033_pair__list__split,axiom,
% 2.52/2.82 ! [L: list_P5707943133018811711nt_int] :
% 2.52/2.82 ~ ! [L1: list_int,L2: list_int] :
% 2.52/2.82 ( ( L
% 2.52/2.82 = ( zip_int_int @ L1 @ L2 ) )
% 2.52/2.82 => ( ( ( size_size_list_int @ L1 )
% 2.52/2.82 = ( size_size_list_int @ L2 ) )
% 2.52/2.82 => ( ( size_s5157815400016825771nt_int @ L )
% 2.52/2.82 != ( size_size_list_int @ L2 ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % pair_list_split
% 2.52/2.82 thf(fact_5034_pair__list__split,axiom,
% 2.52/2.82 ! [L: list_P8198026277950538467nt_nat] :
% 2.52/2.82 ~ ! [L1: list_int,L2: list_nat] :
% 2.52/2.82 ( ( L
% 2.52/2.82 = ( zip_int_nat @ L1 @ L2 ) )
% 2.52/2.82 => ( ( ( size_size_list_int @ L1 )
% 2.52/2.82 = ( size_size_list_nat @ L2 ) )
% 2.52/2.82 => ( ( size_s7647898544948552527nt_nat @ L )
% 2.52/2.82 != ( size_size_list_nat @ L2 ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % pair_list_split
% 2.52/2.82 thf(fact_5035_pair__list__split,axiom,
% 2.52/2.82 ! [L: list_P3521021558325789923at_int] :
% 2.52/2.82 ~ ! [L1: list_nat,L2: list_int] :
% 2.52/2.82 ( ( L
% 2.52/2.82 = ( zip_nat_int @ L1 @ L2 ) )
% 2.52/2.82 => ( ( ( size_size_list_nat @ L1 )
% 2.52/2.82 = ( size_size_list_int @ L2 ) )
% 2.52/2.82 => ( ( size_s2970893825323803983at_int @ L )
% 2.52/2.82 != ( size_size_list_int @ L2 ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % pair_list_split
% 2.52/2.82 thf(fact_5036_pair__list__split,axiom,
% 2.52/2.82 ! [L: list_P6011104703257516679at_nat] :
% 2.52/2.82 ~ ! [L1: list_nat,L2: list_nat] :
% 2.52/2.82 ( ( L
% 2.52/2.82 = ( zip_nat_nat @ L1 @ L2 ) )
% 2.52/2.82 => ( ( ( size_size_list_nat @ L1 )
% 2.52/2.82 = ( size_size_list_nat @ L2 ) )
% 2.52/2.82 => ( ( size_s5460976970255530739at_nat @ L )
% 2.52/2.82 != ( size_size_list_nat @ L2 ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % pair_list_split
% 2.52/2.82 thf(fact_5037_bit__iff__and__drop__bit__eq__1,axiom,
% 2.52/2.82 ( bit_se9216721137139052372nteger
% 2.52/2.82 = ( ^ [A2: code_integer,N3: nat] :
% 2.52/2.82 ( ( bit_se3949692690581998587nteger @ ( bit_se3928097537394005634nteger @ N3 @ A2 ) @ one_one_Code_integer )
% 2.52/2.82 = one_one_Code_integer ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % bit_iff_and_drop_bit_eq_1
% 2.52/2.82 thf(fact_5038_bit__iff__and__drop__bit__eq__1,axiom,
% 2.52/2.82 ( bit_se1148574629649215175it_nat
% 2.52/2.82 = ( ^ [A2: nat,N3: nat] :
% 2.52/2.82 ( ( bit_se727722235901077358nd_nat @ ( bit_se8570568707652914677it_nat @ N3 @ A2 ) @ one_one_nat )
% 2.52/2.82 = one_one_nat ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % bit_iff_and_drop_bit_eq_1
% 2.52/2.82 thf(fact_5039_bit__iff__and__drop__bit__eq__1,axiom,
% 2.52/2.82 ( bit_se1146084159140164899it_int
% 2.52/2.82 = ( ^ [A2: int,N3: nat] :
% 2.52/2.82 ( ( bit_se725231765392027082nd_int @ ( bit_se8568078237143864401it_int @ N3 @ A2 ) @ one_one_int )
% 2.52/2.82 = one_one_int ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % bit_iff_and_drop_bit_eq_1
% 2.52/2.82 thf(fact_5040_max_OcoboundedI2,axiom,
% 2.52/2.82 ! [C: rat,B: rat,A: rat] :
% 2.52/2.82 ( ( ord_less_eq_rat @ C @ B )
% 2.52/2.82 => ( ord_less_eq_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.coboundedI2
% 2.52/2.82 thf(fact_5041_max_OcoboundedI2,axiom,
% 2.52/2.82 ! [C: nat,B: nat,A: nat] :
% 2.52/2.82 ( ( ord_less_eq_nat @ C @ B )
% 2.52/2.82 => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.coboundedI2
% 2.52/2.82 thf(fact_5042_max_OcoboundedI2,axiom,
% 2.52/2.82 ! [C: int,B: int,A: int] :
% 2.52/2.82 ( ( ord_less_eq_int @ C @ B )
% 2.52/2.82 => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.coboundedI2
% 2.52/2.82 thf(fact_5043_max_OcoboundedI1,axiom,
% 2.52/2.82 ! [C: rat,A: rat,B: rat] :
% 2.52/2.82 ( ( ord_less_eq_rat @ C @ A )
% 2.52/2.82 => ( ord_less_eq_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.coboundedI1
% 2.52/2.82 thf(fact_5044_max_OcoboundedI1,axiom,
% 2.52/2.82 ! [C: nat,A: nat,B: nat] :
% 2.52/2.82 ( ( ord_less_eq_nat @ C @ A )
% 2.52/2.82 => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.coboundedI1
% 2.52/2.82 thf(fact_5045_max_OcoboundedI1,axiom,
% 2.52/2.82 ! [C: int,A: int,B: int] :
% 2.52/2.82 ( ( ord_less_eq_int @ C @ A )
% 2.52/2.82 => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.coboundedI1
% 2.52/2.82 thf(fact_5046_max_Oabsorb__iff2,axiom,
% 2.52/2.82 ( ord_less_eq_rat
% 2.52/2.82 = ( ^ [A2: rat,B2: rat] :
% 2.52/2.82 ( ( ord_max_rat @ A2 @ B2 )
% 2.52/2.82 = B2 ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.absorb_iff2
% 2.52/2.82 thf(fact_5047_max_Oabsorb__iff2,axiom,
% 2.52/2.82 ( ord_less_eq_nat
% 2.52/2.82 = ( ^ [A2: nat,B2: nat] :
% 2.52/2.82 ( ( ord_max_nat @ A2 @ B2 )
% 2.52/2.82 = B2 ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.absorb_iff2
% 2.52/2.82 thf(fact_5048_max_Oabsorb__iff2,axiom,
% 2.52/2.82 ( ord_less_eq_int
% 2.52/2.82 = ( ^ [A2: int,B2: int] :
% 2.52/2.82 ( ( ord_max_int @ A2 @ B2 )
% 2.52/2.82 = B2 ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.absorb_iff2
% 2.52/2.82 thf(fact_5049_max_Oabsorb__iff1,axiom,
% 2.52/2.82 ( ord_less_eq_rat
% 2.52/2.82 = ( ^ [B2: rat,A2: rat] :
% 2.52/2.82 ( ( ord_max_rat @ A2 @ B2 )
% 2.52/2.82 = A2 ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.absorb_iff1
% 2.52/2.82 thf(fact_5050_max_Oabsorb__iff1,axiom,
% 2.52/2.82 ( ord_less_eq_nat
% 2.52/2.82 = ( ^ [B2: nat,A2: nat] :
% 2.52/2.82 ( ( ord_max_nat @ A2 @ B2 )
% 2.52/2.82 = A2 ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.absorb_iff1
% 2.52/2.82 thf(fact_5051_max_Oabsorb__iff1,axiom,
% 2.52/2.82 ( ord_less_eq_int
% 2.52/2.82 = ( ^ [B2: int,A2: int] :
% 2.52/2.82 ( ( ord_max_int @ A2 @ B2 )
% 2.52/2.82 = A2 ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.absorb_iff1
% 2.52/2.82 thf(fact_5052_le__max__iff__disj,axiom,
% 2.52/2.82 ! [Z: rat,X: rat,Y: rat] :
% 2.52/2.82 ( ( ord_less_eq_rat @ Z @ ( ord_max_rat @ X @ Y ) )
% 2.52/2.82 = ( ( ord_less_eq_rat @ Z @ X )
% 2.52/2.82 | ( ord_less_eq_rat @ Z @ Y ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % le_max_iff_disj
% 2.52/2.82 thf(fact_5053_le__max__iff__disj,axiom,
% 2.52/2.82 ! [Z: nat,X: nat,Y: nat] :
% 2.52/2.82 ( ( ord_less_eq_nat @ Z @ ( ord_max_nat @ X @ Y ) )
% 2.52/2.82 = ( ( ord_less_eq_nat @ Z @ X )
% 2.52/2.82 | ( ord_less_eq_nat @ Z @ Y ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % le_max_iff_disj
% 2.52/2.82 thf(fact_5054_le__max__iff__disj,axiom,
% 2.52/2.82 ! [Z: int,X: int,Y: int] :
% 2.52/2.82 ( ( ord_less_eq_int @ Z @ ( ord_max_int @ X @ Y ) )
% 2.52/2.82 = ( ( ord_less_eq_int @ Z @ X )
% 2.52/2.82 | ( ord_less_eq_int @ Z @ Y ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % le_max_iff_disj
% 2.52/2.82 thf(fact_5055_max_Ocobounded2,axiom,
% 2.52/2.82 ! [B: rat,A: rat] : ( ord_less_eq_rat @ B @ ( ord_max_rat @ A @ B ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.cobounded2
% 2.52/2.82 thf(fact_5056_max_Ocobounded2,axiom,
% 2.52/2.82 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( ord_max_nat @ A @ B ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.cobounded2
% 2.52/2.82 thf(fact_5057_max_Ocobounded2,axiom,
% 2.52/2.82 ! [B: int,A: int] : ( ord_less_eq_int @ B @ ( ord_max_int @ A @ B ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.cobounded2
% 2.52/2.82 thf(fact_5058_max_Ocobounded1,axiom,
% 2.52/2.82 ! [A: rat,B: rat] : ( ord_less_eq_rat @ A @ ( ord_max_rat @ A @ B ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.cobounded1
% 2.52/2.82 thf(fact_5059_max_Ocobounded1,axiom,
% 2.52/2.82 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( ord_max_nat @ A @ B ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.cobounded1
% 2.52/2.82 thf(fact_5060_max_Ocobounded1,axiom,
% 2.52/2.82 ! [A: int,B: int] : ( ord_less_eq_int @ A @ ( ord_max_int @ A @ B ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.cobounded1
% 2.52/2.82 thf(fact_5061_max_Oorder__iff,axiom,
% 2.52/2.82 ( ord_less_eq_rat
% 2.52/2.82 = ( ^ [B2: rat,A2: rat] :
% 2.52/2.82 ( A2
% 2.52/2.82 = ( ord_max_rat @ A2 @ B2 ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.order_iff
% 2.52/2.82 thf(fact_5062_max_Oorder__iff,axiom,
% 2.52/2.82 ( ord_less_eq_nat
% 2.52/2.82 = ( ^ [B2: nat,A2: nat] :
% 2.52/2.82 ( A2
% 2.52/2.82 = ( ord_max_nat @ A2 @ B2 ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.order_iff
% 2.52/2.82 thf(fact_5063_max_Oorder__iff,axiom,
% 2.52/2.82 ( ord_less_eq_int
% 2.52/2.82 = ( ^ [B2: int,A2: int] :
% 2.52/2.82 ( A2
% 2.52/2.82 = ( ord_max_int @ A2 @ B2 ) ) ) ) ).
% 2.52/2.82
% 2.52/2.82 % max.order_iff
% 2.52/2.82 thf(fact_5064_max_OboundedI,axiom,
% 2.52/2.83 ! [B: rat,A: rat,C: rat] :
% 2.52/2.83 ( ( ord_less_eq_rat @ B @ A )
% 2.52/2.83 => ( ( ord_less_eq_rat @ C @ A )
% 2.52/2.83 => ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % max.boundedI
% 2.52/2.83 thf(fact_5065_max_OboundedI,axiom,
% 2.52/2.83 ! [B: nat,A: nat,C: nat] :
% 2.52/2.83 ( ( ord_less_eq_nat @ B @ A )
% 2.52/2.83 => ( ( ord_less_eq_nat @ C @ A )
% 2.52/2.83 => ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % max.boundedI
% 2.52/2.83 thf(fact_5066_max_OboundedI,axiom,
% 2.52/2.83 ! [B: int,A: int,C: int] :
% 2.52/2.83 ( ( ord_less_eq_int @ B @ A )
% 2.52/2.83 => ( ( ord_less_eq_int @ C @ A )
% 2.52/2.83 => ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % max.boundedI
% 2.52/2.83 thf(fact_5067_max_OboundedE,axiom,
% 2.52/2.83 ! [B: rat,C: rat,A: rat] :
% 2.52/2.83 ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A )
% 2.52/2.83 => ~ ( ( ord_less_eq_rat @ B @ A )
% 2.52/2.83 => ~ ( ord_less_eq_rat @ C @ A ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % max.boundedE
% 2.52/2.83 thf(fact_5068_max_OboundedE,axiom,
% 2.52/2.83 ! [B: nat,C: nat,A: nat] :
% 2.52/2.83 ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 2.52/2.83 => ~ ( ( ord_less_eq_nat @ B @ A )
% 2.52/2.83 => ~ ( ord_less_eq_nat @ C @ A ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % max.boundedE
% 2.52/2.83 thf(fact_5069_max_OboundedE,axiom,
% 2.52/2.83 ! [B: int,C: int,A: int] :
% 2.52/2.83 ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 2.52/2.83 => ~ ( ( ord_less_eq_int @ B @ A )
% 2.52/2.83 => ~ ( ord_less_eq_int @ C @ A ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % max.boundedE
% 2.52/2.83 thf(fact_5070_max_OorderI,axiom,
% 2.52/2.83 ! [A: rat,B: rat] :
% 2.52/2.83 ( ( A
% 2.52/2.83 = ( ord_max_rat @ A @ B ) )
% 2.52/2.83 => ( ord_less_eq_rat @ B @ A ) ) ).
% 2.52/2.83
% 2.52/2.83 % max.orderI
% 2.52/2.83 thf(fact_5071_max_OorderI,axiom,
% 2.52/2.83 ! [A: nat,B: nat] :
% 2.52/2.83 ( ( A
% 2.52/2.83 = ( ord_max_nat @ A @ B ) )
% 2.52/2.83 => ( ord_less_eq_nat @ B @ A ) ) ).
% 2.52/2.83
% 2.52/2.83 % max.orderI
% 2.52/2.83 thf(fact_5072_max_OorderI,axiom,
% 2.52/2.83 ! [A: int,B: int] :
% 2.52/2.83 ( ( A
% 2.52/2.83 = ( ord_max_int @ A @ B ) )
% 2.52/2.83 => ( ord_less_eq_int @ B @ A ) ) ).
% 2.52/2.83
% 2.52/2.83 % max.orderI
% 2.52/2.83 thf(fact_5073_max_OorderE,axiom,
% 2.52/2.83 ! [B: rat,A: rat] :
% 2.52/2.83 ( ( ord_less_eq_rat @ B @ A )
% 2.52/2.83 => ( A
% 2.52/2.83 = ( ord_max_rat @ A @ B ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % max.orderE
% 2.52/2.83 thf(fact_5074_max_OorderE,axiom,
% 2.52/2.83 ! [B: nat,A: nat] :
% 2.52/2.83 ( ( ord_less_eq_nat @ B @ A )
% 2.52/2.83 => ( A
% 2.52/2.83 = ( ord_max_nat @ A @ B ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % max.orderE
% 2.52/2.83 thf(fact_5075_max_OorderE,axiom,
% 2.52/2.83 ! [B: int,A: int] :
% 2.52/2.83 ( ( ord_less_eq_int @ B @ A )
% 2.52/2.83 => ( A
% 2.52/2.83 = ( ord_max_int @ A @ B ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % max.orderE
% 2.52/2.83 thf(fact_5076_max_Omono,axiom,
% 2.52/2.83 ! [C: rat,A: rat,D2: rat,B: rat] :
% 2.52/2.83 ( ( ord_less_eq_rat @ C @ A )
% 2.52/2.83 => ( ( ord_less_eq_rat @ D2 @ B )
% 2.52/2.83 => ( ord_less_eq_rat @ ( ord_max_rat @ C @ D2 ) @ ( ord_max_rat @ A @ B ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % max.mono
% 2.52/2.83 thf(fact_5077_max_Omono,axiom,
% 2.52/2.83 ! [C: nat,A: nat,D2: nat,B: nat] :
% 2.52/2.83 ( ( ord_less_eq_nat @ C @ A )
% 2.52/2.83 => ( ( ord_less_eq_nat @ D2 @ B )
% 2.52/2.83 => ( ord_less_eq_nat @ ( ord_max_nat @ C @ D2 ) @ ( ord_max_nat @ A @ B ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % max.mono
% 2.52/2.83 thf(fact_5078_max_Omono,axiom,
% 2.52/2.83 ! [C: int,A: int,D2: int,B: int] :
% 2.52/2.83 ( ( ord_less_eq_int @ C @ A )
% 2.52/2.83 => ( ( ord_less_eq_int @ D2 @ B )
% 2.52/2.83 => ( ord_less_eq_int @ ( ord_max_int @ C @ D2 ) @ ( ord_max_int @ A @ B ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % max.mono
% 2.52/2.83 thf(fact_5079_max_Ostrict__coboundedI2,axiom,
% 2.52/2.83 ! [C: code_integer,B: code_integer,A: code_integer] :
% 2.52/2.83 ( ( ord_le6747313008572928689nteger @ C @ B )
% 2.52/2.83 => ( ord_le6747313008572928689nteger @ C @ ( ord_max_Code_integer @ A @ B ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % max.strict_coboundedI2
% 2.52/2.83 thf(fact_5080_max_Ostrict__coboundedI2,axiom,
% 2.52/2.83 ! [C: rat,B: rat,A: rat] :
% 2.52/2.83 ( ( ord_less_rat @ C @ B )
% 2.52/2.83 => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % max.strict_coboundedI2
% 2.52/2.83 thf(fact_5081_max_Ostrict__coboundedI2,axiom,
% 2.52/2.83 ! [C: nat,B: nat,A: nat] :
% 2.52/2.83 ( ( ord_less_nat @ C @ B )
% 2.52/2.83 => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % max.strict_coboundedI2
% 2.52/2.83 thf(fact_5082_max_Ostrict__coboundedI2,axiom,
% 2.52/2.83 ! [C: int,B: int,A: int] :
% 2.52/2.83 ( ( ord_less_int @ C @ B )
% 2.52/2.83 => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % max.strict_coboundedI2
% 2.52/2.83 thf(fact_5083_max_Ostrict__coboundedI1,axiom,
% 2.52/2.83 ! [C: code_integer,A: code_integer,B: code_integer] :
% 2.52/2.83 ( ( ord_le6747313008572928689nteger @ C @ A )
% 2.52/2.83 => ( ord_le6747313008572928689nteger @ C @ ( ord_max_Code_integer @ A @ B ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % max.strict_coboundedI1
% 2.52/2.83 thf(fact_5084_max_Ostrict__coboundedI1,axiom,
% 2.52/2.83 ! [C: rat,A: rat,B: rat] :
% 2.52/2.83 ( ( ord_less_rat @ C @ A )
% 2.52/2.83 => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % max.strict_coboundedI1
% 2.52/2.83 thf(fact_5085_max_Ostrict__coboundedI1,axiom,
% 2.52/2.83 ! [C: nat,A: nat,B: nat] :
% 2.52/2.83 ( ( ord_less_nat @ C @ A )
% 2.52/2.83 => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % max.strict_coboundedI1
% 2.52/2.83 thf(fact_5086_max_Ostrict__coboundedI1,axiom,
% 2.52/2.83 ! [C: int,A: int,B: int] :
% 2.52/2.83 ( ( ord_less_int @ C @ A )
% 2.52/2.83 => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % max.strict_coboundedI1
% 2.52/2.83 thf(fact_5087_max_Ostrict__order__iff,axiom,
% 2.52/2.83 ( ord_le6747313008572928689nteger
% 2.52/2.83 = ( ^ [B2: code_integer,A2: code_integer] :
% 2.52/2.83 ( ( A2
% 2.52/2.83 = ( ord_max_Code_integer @ A2 @ B2 ) )
% 2.52/2.83 & ( A2 != B2 ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % max.strict_order_iff
% 2.52/2.83 thf(fact_5088_max_Ostrict__order__iff,axiom,
% 2.52/2.83 ( ord_less_rat
% 2.52/2.83 = ( ^ [B2: rat,A2: rat] :
% 2.52/2.83 ( ( A2
% 2.52/2.83 = ( ord_max_rat @ A2 @ B2 ) )
% 2.52/2.83 & ( A2 != B2 ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % max.strict_order_iff
% 2.52/2.83 thf(fact_5089_max_Ostrict__order__iff,axiom,
% 2.52/2.83 ( ord_less_nat
% 2.52/2.83 = ( ^ [B2: nat,A2: nat] :
% 2.52/2.83 ( ( A2
% 2.52/2.83 = ( ord_max_nat @ A2 @ B2 ) )
% 2.52/2.83 & ( A2 != B2 ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % max.strict_order_iff
% 2.52/2.83 thf(fact_5090_max_Ostrict__order__iff,axiom,
% 2.52/2.83 ( ord_less_int
% 2.52/2.83 = ( ^ [B2: int,A2: int] :
% 2.52/2.83 ( ( A2
% 2.52/2.83 = ( ord_max_int @ A2 @ B2 ) )
% 2.52/2.83 & ( A2 != B2 ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % max.strict_order_iff
% 2.52/2.83 thf(fact_5091_max_Ostrict__boundedE,axiom,
% 2.52/2.83 ! [B: code_integer,C: code_integer,A: code_integer] :
% 2.52/2.83 ( ( ord_le6747313008572928689nteger @ ( ord_max_Code_integer @ B @ C ) @ A )
% 2.52/2.83 => ~ ( ( ord_le6747313008572928689nteger @ B @ A )
% 2.52/2.83 => ~ ( ord_le6747313008572928689nteger @ C @ A ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % max.strict_boundedE
% 2.52/2.83 thf(fact_5092_max_Ostrict__boundedE,axiom,
% 2.52/2.83 ! [B: rat,C: rat,A: rat] :
% 2.52/2.83 ( ( ord_less_rat @ ( ord_max_rat @ B @ C ) @ A )
% 2.52/2.83 => ~ ( ( ord_less_rat @ B @ A )
% 2.52/2.83 => ~ ( ord_less_rat @ C @ A ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % max.strict_boundedE
% 2.52/2.83 thf(fact_5093_max_Ostrict__boundedE,axiom,
% 2.52/2.83 ! [B: nat,C: nat,A: nat] :
% 2.52/2.83 ( ( ord_less_nat @ ( ord_max_nat @ B @ C ) @ A )
% 2.52/2.83 => ~ ( ( ord_less_nat @ B @ A )
% 2.52/2.83 => ~ ( ord_less_nat @ C @ A ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % max.strict_boundedE
% 2.52/2.83 thf(fact_5094_max_Ostrict__boundedE,axiom,
% 2.52/2.83 ! [B: int,C: int,A: int] :
% 2.52/2.83 ( ( ord_less_int @ ( ord_max_int @ B @ C ) @ A )
% 2.52/2.83 => ~ ( ( ord_less_int @ B @ A )
% 2.52/2.83 => ~ ( ord_less_int @ C @ A ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % max.strict_boundedE
% 2.52/2.83 thf(fact_5095_less__max__iff__disj,axiom,
% 2.52/2.83 ! [Z: code_integer,X: code_integer,Y: code_integer] :
% 2.52/2.83 ( ( ord_le6747313008572928689nteger @ Z @ ( ord_max_Code_integer @ X @ Y ) )
% 2.52/2.83 = ( ( ord_le6747313008572928689nteger @ Z @ X )
% 2.52/2.83 | ( ord_le6747313008572928689nteger @ Z @ Y ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % less_max_iff_disj
% 2.52/2.83 thf(fact_5096_less__max__iff__disj,axiom,
% 2.52/2.83 ! [Z: rat,X: rat,Y: rat] :
% 2.52/2.83 ( ( ord_less_rat @ Z @ ( ord_max_rat @ X @ Y ) )
% 2.52/2.83 = ( ( ord_less_rat @ Z @ X )
% 2.52/2.83 | ( ord_less_rat @ Z @ Y ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % less_max_iff_disj
% 2.52/2.83 thf(fact_5097_less__max__iff__disj,axiom,
% 2.52/2.83 ! [Z: nat,X: nat,Y: nat] :
% 2.52/2.83 ( ( ord_less_nat @ Z @ ( ord_max_nat @ X @ Y ) )
% 2.52/2.83 = ( ( ord_less_nat @ Z @ X )
% 2.52/2.83 | ( ord_less_nat @ Z @ Y ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % less_max_iff_disj
% 2.52/2.83 thf(fact_5098_less__max__iff__disj,axiom,
% 2.52/2.83 ! [Z: int,X: int,Y: int] :
% 2.52/2.83 ( ( ord_less_int @ Z @ ( ord_max_int @ X @ Y ) )
% 2.52/2.83 = ( ( ord_less_int @ Z @ X )
% 2.52/2.83 | ( ord_less_int @ Z @ Y ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % less_max_iff_disj
% 2.52/2.83 thf(fact_5099_max__add__distrib__right,axiom,
% 2.52/2.83 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 2.52/2.83 ( ( plus_p5714425477246183910nteger @ X @ ( ord_max_Code_integer @ Y @ Z ) )
% 2.52/2.83 = ( ord_max_Code_integer @ ( plus_p5714425477246183910nteger @ X @ Y ) @ ( plus_p5714425477246183910nteger @ X @ Z ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % max_add_distrib_right
% 2.52/2.83 thf(fact_5100_max__add__distrib__right,axiom,
% 2.52/2.83 ! [X: rat,Y: rat,Z: rat] :
% 2.52/2.83 ( ( plus_plus_rat @ X @ ( ord_max_rat @ Y @ Z ) )
% 2.52/2.83 = ( ord_max_rat @ ( plus_plus_rat @ X @ Y ) @ ( plus_plus_rat @ X @ Z ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % max_add_distrib_right
% 2.52/2.83 thf(fact_5101_max__add__distrib__right,axiom,
% 2.52/2.83 ! [X: nat,Y: nat,Z: nat] :
% 2.52/2.83 ( ( plus_plus_nat @ X @ ( ord_max_nat @ Y @ Z ) )
% 2.52/2.83 = ( ord_max_nat @ ( plus_plus_nat @ X @ Y ) @ ( plus_plus_nat @ X @ Z ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % max_add_distrib_right
% 2.52/2.83 thf(fact_5102_max__add__distrib__right,axiom,
% 2.52/2.83 ! [X: int,Y: int,Z: int] :
% 2.52/2.83 ( ( plus_plus_int @ X @ ( ord_max_int @ Y @ Z ) )
% 2.52/2.83 = ( ord_max_int @ ( plus_plus_int @ X @ Y ) @ ( plus_plus_int @ X @ Z ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % max_add_distrib_right
% 2.52/2.83 thf(fact_5103_max__add__distrib__left,axiom,
% 2.52/2.83 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 2.52/2.83 ( ( plus_p5714425477246183910nteger @ ( ord_max_Code_integer @ X @ Y ) @ Z )
% 2.52/2.83 = ( ord_max_Code_integer @ ( plus_p5714425477246183910nteger @ X @ Z ) @ ( plus_p5714425477246183910nteger @ Y @ Z ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % max_add_distrib_left
% 2.52/2.83 thf(fact_5104_max__add__distrib__left,axiom,
% 2.52/2.83 ! [X: rat,Y: rat,Z: rat] :
% 2.52/2.83 ( ( plus_plus_rat @ ( ord_max_rat @ X @ Y ) @ Z )
% 2.52/2.83 = ( ord_max_rat @ ( plus_plus_rat @ X @ Z ) @ ( plus_plus_rat @ Y @ Z ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % max_add_distrib_left
% 2.52/2.83 thf(fact_5105_max__add__distrib__left,axiom,
% 2.52/2.83 ! [X: nat,Y: nat,Z: nat] :
% 2.52/2.83 ( ( plus_plus_nat @ ( ord_max_nat @ X @ Y ) @ Z )
% 2.52/2.83 = ( ord_max_nat @ ( plus_plus_nat @ X @ Z ) @ ( plus_plus_nat @ Y @ Z ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % max_add_distrib_left
% 2.52/2.83 thf(fact_5106_max__add__distrib__left,axiom,
% 2.52/2.83 ! [X: int,Y: int,Z: int] :
% 2.52/2.83 ( ( plus_plus_int @ ( ord_max_int @ X @ Y ) @ Z )
% 2.52/2.83 = ( ord_max_int @ ( plus_plus_int @ X @ Z ) @ ( plus_plus_int @ Y @ Z ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % max_add_distrib_left
% 2.52/2.83 thf(fact_5107_max__diff__distrib__left,axiom,
% 2.52/2.83 ! [X: int,Y: int,Z: int] :
% 2.52/2.83 ( ( minus_minus_int @ ( ord_max_int @ X @ Y ) @ Z )
% 2.52/2.83 = ( ord_max_int @ ( minus_minus_int @ X @ Z ) @ ( minus_minus_int @ Y @ Z ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % max_diff_distrib_left
% 2.52/2.83 thf(fact_5108_max__diff__distrib__left,axiom,
% 2.52/2.83 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 2.52/2.83 ( ( minus_8373710615458151222nteger @ ( ord_max_Code_integer @ X @ Y ) @ Z )
% 2.52/2.83 = ( ord_max_Code_integer @ ( minus_8373710615458151222nteger @ X @ Z ) @ ( minus_8373710615458151222nteger @ Y @ Z ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % max_diff_distrib_left
% 2.52/2.83 thf(fact_5109_sup__max,axiom,
% 2.52/2.83 sup_sup_int = ord_max_int ).
% 2.52/2.83
% 2.52/2.83 % sup_max
% 2.52/2.83 thf(fact_5110_length__induct,axiom,
% 2.52/2.83 ! [P2: list_int > $o,Xs: list_int] :
% 2.52/2.83 ( ! [Xs2: list_int] :
% 2.52/2.83 ( ! [Ys5: list_int] :
% 2.52/2.83 ( ( ord_less_nat @ ( size_size_list_int @ Ys5 ) @ ( size_size_list_int @ Xs2 ) )
% 2.52/2.83 => ( P2 @ Ys5 ) )
% 2.52/2.83 => ( P2 @ Xs2 ) )
% 2.52/2.83 => ( P2 @ Xs ) ) ).
% 2.52/2.83
% 2.52/2.83 % length_induct
% 2.52/2.83 thf(fact_5111_length__induct,axiom,
% 2.52/2.83 ! [P2: list_nat > $o,Xs: list_nat] :
% 2.52/2.83 ( ! [Xs2: list_nat] :
% 2.52/2.83 ( ! [Ys5: list_nat] :
% 2.52/2.83 ( ( ord_less_nat @ ( size_size_list_nat @ Ys5 ) @ ( size_size_list_nat @ Xs2 ) )
% 2.52/2.83 => ( P2 @ Ys5 ) )
% 2.52/2.83 => ( P2 @ Xs2 ) )
% 2.52/2.83 => ( P2 @ Xs ) ) ).
% 2.52/2.83
% 2.52/2.83 % length_induct
% 2.52/2.83 thf(fact_5112_finite__maxlen,axiom,
% 2.52/2.83 ! [M: set_list_int] :
% 2.52/2.83 ( ( finite3922522038869484883st_int @ M )
% 2.52/2.83 => ? [N4: nat] :
% 2.52/2.83 ! [X4: list_int] :
% 2.52/2.83 ( ( member_list_int @ X4 @ M )
% 2.52/2.83 => ( ord_less_nat @ ( size_size_list_int @ X4 ) @ N4 ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % finite_maxlen
% 2.52/2.83 thf(fact_5113_finite__maxlen,axiom,
% 2.52/2.83 ! [M: set_list_nat] :
% 2.52/2.83 ( ( finite8100373058378681591st_nat @ M )
% 2.52/2.83 => ? [N4: nat] :
% 2.52/2.83 ! [X4: list_nat] :
% 2.52/2.83 ( ( member_list_nat @ X4 @ M )
% 2.52/2.83 => ( ord_less_nat @ ( size_size_list_nat @ X4 ) @ N4 ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % finite_maxlen
% 2.52/2.83 thf(fact_5114_map__eq__imp__length__eq,axiom,
% 2.52/2.83 ! [F2: produc6575502325842934193n_assn > assn,Xs: list_P8527749157015355191n_assn,G3: produc6575502325842934193n_assn > assn,Ys: list_P8527749157015355191n_assn] :
% 2.52/2.83 ( ( ( map_Pr8991440229025900053n_assn @ F2 @ Xs )
% 2.52/2.83 = ( map_Pr8991440229025900053n_assn @ G3 @ Ys ) )
% 2.52/2.83 => ( ( size_s6829681357464350627n_assn @ Xs )
% 2.52/2.83 = ( size_s6829681357464350627n_assn @ Ys ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % map_eq_imp_length_eq
% 2.52/2.83 thf(fact_5115_map__eq__imp__length__eq,axiom,
% 2.52/2.83 ! [F2: produc6575502325842934193n_assn > assn,Xs: list_P8527749157015355191n_assn,G3: int > assn,Ys: list_int] :
% 2.52/2.83 ( ( ( map_Pr8991440229025900053n_assn @ F2 @ Xs )
% 2.52/2.83 = ( map_int_assn @ G3 @ Ys ) )
% 2.52/2.83 => ( ( size_s6829681357464350627n_assn @ Xs )
% 2.52/2.83 = ( size_size_list_int @ Ys ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % map_eq_imp_length_eq
% 2.52/2.83 thf(fact_5116_map__eq__imp__length__eq,axiom,
% 2.52/2.83 ! [F2: produc6575502325842934193n_assn > assn,Xs: list_P8527749157015355191n_assn,G3: nat > assn,Ys: list_nat] :
% 2.52/2.83 ( ( ( map_Pr8991440229025900053n_assn @ F2 @ Xs )
% 2.52/2.83 = ( map_nat_assn @ G3 @ Ys ) )
% 2.52/2.83 => ( ( size_s6829681357464350627n_assn @ Xs )
% 2.52/2.83 = ( size_size_list_nat @ Ys ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % map_eq_imp_length_eq
% 2.52/2.83 thf(fact_5117_map__eq__imp__length__eq,axiom,
% 2.52/2.83 ! [F2: int > assn,Xs: list_int,G3: produc6575502325842934193n_assn > assn,Ys: list_P8527749157015355191n_assn] :
% 2.52/2.83 ( ( ( map_int_assn @ F2 @ Xs )
% 2.52/2.83 = ( map_Pr8991440229025900053n_assn @ G3 @ Ys ) )
% 2.52/2.83 => ( ( size_size_list_int @ Xs )
% 2.52/2.83 = ( size_s6829681357464350627n_assn @ Ys ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % map_eq_imp_length_eq
% 2.52/2.83 thf(fact_5118_map__eq__imp__length__eq,axiom,
% 2.52/2.83 ! [F2: int > nat,Xs: list_int,G3: nat > nat,Ys: list_nat] :
% 2.52/2.83 ( ( ( map_int_nat @ F2 @ Xs )
% 2.52/2.83 = ( map_nat_nat @ G3 @ Ys ) )
% 2.52/2.83 => ( ( size_size_list_int @ Xs )
% 2.52/2.83 = ( size_size_list_nat @ Ys ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % map_eq_imp_length_eq
% 2.52/2.83 thf(fact_5119_map__eq__imp__length__eq,axiom,
% 2.52/2.83 ! [F2: nat > assn,Xs: list_nat,G3: produc6575502325842934193n_assn > assn,Ys: list_P8527749157015355191n_assn] :
% 2.52/2.83 ( ( ( map_nat_assn @ F2 @ Xs )
% 2.52/2.83 = ( map_Pr8991440229025900053n_assn @ G3 @ Ys ) )
% 2.52/2.83 => ( ( size_size_list_nat @ Xs )
% 2.52/2.83 = ( size_s6829681357464350627n_assn @ Ys ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % map_eq_imp_length_eq
% 2.52/2.83 thf(fact_5120_map__eq__imp__length__eq,axiom,
% 2.52/2.83 ! [F2: nat > nat,Xs: list_nat,G3: int > nat,Ys: list_int] :
% 2.52/2.83 ( ( ( map_nat_nat @ F2 @ Xs )
% 2.52/2.83 = ( map_int_nat @ G3 @ Ys ) )
% 2.52/2.83 => ( ( size_size_list_nat @ Xs )
% 2.52/2.83 = ( size_size_list_int @ Ys ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % map_eq_imp_length_eq
% 2.52/2.83 thf(fact_5121_map__eq__imp__length__eq,axiom,
% 2.52/2.83 ! [F2: nat > nat,Xs: list_nat,G3: nat > nat,Ys: list_nat] :
% 2.52/2.83 ( ( ( map_nat_nat @ F2 @ Xs )
% 2.52/2.83 = ( map_nat_nat @ G3 @ Ys ) )
% 2.52/2.83 => ( ( size_size_list_nat @ Xs )
% 2.52/2.83 = ( size_size_list_nat @ Ys ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % map_eq_imp_length_eq
% 2.52/2.83 thf(fact_5122_max_Oabel__semigroup__axioms,axiom,
% 2.52/2.83 abel_semigroup_int @ ord_max_int ).
% 2.52/2.83
% 2.52/2.83 % max.abel_semigroup_axioms
% 2.52/2.83 thf(fact_5123_zip__inj,axiom,
% 2.52/2.83 ! [A: list_int,B: list_int,A5: list_int,B6: list_int] :
% 2.52/2.83 ( ( ( size_size_list_int @ A )
% 2.52/2.83 = ( size_size_list_int @ B ) )
% 2.52/2.83 => ( ( ( size_size_list_int @ A5 )
% 2.52/2.83 = ( size_size_list_int @ B6 ) )
% 2.52/2.83 => ( ( ( zip_int_int @ A @ B )
% 2.52/2.83 = ( zip_int_int @ A5 @ B6 ) )
% 2.52/2.83 => ( ( A = A5 )
% 2.52/2.83 & ( B = B6 ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % zip_inj
% 2.52/2.83 thf(fact_5124_zip__inj,axiom,
% 2.52/2.83 ! [A: list_int,B: list_nat,A5: list_int,B6: list_nat] :
% 2.52/2.83 ( ( ( size_size_list_int @ A )
% 2.52/2.83 = ( size_size_list_nat @ B ) )
% 2.52/2.83 => ( ( ( size_size_list_int @ A5 )
% 2.52/2.83 = ( size_size_list_nat @ B6 ) )
% 2.52/2.83 => ( ( ( zip_int_nat @ A @ B )
% 2.52/2.83 = ( zip_int_nat @ A5 @ B6 ) )
% 2.52/2.83 => ( ( A = A5 )
% 2.52/2.83 & ( B = B6 ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % zip_inj
% 2.52/2.83 thf(fact_5125_zip__inj,axiom,
% 2.52/2.83 ! [A: list_nat,B: list_int,A5: list_nat,B6: list_int] :
% 2.52/2.83 ( ( ( size_size_list_nat @ A )
% 2.52/2.83 = ( size_size_list_int @ B ) )
% 2.52/2.83 => ( ( ( size_size_list_nat @ A5 )
% 2.52/2.83 = ( size_size_list_int @ B6 ) )
% 2.52/2.83 => ( ( ( zip_nat_int @ A @ B )
% 2.52/2.83 = ( zip_nat_int @ A5 @ B6 ) )
% 2.52/2.83 => ( ( A = A5 )
% 2.52/2.83 & ( B = B6 ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % zip_inj
% 2.52/2.83 thf(fact_5126_zip__inj,axiom,
% 2.52/2.83 ! [A: list_nat,B: list_nat,A5: list_nat,B6: list_nat] :
% 2.52/2.83 ( ( ( size_size_list_nat @ A )
% 2.52/2.83 = ( size_size_list_nat @ B ) )
% 2.52/2.83 => ( ( ( size_size_list_nat @ A5 )
% 2.52/2.83 = ( size_size_list_nat @ B6 ) )
% 2.52/2.83 => ( ( ( zip_nat_nat @ A @ B )
% 2.52/2.83 = ( zip_nat_nat @ A5 @ B6 ) )
% 2.52/2.83 => ( ( A = A5 )
% 2.52/2.83 & ( B = B6 ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % zip_inj
% 2.52/2.83 thf(fact_5127_max_Osemilattice__axioms,axiom,
% 2.52/2.83 semilattice_int @ ord_max_int ).
% 2.52/2.83
% 2.52/2.83 % max.semilattice_axioms
% 2.52/2.83 thf(fact_5128_max_Osemigroup__axioms,axiom,
% 2.52/2.83 semigroup_int @ ord_max_int ).
% 2.52/2.83
% 2.52/2.83 % max.semigroup_axioms
% 2.52/2.83 thf(fact_5129_bit__1__iff,axiom,
% 2.52/2.83 ! [N: nat] :
% 2.52/2.83 ( ( bit_se9216721137139052372nteger @ one_one_Code_integer @ N )
% 2.52/2.83 = ( N = zero_zero_nat ) ) ).
% 2.52/2.83
% 2.52/2.83 % bit_1_iff
% 2.52/2.83 thf(fact_5130_bit__1__iff,axiom,
% 2.52/2.83 ! [N: nat] :
% 2.52/2.83 ( ( bit_se1148574629649215175it_nat @ one_one_nat @ N )
% 2.52/2.83 = ( N = zero_zero_nat ) ) ).
% 2.52/2.83
% 2.52/2.83 % bit_1_iff
% 2.52/2.83 thf(fact_5131_bit__1__iff,axiom,
% 2.52/2.83 ! [N: nat] :
% 2.52/2.83 ( ( bit_se1146084159140164899it_int @ one_one_int @ N )
% 2.52/2.83 = ( N = zero_zero_nat ) ) ).
% 2.52/2.83
% 2.52/2.83 % bit_1_iff
% 2.52/2.83 thf(fact_5132_not__bit__1__Suc,axiom,
% 2.52/2.83 ! [N: nat] :
% 2.52/2.83 ~ ( bit_se9216721137139052372nteger @ one_one_Code_integer @ ( suc @ N ) ) ).
% 2.52/2.83
% 2.52/2.83 % not_bit_1_Suc
% 2.52/2.83 thf(fact_5133_not__bit__1__Suc,axiom,
% 2.52/2.83 ! [N: nat] :
% 2.52/2.83 ~ ( bit_se1148574629649215175it_nat @ one_one_nat @ ( suc @ N ) ) ).
% 2.52/2.83
% 2.52/2.83 % not_bit_1_Suc
% 2.52/2.83 thf(fact_5134_not__bit__1__Suc,axiom,
% 2.52/2.83 ! [N: nat] :
% 2.52/2.83 ~ ( bit_se1146084159140164899it_int @ one_one_int @ ( suc @ N ) ) ).
% 2.52/2.83
% 2.52/2.83 % not_bit_1_Suc
% 2.52/2.83 thf(fact_5135_bit__numeral__simps_I1_J,axiom,
% 2.52/2.83 ! [N: num] :
% 2.52/2.83 ~ ( bit_se9216721137139052372nteger @ one_one_Code_integer @ ( numeral_numeral_nat @ N ) ) ).
% 2.52/2.83
% 2.52/2.83 % bit_numeral_simps(1)
% 2.52/2.83 thf(fact_5136_bit__numeral__simps_I1_J,axiom,
% 2.52/2.83 ! [N: num] :
% 2.52/2.83 ~ ( bit_se1148574629649215175it_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) ) ).
% 2.52/2.83
% 2.52/2.83 % bit_numeral_simps(1)
% 2.52/2.83 thf(fact_5137_bit__numeral__simps_I1_J,axiom,
% 2.52/2.83 ! [N: num] :
% 2.52/2.83 ~ ( bit_se1146084159140164899it_int @ one_one_int @ ( numeral_numeral_nat @ N ) ) ).
% 2.52/2.83
% 2.52/2.83 % bit_numeral_simps(1)
% 2.52/2.83 thf(fact_5138_list__induct4,axiom,
% 2.52/2.83 ! [Xs: list_int,Ys: list_int,Zs: list_int,Ws: list_int,P2: list_int > list_int > list_int > list_int > $o] :
% 2.52/2.83 ( ( ( size_size_list_int @ Xs )
% 2.52/2.83 = ( size_size_list_int @ Ys ) )
% 2.52/2.83 => ( ( ( size_size_list_int @ Ys )
% 2.52/2.83 = ( size_size_list_int @ Zs ) )
% 2.52/2.83 => ( ( ( size_size_list_int @ Zs )
% 2.52/2.83 = ( size_size_list_int @ Ws ) )
% 2.52/2.83 => ( ( P2 @ nil_int @ nil_int @ nil_int @ nil_int )
% 2.52/2.83 => ( ! [X3: int,Xs2: list_int,Y3: int,Ys3: list_int,Z2: int,Zs3: list_int,W3: int,Ws2: list_int] :
% 2.52/2.83 ( ( ( size_size_list_int @ Xs2 )
% 2.52/2.83 = ( size_size_list_int @ Ys3 ) )
% 2.52/2.83 => ( ( ( size_size_list_int @ Ys3 )
% 2.52/2.83 = ( size_size_list_int @ Zs3 ) )
% 2.52/2.83 => ( ( ( size_size_list_int @ Zs3 )
% 2.52/2.83 = ( size_size_list_int @ Ws2 ) )
% 2.52/2.83 => ( ( P2 @ Xs2 @ Ys3 @ Zs3 @ Ws2 )
% 2.52/2.83 => ( P2 @ ( cons_int @ X3 @ Xs2 ) @ ( cons_int @ Y3 @ Ys3 ) @ ( cons_int @ Z2 @ Zs3 ) @ ( cons_int @ W3 @ Ws2 ) ) ) ) ) )
% 2.52/2.83 => ( P2 @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % list_induct4
% 2.52/2.83 thf(fact_5139_list__induct4,axiom,
% 2.52/2.83 ! [Xs: list_int,Ys: list_int,Zs: list_int,Ws: list_nat,P2: list_int > list_int > list_int > list_nat > $o] :
% 2.52/2.83 ( ( ( size_size_list_int @ Xs )
% 2.52/2.83 = ( size_size_list_int @ Ys ) )
% 2.52/2.83 => ( ( ( size_size_list_int @ Ys )
% 2.52/2.83 = ( size_size_list_int @ Zs ) )
% 2.52/2.83 => ( ( ( size_size_list_int @ Zs )
% 2.52/2.83 = ( size_size_list_nat @ Ws ) )
% 2.52/2.83 => ( ( P2 @ nil_int @ nil_int @ nil_int @ nil_nat )
% 2.52/2.83 => ( ! [X3: int,Xs2: list_int,Y3: int,Ys3: list_int,Z2: int,Zs3: list_int,W3: nat,Ws2: list_nat] :
% 2.52/2.83 ( ( ( size_size_list_int @ Xs2 )
% 2.52/2.83 = ( size_size_list_int @ Ys3 ) )
% 2.52/2.83 => ( ( ( size_size_list_int @ Ys3 )
% 2.52/2.83 = ( size_size_list_int @ Zs3 ) )
% 2.52/2.83 => ( ( ( size_size_list_int @ Zs3 )
% 2.52/2.83 = ( size_size_list_nat @ Ws2 ) )
% 2.52/2.83 => ( ( P2 @ Xs2 @ Ys3 @ Zs3 @ Ws2 )
% 2.52/2.83 => ( P2 @ ( cons_int @ X3 @ Xs2 ) @ ( cons_int @ Y3 @ Ys3 ) @ ( cons_int @ Z2 @ Zs3 ) @ ( cons_nat @ W3 @ Ws2 ) ) ) ) ) )
% 2.52/2.83 => ( P2 @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % list_induct4
% 2.52/2.83 thf(fact_5140_list__induct4,axiom,
% 2.52/2.83 ! [Xs: list_int,Ys: list_int,Zs: list_nat,Ws: list_int,P2: list_int > list_int > list_nat > list_int > $o] :
% 2.52/2.83 ( ( ( size_size_list_int @ Xs )
% 2.52/2.83 = ( size_size_list_int @ Ys ) )
% 2.52/2.83 => ( ( ( size_size_list_int @ Ys )
% 2.52/2.83 = ( size_size_list_nat @ Zs ) )
% 2.52/2.83 => ( ( ( size_size_list_nat @ Zs )
% 2.52/2.83 = ( size_size_list_int @ Ws ) )
% 2.52/2.83 => ( ( P2 @ nil_int @ nil_int @ nil_nat @ nil_int )
% 2.52/2.83 => ( ! [X3: int,Xs2: list_int,Y3: int,Ys3: list_int,Z2: nat,Zs3: list_nat,W3: int,Ws2: list_int] :
% 2.52/2.83 ( ( ( size_size_list_int @ Xs2 )
% 2.52/2.83 = ( size_size_list_int @ Ys3 ) )
% 2.52/2.83 => ( ( ( size_size_list_int @ Ys3 )
% 2.52/2.83 = ( size_size_list_nat @ Zs3 ) )
% 2.52/2.83 => ( ( ( size_size_list_nat @ Zs3 )
% 2.52/2.83 = ( size_size_list_int @ Ws2 ) )
% 2.52/2.83 => ( ( P2 @ Xs2 @ Ys3 @ Zs3 @ Ws2 )
% 2.52/2.83 => ( P2 @ ( cons_int @ X3 @ Xs2 ) @ ( cons_int @ Y3 @ Ys3 ) @ ( cons_nat @ Z2 @ Zs3 ) @ ( cons_int @ W3 @ Ws2 ) ) ) ) ) )
% 2.52/2.83 => ( P2 @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % list_induct4
% 2.52/2.83 thf(fact_5141_list__induct4,axiom,
% 2.52/2.83 ! [Xs: list_int,Ys: list_int,Zs: list_nat,Ws: list_nat,P2: list_int > list_int > list_nat > list_nat > $o] :
% 2.52/2.83 ( ( ( size_size_list_int @ Xs )
% 2.52/2.83 = ( size_size_list_int @ Ys ) )
% 2.52/2.83 => ( ( ( size_size_list_int @ Ys )
% 2.52/2.83 = ( size_size_list_nat @ Zs ) )
% 2.52/2.83 => ( ( ( size_size_list_nat @ Zs )
% 2.52/2.83 = ( size_size_list_nat @ Ws ) )
% 2.52/2.83 => ( ( P2 @ nil_int @ nil_int @ nil_nat @ nil_nat )
% 2.52/2.83 => ( ! [X3: int,Xs2: list_int,Y3: int,Ys3: list_int,Z2: nat,Zs3: list_nat,W3: nat,Ws2: list_nat] :
% 2.52/2.83 ( ( ( size_size_list_int @ Xs2 )
% 2.52/2.83 = ( size_size_list_int @ Ys3 ) )
% 2.52/2.83 => ( ( ( size_size_list_int @ Ys3 )
% 2.52/2.83 = ( size_size_list_nat @ Zs3 ) )
% 2.52/2.83 => ( ( ( size_size_list_nat @ Zs3 )
% 2.52/2.83 = ( size_size_list_nat @ Ws2 ) )
% 2.52/2.83 => ( ( P2 @ Xs2 @ Ys3 @ Zs3 @ Ws2 )
% 2.52/2.83 => ( P2 @ ( cons_int @ X3 @ Xs2 ) @ ( cons_int @ Y3 @ Ys3 ) @ ( cons_nat @ Z2 @ Zs3 ) @ ( cons_nat @ W3 @ Ws2 ) ) ) ) ) )
% 2.52/2.83 => ( P2 @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % list_induct4
% 2.52/2.83 thf(fact_5142_list__induct4,axiom,
% 2.52/2.83 ! [Xs: list_int,Ys: list_nat,Zs: list_int,Ws: list_int,P2: list_int > list_nat > list_int > list_int > $o] :
% 2.52/2.83 ( ( ( size_size_list_int @ Xs )
% 2.52/2.83 = ( size_size_list_nat @ Ys ) )
% 2.52/2.83 => ( ( ( size_size_list_nat @ Ys )
% 2.52/2.83 = ( size_size_list_int @ Zs ) )
% 2.52/2.83 => ( ( ( size_size_list_int @ Zs )
% 2.52/2.83 = ( size_size_list_int @ Ws ) )
% 2.52/2.83 => ( ( P2 @ nil_int @ nil_nat @ nil_int @ nil_int )
% 2.52/2.83 => ( ! [X3: int,Xs2: list_int,Y3: nat,Ys3: list_nat,Z2: int,Zs3: list_int,W3: int,Ws2: list_int] :
% 2.52/2.83 ( ( ( size_size_list_int @ Xs2 )
% 2.52/2.83 = ( size_size_list_nat @ Ys3 ) )
% 2.52/2.83 => ( ( ( size_size_list_nat @ Ys3 )
% 2.52/2.83 = ( size_size_list_int @ Zs3 ) )
% 2.52/2.83 => ( ( ( size_size_list_int @ Zs3 )
% 2.52/2.83 = ( size_size_list_int @ Ws2 ) )
% 2.52/2.83 => ( ( P2 @ Xs2 @ Ys3 @ Zs3 @ Ws2 )
% 2.52/2.83 => ( P2 @ ( cons_int @ X3 @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) @ ( cons_int @ Z2 @ Zs3 ) @ ( cons_int @ W3 @ Ws2 ) ) ) ) ) )
% 2.52/2.83 => ( P2 @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % list_induct4
% 2.52/2.83 thf(fact_5143_list__induct4,axiom,
% 2.52/2.83 ! [Xs: list_int,Ys: list_nat,Zs: list_int,Ws: list_nat,P2: list_int > list_nat > list_int > list_nat > $o] :
% 2.52/2.83 ( ( ( size_size_list_int @ Xs )
% 2.52/2.83 = ( size_size_list_nat @ Ys ) )
% 2.52/2.83 => ( ( ( size_size_list_nat @ Ys )
% 2.52/2.83 = ( size_size_list_int @ Zs ) )
% 2.52/2.83 => ( ( ( size_size_list_int @ Zs )
% 2.52/2.83 = ( size_size_list_nat @ Ws ) )
% 2.52/2.83 => ( ( P2 @ nil_int @ nil_nat @ nil_int @ nil_nat )
% 2.52/2.83 => ( ! [X3: int,Xs2: list_int,Y3: nat,Ys3: list_nat,Z2: int,Zs3: list_int,W3: nat,Ws2: list_nat] :
% 2.52/2.83 ( ( ( size_size_list_int @ Xs2 )
% 2.52/2.83 = ( size_size_list_nat @ Ys3 ) )
% 2.52/2.83 => ( ( ( size_size_list_nat @ Ys3 )
% 2.52/2.83 = ( size_size_list_int @ Zs3 ) )
% 2.52/2.83 => ( ( ( size_size_list_int @ Zs3 )
% 2.52/2.83 = ( size_size_list_nat @ Ws2 ) )
% 2.52/2.83 => ( ( P2 @ Xs2 @ Ys3 @ Zs3 @ Ws2 )
% 2.52/2.83 => ( P2 @ ( cons_int @ X3 @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) @ ( cons_int @ Z2 @ Zs3 ) @ ( cons_nat @ W3 @ Ws2 ) ) ) ) ) )
% 2.52/2.83 => ( P2 @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % list_induct4
% 2.52/2.83 thf(fact_5144_list__induct4,axiom,
% 2.52/2.83 ! [Xs: list_int,Ys: list_nat,Zs: list_nat,Ws: list_int,P2: list_int > list_nat > list_nat > list_int > $o] :
% 2.52/2.83 ( ( ( size_size_list_int @ Xs )
% 2.52/2.83 = ( size_size_list_nat @ Ys ) )
% 2.52/2.83 => ( ( ( size_size_list_nat @ Ys )
% 2.52/2.83 = ( size_size_list_nat @ Zs ) )
% 2.52/2.83 => ( ( ( size_size_list_nat @ Zs )
% 2.52/2.83 = ( size_size_list_int @ Ws ) )
% 2.52/2.83 => ( ( P2 @ nil_int @ nil_nat @ nil_nat @ nil_int )
% 2.52/2.83 => ( ! [X3: int,Xs2: list_int,Y3: nat,Ys3: list_nat,Z2: nat,Zs3: list_nat,W3: int,Ws2: list_int] :
% 2.52/2.83 ( ( ( size_size_list_int @ Xs2 )
% 2.52/2.83 = ( size_size_list_nat @ Ys3 ) )
% 2.52/2.83 => ( ( ( size_size_list_nat @ Ys3 )
% 2.52/2.83 = ( size_size_list_nat @ Zs3 ) )
% 2.52/2.83 => ( ( ( size_size_list_nat @ Zs3 )
% 2.52/2.83 = ( size_size_list_int @ Ws2 ) )
% 2.52/2.83 => ( ( P2 @ Xs2 @ Ys3 @ Zs3 @ Ws2 )
% 2.52/2.83 => ( P2 @ ( cons_int @ X3 @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) @ ( cons_nat @ Z2 @ Zs3 ) @ ( cons_int @ W3 @ Ws2 ) ) ) ) ) )
% 2.52/2.83 => ( P2 @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % list_induct4
% 2.52/2.83 thf(fact_5145_list__induct4,axiom,
% 2.52/2.83 ! [Xs: list_int,Ys: list_nat,Zs: list_nat,Ws: list_nat,P2: list_int > list_nat > list_nat > list_nat > $o] :
% 2.52/2.83 ( ( ( size_size_list_int @ Xs )
% 2.52/2.83 = ( size_size_list_nat @ Ys ) )
% 2.52/2.83 => ( ( ( size_size_list_nat @ Ys )
% 2.52/2.83 = ( size_size_list_nat @ Zs ) )
% 2.52/2.83 => ( ( ( size_size_list_nat @ Zs )
% 2.52/2.83 = ( size_size_list_nat @ Ws ) )
% 2.52/2.83 => ( ( P2 @ nil_int @ nil_nat @ nil_nat @ nil_nat )
% 2.52/2.83 => ( ! [X3: int,Xs2: list_int,Y3: nat,Ys3: list_nat,Z2: nat,Zs3: list_nat,W3: nat,Ws2: list_nat] :
% 2.52/2.83 ( ( ( size_size_list_int @ Xs2 )
% 2.52/2.83 = ( size_size_list_nat @ Ys3 ) )
% 2.52/2.83 => ( ( ( size_size_list_nat @ Ys3 )
% 2.52/2.83 = ( size_size_list_nat @ Zs3 ) )
% 2.52/2.83 => ( ( ( size_size_list_nat @ Zs3 )
% 2.52/2.83 = ( size_size_list_nat @ Ws2 ) )
% 2.52/2.83 => ( ( P2 @ Xs2 @ Ys3 @ Zs3 @ Ws2 )
% 2.52/2.83 => ( P2 @ ( cons_int @ X3 @ Xs2 ) @ ( cons_nat @ Y3 @ Ys3 ) @ ( cons_nat @ Z2 @ Zs3 ) @ ( cons_nat @ W3 @ Ws2 ) ) ) ) ) )
% 2.52/2.83 => ( P2 @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % list_induct4
% 2.52/2.83 thf(fact_5146_list__induct4,axiom,
% 2.52/2.83 ! [Xs: list_nat,Ys: list_int,Zs: list_int,Ws: list_int,P2: list_nat > list_int > list_int > list_int > $o] :
% 2.52/2.83 ( ( ( size_size_list_nat @ Xs )
% 2.52/2.83 = ( size_size_list_int @ Ys ) )
% 2.52/2.83 => ( ( ( size_size_list_int @ Ys )
% 2.52/2.83 = ( size_size_list_int @ Zs ) )
% 2.52/2.83 => ( ( ( size_size_list_int @ Zs )
% 2.52/2.83 = ( size_size_list_int @ Ws ) )
% 2.52/2.83 => ( ( P2 @ nil_nat @ nil_int @ nil_int @ nil_int )
% 2.52/2.83 => ( ! [X3: nat,Xs2: list_nat,Y3: int,Ys3: list_int,Z2: int,Zs3: list_int,W3: int,Ws2: list_int] :
% 2.52/2.83 ( ( ( size_size_list_nat @ Xs2 )
% 2.52/2.83 = ( size_size_list_int @ Ys3 ) )
% 2.52/2.83 => ( ( ( size_size_list_int @ Ys3 )
% 2.52/2.83 = ( size_size_list_int @ Zs3 ) )
% 2.52/2.83 => ( ( ( size_size_list_int @ Zs3 )
% 2.52/2.83 = ( size_size_list_int @ Ws2 ) )
% 2.52/2.83 => ( ( P2 @ Xs2 @ Ys3 @ Zs3 @ Ws2 )
% 2.52/2.83 => ( P2 @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_int @ Y3 @ Ys3 ) @ ( cons_int @ Z2 @ Zs3 ) @ ( cons_int @ W3 @ Ws2 ) ) ) ) ) )
% 2.52/2.83 => ( P2 @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % list_induct4
% 2.52/2.83 thf(fact_5147_list__induct4,axiom,
% 2.52/2.83 ! [Xs: list_nat,Ys: list_int,Zs: list_int,Ws: list_nat,P2: list_nat > list_int > list_int > list_nat > $o] :
% 2.52/2.83 ( ( ( size_size_list_nat @ Xs )
% 2.52/2.83 = ( size_size_list_int @ Ys ) )
% 2.52/2.83 => ( ( ( size_size_list_int @ Ys )
% 2.52/2.83 = ( size_size_list_int @ Zs ) )
% 2.52/2.83 => ( ( ( size_size_list_int @ Zs )
% 2.52/2.83 = ( size_size_list_nat @ Ws ) )
% 2.52/2.83 => ( ( P2 @ nil_nat @ nil_int @ nil_int @ nil_nat )
% 2.52/2.83 => ( ! [X3: nat,Xs2: list_nat,Y3: int,Ys3: list_int,Z2: int,Zs3: list_int,W3: nat,Ws2: list_nat] :
% 2.52/2.83 ( ( ( size_size_list_nat @ Xs2 )
% 2.52/2.83 = ( size_size_list_int @ Ys3 ) )
% 2.52/2.83 => ( ( ( size_size_list_int @ Ys3 )
% 2.52/2.83 = ( size_size_list_int @ Zs3 ) )
% 2.52/2.83 => ( ( ( size_size_list_int @ Zs3 )
% 2.52/2.83 = ( size_size_list_nat @ Ws2 ) )
% 2.52/2.83 => ( ( P2 @ Xs2 @ Ys3 @ Zs3 @ Ws2 )
% 2.52/2.83 => ( P2 @ ( cons_nat @ X3 @ Xs2 ) @ ( cons_int @ Y3 @ Ys3 ) @ ( cons_int @ Z2 @ Zs3 ) @ ( cons_nat @ W3 @ Ws2 ) ) ) ) ) )
% 2.52/2.83 => ( P2 @ Xs @ Ys @ Zs @ Ws ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % list_induct4
% 2.52/2.83 thf(fact_5148_bit__not__int__iff_H,axiom,
% 2.52/2.83 ! [K: int,N: nat] :
% 2.52/2.83 ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ ( uminus_uminus_int @ K ) @ one_one_int ) @ N )
% 2.52/2.83 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % bit_not_int_iff'
% 2.52/2.83 thf(fact_5149_bit__minus__int__iff,axiom,
% 2.52/2.83 ! [K: int,N: nat] :
% 2.52/2.83 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ K ) @ N )
% 2.52/2.83 = ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ K @ one_one_int ) ) @ N ) ) ).
% 2.52/2.83
% 2.52/2.83 % bit_minus_int_iff
% 2.52/2.83 thf(fact_5150_int__bit__bound,axiom,
% 2.52/2.83 ! [K: int] :
% 2.52/2.83 ~ ! [N4: nat] :
% 2.52/2.83 ( ! [M4: nat] :
% 2.52/2.83 ( ( ord_less_eq_nat @ N4 @ M4 )
% 2.52/2.83 => ( ( bit_se1146084159140164899it_int @ K @ M4 )
% 2.52/2.83 = ( bit_se1146084159140164899it_int @ K @ N4 ) ) )
% 2.52/2.83 => ~ ( ( ord_less_nat @ zero_zero_nat @ N4 )
% 2.52/2.83 => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N4 @ one_one_nat ) )
% 2.52/2.83 = ( ~ ( bit_se1146084159140164899it_int @ K @ N4 ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % int_bit_bound
% 2.52/2.83 thf(fact_5151_nat__numeral__diff__1,axiom,
% 2.52/2.83 ! [V2: num] :
% 2.52/2.83 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V2 ) @ one_one_nat )
% 2.52/2.83 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V2 ) @ one_one_int ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % nat_numeral_diff_1
% 2.52/2.83 thf(fact_5152_nat__1,axiom,
% 2.52/2.83 ( ( nat2 @ one_one_int )
% 2.52/2.83 = ( suc @ zero_zero_nat ) ) ).
% 2.52/2.83
% 2.52/2.83 % nat_1
% 2.52/2.83 thf(fact_5153_length__upto,axiom,
% 2.52/2.83 ! [I2: int,J: int] :
% 2.52/2.83 ( ( size_size_list_int @ ( upto @ I2 @ J ) )
% 2.52/2.83 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ J @ I2 ) @ one_one_int ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % length_upto
% 2.52/2.83 thf(fact_5154_one__less__nat__eq,axiom,
% 2.52/2.83 ! [Z: int] :
% 2.52/2.83 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z ) )
% 2.52/2.83 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 2.52/2.83
% 2.52/2.83 % one_less_nat_eq
% 2.52/2.83 thf(fact_5155_sorted__wrt__less__idx,axiom,
% 2.52/2.83 ! [Ns: list_nat,I2: nat] :
% 2.52/2.83 ( ( sorted_wrt_nat @ ord_less_nat @ Ns )
% 2.52/2.83 => ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Ns ) )
% 2.52/2.83 => ( ord_less_eq_nat @ I2 @ ( nth_nat @ Ns @ I2 ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % sorted_wrt_less_idx
% 2.52/2.83 thf(fact_5156_sorted__upto,axiom,
% 2.52/2.83 ! [M2: int,N: int] : ( sorted_wrt_int @ ord_less_eq_int @ ( upto @ M2 @ N ) ) ).
% 2.52/2.83
% 2.52/2.83 % sorted_upto
% 2.52/2.83 thf(fact_5157_sorted__wrt__upto,axiom,
% 2.52/2.83 ! [I2: int,J: int] : ( sorted_wrt_int @ ord_less_int @ ( upto @ I2 @ J ) ) ).
% 2.52/2.83
% 2.52/2.83 % sorted_wrt_upto
% 2.52/2.83 thf(fact_5158_nat__one__as__int,axiom,
% 2.52/2.83 ( one_one_nat
% 2.52/2.83 = ( nat2 @ one_one_int ) ) ).
% 2.52/2.83
% 2.52/2.83 % nat_one_as_int
% 2.52/2.83 thf(fact_5159_Suc__nat__eq__nat__zadd1,axiom,
% 2.52/2.83 ! [Z: int] :
% 2.52/2.83 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 2.52/2.83 => ( ( suc @ ( nat2 @ Z ) )
% 2.52/2.83 = ( nat2 @ ( plus_plus_int @ one_one_int @ Z ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % Suc_nat_eq_nat_zadd1
% 2.52/2.83 thf(fact_5160_upto__rec2,axiom,
% 2.52/2.83 ! [I2: int,J: int] :
% 2.52/2.83 ( ( ord_less_eq_int @ I2 @ J )
% 2.52/2.83 => ( ( upto @ I2 @ J )
% 2.52/2.83 = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ nil_int ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % upto_rec2
% 2.52/2.83 thf(fact_5161_normalize__denom__zero,axiom,
% 2.52/2.83 ! [P5: int] :
% 2.52/2.83 ( ( normalize @ ( product_Pair_int_int @ P5 @ zero_zero_int ) )
% 2.52/2.83 = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 2.52/2.83
% 2.52/2.83 % normalize_denom_zero
% 2.52/2.83 thf(fact_5162_upt__conv__Nil,axiom,
% 2.52/2.83 ! [J: nat,I2: nat] :
% 2.52/2.83 ( ( ord_less_eq_nat @ J @ I2 )
% 2.52/2.83 => ( ( upt @ I2 @ J )
% 2.52/2.83 = nil_nat ) ) ).
% 2.52/2.83
% 2.52/2.83 % upt_conv_Nil
% 2.52/2.83 thf(fact_5163_upt__eq__Nil__conv,axiom,
% 2.52/2.83 ! [I2: nat,J: nat] :
% 2.52/2.83 ( ( ( upt @ I2 @ J )
% 2.52/2.83 = nil_nat )
% 2.52/2.83 = ( ( J = zero_zero_nat )
% 2.52/2.83 | ( ord_less_eq_nat @ J @ I2 ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % upt_eq_Nil_conv
% 2.52/2.83 thf(fact_5164_length__upt,axiom,
% 2.52/2.83 ! [I2: nat,J: nat] :
% 2.52/2.83 ( ( size_size_list_nat @ ( upt @ I2 @ J ) )
% 2.52/2.83 = ( minus_minus_nat @ J @ I2 ) ) ).
% 2.52/2.83
% 2.52/2.83 % length_upt
% 2.52/2.83 thf(fact_5165_upt__rec__numeral,axiom,
% 2.52/2.83 ! [M2: num,N: num] :
% 2.52/2.83 ( ( ( ord_less_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 2.52/2.83 => ( ( upt @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 2.52/2.83 = ( cons_nat @ ( numeral_numeral_nat @ M2 ) @ ( upt @ ( suc @ ( numeral_numeral_nat @ M2 ) ) @ ( numeral_numeral_nat @ N ) ) ) ) )
% 2.52/2.83 & ( ~ ( ord_less_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 2.52/2.83 => ( ( upt @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 2.52/2.83 = nil_nat ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % upt_rec_numeral
% 2.52/2.83 thf(fact_5166_nth__upt,axiom,
% 2.52/2.83 ! [I2: nat,K: nat,J: nat] :
% 2.52/2.83 ( ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ J )
% 2.52/2.83 => ( ( nth_nat @ ( upt @ I2 @ J ) @ K )
% 2.52/2.83 = ( plus_plus_nat @ I2 @ K ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % nth_upt
% 2.52/2.83 thf(fact_5167_upt__0,axiom,
% 2.52/2.83 ! [I2: nat] :
% 2.52/2.83 ( ( upt @ I2 @ zero_zero_nat )
% 2.52/2.83 = nil_nat ) ).
% 2.52/2.83
% 2.52/2.83 % upt_0
% 2.52/2.83 thf(fact_5168_map__Suc__upt,axiom,
% 2.52/2.83 ! [M2: nat,N: nat] :
% 2.52/2.83 ( ( map_nat_nat @ suc @ ( upt @ M2 @ N ) )
% 2.52/2.83 = ( upt @ ( suc @ M2 ) @ ( suc @ N ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % map_Suc_upt
% 2.52/2.83 thf(fact_5169_upt__conv__Cons__Cons,axiom,
% 2.52/2.83 ! [M2: nat,N: nat,Ns: list_nat,Q4: nat] :
% 2.52/2.83 ( ( ( cons_nat @ M2 @ ( cons_nat @ N @ Ns ) )
% 2.52/2.83 = ( upt @ M2 @ Q4 ) )
% 2.52/2.83 = ( ( cons_nat @ N @ Ns )
% 2.52/2.83 = ( upt @ ( suc @ M2 ) @ Q4 ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % upt_conv_Cons_Cons
% 2.52/2.83 thf(fact_5170_upt__conv__Cons,axiom,
% 2.52/2.83 ! [I2: nat,J: nat] :
% 2.52/2.83 ( ( ord_less_nat @ I2 @ J )
% 2.52/2.83 => ( ( upt @ I2 @ J )
% 2.52/2.83 = ( cons_nat @ I2 @ ( upt @ ( suc @ I2 ) @ J ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % upt_conv_Cons
% 2.52/2.83 thf(fact_5171_upt__rec,axiom,
% 2.52/2.83 ( upt
% 2.52/2.83 = ( ^ [I4: nat,J2: nat] : ( if_list_nat @ ( ord_less_nat @ I4 @ J2 ) @ ( cons_nat @ I4 @ ( upt @ ( suc @ I4 ) @ J2 ) ) @ nil_nat ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % upt_rec
% 2.52/2.83 thf(fact_5172_sorted__wrt__upt,axiom,
% 2.52/2.83 ! [M2: nat,N: nat] : ( sorted_wrt_nat @ ord_less_nat @ ( upt @ M2 @ N ) ) ).
% 2.52/2.83
% 2.52/2.83 % sorted_wrt_upt
% 2.52/2.83 thf(fact_5173_sorted__upt,axiom,
% 2.52/2.83 ! [M2: nat,N: nat] : ( sorted_wrt_nat @ ord_less_eq_nat @ ( upt @ M2 @ N ) ) ).
% 2.52/2.83
% 2.52/2.83 % sorted_upt
% 2.52/2.83 thf(fact_5174_upt__eq__Cons__conv,axiom,
% 2.52/2.83 ! [I2: nat,J: nat,X: nat,Xs: list_nat] :
% 2.52/2.83 ( ( ( upt @ I2 @ J )
% 2.52/2.83 = ( cons_nat @ X @ Xs ) )
% 2.52/2.83 = ( ( ord_less_nat @ I2 @ J )
% 2.52/2.83 & ( I2 = X )
% 2.52/2.83 & ( ( upt @ ( plus_plus_nat @ I2 @ one_one_nat ) @ J )
% 2.52/2.83 = Xs ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % upt_eq_Cons_conv
% 2.52/2.83 thf(fact_5175_upto__aux__def,axiom,
% 2.52/2.83 ( upto_aux
% 2.52/2.83 = ( ^ [I4: int,J2: int] : ( append_int @ ( upto @ I4 @ J2 ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % upto_aux_def
% 2.52/2.83 thf(fact_5176_upto__split2,axiom,
% 2.52/2.83 ! [I2: int,J: int,K: int] :
% 2.52/2.83 ( ( ord_less_eq_int @ I2 @ J )
% 2.52/2.83 => ( ( ord_less_eq_int @ J @ K )
% 2.52/2.83 => ( ( upto @ I2 @ K )
% 2.52/2.83 = ( append_int @ ( upto @ I2 @ J ) @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % upto_split2
% 2.52/2.83 thf(fact_5177_upto__split1,axiom,
% 2.52/2.83 ! [I2: int,J: int,K: int] :
% 2.52/2.83 ( ( ord_less_eq_int @ I2 @ J )
% 2.52/2.83 => ( ( ord_less_eq_int @ J @ K )
% 2.52/2.83 => ( ( upto @ I2 @ K )
% 2.52/2.83 = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J @ one_one_int ) ) @ ( upto @ J @ K ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % upto_split1
% 2.52/2.83 thf(fact_5178_upto__split3,axiom,
% 2.52/2.83 ! [I2: int,J: int,K: int] :
% 2.52/2.83 ( ( ord_less_eq_int @ I2 @ J )
% 2.52/2.83 => ( ( ord_less_eq_int @ J @ K )
% 2.52/2.83 => ( ( upto @ I2 @ K )
% 2.52/2.83 = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % upto_split3
% 2.52/2.83 thf(fact_5179_bezw__0,axiom,
% 2.52/2.83 ! [X: nat] :
% 2.52/2.83 ( ( bezw @ X @ zero_zero_nat )
% 2.52/2.83 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) ).
% 2.52/2.83
% 2.52/2.83 % bezw_0
% 2.52/2.83 thf(fact_5180_upt__Suc__append,axiom,
% 2.52/2.83 ! [I2: nat,J: nat] :
% 2.52/2.83 ( ( ord_less_eq_nat @ I2 @ J )
% 2.52/2.83 => ( ( upt @ I2 @ ( suc @ J ) )
% 2.52/2.83 = ( append_nat @ ( upt @ I2 @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % upt_Suc_append
% 2.52/2.83 thf(fact_5181_upt__Suc,axiom,
% 2.52/2.83 ! [I2: nat,J: nat] :
% 2.52/2.83 ( ( ( ord_less_eq_nat @ I2 @ J )
% 2.52/2.83 => ( ( upt @ I2 @ ( suc @ J ) )
% 2.52/2.83 = ( append_nat @ ( upt @ I2 @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) )
% 2.52/2.83 & ( ~ ( ord_less_eq_nat @ I2 @ J )
% 2.52/2.83 => ( ( upt @ I2 @ ( suc @ J ) )
% 2.52/2.83 = nil_nat ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % upt_Suc
% 2.52/2.83 thf(fact_5182_upt__add__eq__append,axiom,
% 2.52/2.83 ! [I2: nat,J: nat,K: nat] :
% 2.52/2.83 ( ( ord_less_eq_nat @ I2 @ J )
% 2.52/2.83 => ( ( upt @ I2 @ ( plus_plus_nat @ J @ K ) )
% 2.52/2.83 = ( append_nat @ ( upt @ I2 @ J ) @ ( upt @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % upt_add_eq_append
% 2.52/2.83 thf(fact_5183_bezw_Oelims,axiom,
% 2.52/2.83 ! [X: nat,Xa: nat,Y: product_prod_int_int] :
% 2.52/2.83 ( ( ( bezw @ X @ Xa )
% 2.52/2.83 = Y )
% 2.52/2.83 => ( ( ( Xa = zero_zero_nat )
% 2.52/2.83 => ( Y
% 2.52/2.83 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 2.52/2.83 & ( ( Xa != zero_zero_nat )
% 2.52/2.83 => ( Y
% 2.52/2.83 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa ) ) ) ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % bezw.elims
% 2.52/2.83 thf(fact_5184_bezw_Osimps,axiom,
% 2.52/2.83 ( bezw
% 2.52/2.83 = ( ^ [X2: nat,Y2: nat] : ( if_Pro3027730157355071871nt_int @ ( Y2 = zero_zero_nat ) @ ( product_Pair_int_int @ one_one_int @ zero_zero_int ) @ ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y2 @ ( modulo_modulo_nat @ X2 @ Y2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y2 @ ( modulo_modulo_nat @ X2 @ Y2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y2 @ ( modulo_modulo_nat @ X2 @ Y2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X2 @ Y2 ) ) ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % bezw.simps
% 2.52/2.83 thf(fact_5185_nth__upto,axiom,
% 2.52/2.83 ! [I2: int,K: nat,J: int] :
% 2.52/2.83 ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ ( semiri1314217659103216013at_int @ K ) ) @ J )
% 2.52/2.83 => ( ( nth_int @ ( upto @ I2 @ J ) @ K )
% 2.52/2.83 = ( plus_plus_int @ I2 @ ( semiri1314217659103216013at_int @ K ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % nth_upto
% 2.52/2.83 thf(fact_5186_int__ops_I2_J,axiom,
% 2.52/2.83 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 2.52/2.83 = one_one_int ) ).
% 2.52/2.83
% 2.52/2.83 % int_ops(2)
% 2.52/2.83 thf(fact_5187_int__ops_I4_J,axiom,
% 2.52/2.83 ! [A: nat] :
% 2.52/2.83 ( ( semiri1314217659103216013at_int @ ( suc @ A ) )
% 2.52/2.83 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% 2.52/2.83
% 2.52/2.83 % int_ops(4)
% 2.52/2.83 thf(fact_5188_int__Suc,axiom,
% 2.52/2.83 ! [N: nat] :
% 2.52/2.83 ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 2.52/2.83 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ).
% 2.52/2.83
% 2.52/2.83 % int_Suc
% 2.52/2.83 thf(fact_5189_Suc__as__int,axiom,
% 2.52/2.83 ( suc
% 2.52/2.83 = ( ^ [A2: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A2 ) @ one_one_int ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % Suc_as_int
% 2.52/2.83 thf(fact_5190_bezw_Opelims,axiom,
% 2.52/2.83 ! [X: nat,Xa: nat,Y: product_prod_int_int] :
% 2.52/2.83 ( ( ( bezw @ X @ Xa )
% 2.52/2.83 = Y )
% 2.52/2.83 => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa ) )
% 2.52/2.83 => ~ ( ( ( ( Xa = zero_zero_nat )
% 2.52/2.83 => ( Y
% 2.52/2.83 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 2.52/2.83 & ( ( Xa != zero_zero_nat )
% 2.52/2.83 => ( Y
% 2.52/2.83 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa ) ) ) ) ) ) ) )
% 2.52/2.83 => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % bezw.pelims
% 2.52/2.83 thf(fact_5191_take__upt,axiom,
% 2.52/2.83 ! [I2: nat,M2: nat,N: nat] :
% 2.52/2.83 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ M2 ) @ N )
% 2.52/2.83 => ( ( take_nat @ M2 @ ( upt @ I2 @ N ) )
% 2.52/2.83 = ( upt @ I2 @ ( plus_plus_nat @ I2 @ M2 ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % take_upt
% 2.52/2.83 thf(fact_5192_inf__nat__def,axiom,
% 2.52/2.83 inf_inf_nat = ord_min_nat ).
% 2.52/2.83
% 2.52/2.83 % inf_nat_def
% 2.52/2.83 thf(fact_5193_dvd__fact,axiom,
% 2.52/2.83 ! [M2: nat,N: nat] :
% 2.52/2.83 ( ( ord_less_eq_nat @ one_one_nat @ M2 )
% 2.52/2.83 => ( ( ord_less_eq_nat @ M2 @ N )
% 2.52/2.83 => ( dvd_dvd_nat @ M2 @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % dvd_fact
% 2.52/2.83 thf(fact_5194_choose__two,axiom,
% 2.52/2.83 ! [N: nat] :
% 2.52/2.83 ( ( binomial @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.52/2.83 = ( divide_divide_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % choose_two
% 2.52/2.83 thf(fact_5195_binomial__n__n,axiom,
% 2.52/2.83 ! [N: nat] :
% 2.52/2.83 ( ( binomial @ N @ N )
% 2.52/2.83 = one_one_nat ) ).
% 2.52/2.83
% 2.52/2.83 % binomial_n_n
% 2.52/2.83 thf(fact_5196_binomial__n__0,axiom,
% 2.52/2.83 ! [N: nat] :
% 2.52/2.83 ( ( binomial @ N @ zero_zero_nat )
% 2.52/2.83 = one_one_nat ) ).
% 2.52/2.83
% 2.52/2.83 % binomial_n_0
% 2.52/2.83 thf(fact_5197_last__upt,axiom,
% 2.52/2.83 ! [I2: nat,J: nat] :
% 2.52/2.83 ( ( ord_less_nat @ I2 @ J )
% 2.52/2.83 => ( ( last_nat @ ( upt @ I2 @ J ) )
% 2.52/2.83 = ( minus_minus_nat @ J @ one_one_nat ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % last_upt
% 2.52/2.83 thf(fact_5198_choose__one,axiom,
% 2.52/2.83 ! [N: nat] :
% 2.52/2.83 ( ( binomial @ N @ one_one_nat )
% 2.52/2.83 = N ) ).
% 2.52/2.83
% 2.52/2.83 % choose_one
% 2.52/2.83 thf(fact_5199_binomial__absorb__comp,axiom,
% 2.52/2.83 ! [N: nat,K: nat] :
% 2.52/2.83 ( ( times_times_nat @ ( minus_minus_nat @ N @ K ) @ ( binomial @ N @ K ) )
% 2.52/2.83 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % binomial_absorb_comp
% 2.52/2.83 thf(fact_5200_binomial__absorption,axiom,
% 2.52/2.83 ! [K: nat,N: nat] :
% 2.52/2.83 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ N @ ( suc @ K ) ) )
% 2.52/2.83 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % binomial_absorption
% 2.52/2.83 thf(fact_5201_choose__reduce__nat,axiom,
% 2.52/2.83 ! [N: nat,K: nat] :
% 2.52/2.83 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.52/2.83 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 2.52/2.83 => ( ( binomial @ N @ K )
% 2.52/2.83 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % choose_reduce_nat
% 2.52/2.83 thf(fact_5202_times__binomial__minus1__eq,axiom,
% 2.52/2.83 ! [K: nat,N: nat] :
% 2.52/2.83 ( ( ord_less_nat @ zero_zero_nat @ K )
% 2.52/2.83 => ( ( times_times_nat @ K @ ( binomial @ N @ K ) )
% 2.52/2.83 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % times_binomial_minus1_eq
% 2.52/2.83 thf(fact_5203_binomial__code,axiom,
% 2.52/2.83 ( binomial
% 2.52/2.83 = ( ^ [N3: nat,K4: nat] : ( if_nat @ ( ord_less_nat @ N3 @ K4 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N3 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K4 ) ) @ ( binomial @ N3 @ ( minus_minus_nat @ N3 @ K4 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N3 @ K4 ) @ one_one_nat ) @ N3 @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K4 ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % binomial_code
% 2.52/2.83 thf(fact_5204_binomial__addition__formula,axiom,
% 2.52/2.83 ! [N: nat,K: nat] :
% 2.52/2.83 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.52/2.83 => ( ( binomial @ N @ ( suc @ K ) )
% 2.52/2.83 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % binomial_addition_formula
% 2.52/2.83 thf(fact_5205_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 2.52/2.83 ! [N: nat,J: nat,I2: nat] :
% 2.52/2.83 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ ( suc @ I2 ) ) )
% 2.52/2.83 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I2 @ J ) ) @ N )
% 2.52/2.83 = ( suc @ ( plus_plus_nat @ I2 @ N ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % nth_sorted_list_of_set_greaterThanLessThan
% 2.52/2.83 thf(fact_5206_drop__upt,axiom,
% 2.52/2.83 ! [M2: nat,I2: nat,J: nat] :
% 2.52/2.83 ( ( drop_nat @ M2 @ ( upt @ I2 @ J ) )
% 2.52/2.83 = ( upt @ ( plus_plus_nat @ I2 @ M2 ) @ J ) ) ).
% 2.52/2.83
% 2.52/2.83 % drop_upt
% 2.52/2.83 thf(fact_5207_greaterThanLessThan__upt,axiom,
% 2.52/2.83 ( set_or5834768355832116004an_nat
% 2.52/2.83 = ( ^ [N3: nat,M3: nat] : ( set_nat2 @ ( upt @ ( suc @ N3 ) @ M3 ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % greaterThanLessThan_upt
% 2.52/2.83 thf(fact_5208_sorted__list__of__set__greaterThanLessThan,axiom,
% 2.52/2.83 ! [I2: nat,J: nat] :
% 2.52/2.83 ( ( ord_less_nat @ ( suc @ I2 ) @ J )
% 2.52/2.83 => ( ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I2 @ J ) )
% 2.52/2.83 = ( cons_nat @ ( suc @ I2 ) @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ ( suc @ I2 ) @ J ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % sorted_list_of_set_greaterThanLessThan
% 2.52/2.83 thf(fact_5209_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 2.52/2.83 ! [N: nat,J: nat,I2: nat] :
% 2.52/2.83 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ I2 ) )
% 2.52/2.83 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I2 @ J ) ) @ N )
% 2.52/2.83 = ( suc @ ( plus_plus_nat @ I2 @ N ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % nth_sorted_list_of_set_greaterThanAtMost
% 2.52/2.83 thf(fact_5210_sorted__list__of__set__atMost__Suc,axiom,
% 2.52/2.83 ! [K: nat] :
% 2.52/2.83 ( ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ ( suc @ K ) ) )
% 2.52/2.83 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ K ) ) @ ( cons_nat @ ( suc @ K ) @ nil_nat ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % sorted_list_of_set_atMost_Suc
% 2.52/2.83 thf(fact_5211_sorted__list__of__set__lessThan__Suc,axiom,
% 2.52/2.83 ! [K: nat] :
% 2.52/2.83 ( ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ ( suc @ K ) ) )
% 2.52/2.83 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ K ) ) @ ( cons_nat @ K @ nil_nat ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % sorted_list_of_set_lessThan_Suc
% 2.52/2.83 thf(fact_5212_hd__upt,axiom,
% 2.52/2.83 ! [I2: nat,J: nat] :
% 2.52/2.83 ( ( ord_less_nat @ I2 @ J )
% 2.52/2.83 => ( ( hd_nat @ ( upt @ I2 @ J ) )
% 2.52/2.83 = I2 ) ) ).
% 2.52/2.83
% 2.52/2.83 % hd_upt
% 2.52/2.83 thf(fact_5213_distinct__upt,axiom,
% 2.52/2.83 ! [I2: nat,J: nat] : ( distinct_nat @ ( upt @ I2 @ J ) ) ).
% 2.52/2.83
% 2.52/2.83 % distinct_upt
% 2.52/2.83 thf(fact_5214_distinct__upto,axiom,
% 2.52/2.83 ! [I2: int,J: int] : ( distinct_int @ ( upto @ I2 @ J ) ) ).
% 2.52/2.83
% 2.52/2.83 % distinct_upto
% 2.52/2.83 thf(fact_5215_atLeast__upt,axiom,
% 2.52/2.83 ( set_ord_lessThan_nat
% 2.52/2.83 = ( ^ [N3: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ N3 ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % atLeast_upt
% 2.52/2.83 thf(fact_5216_greaterThanAtMost__upt,axiom,
% 2.52/2.83 ( set_or6659071591806873216st_nat
% 2.52/2.83 = ( ^ [N3: nat,M3: nat] : ( set_nat2 @ ( upt @ ( suc @ N3 ) @ ( suc @ M3 ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % greaterThanAtMost_upt
% 2.52/2.83 thf(fact_5217_atMost__upto,axiom,
% 2.52/2.83 ( set_ord_atMost_nat
% 2.52/2.83 = ( ^ [N3: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ ( suc @ N3 ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % atMost_upto
% 2.52/2.83 thf(fact_5218_butlast__upt,axiom,
% 2.52/2.83 ! [M2: nat,N: nat] :
% 2.52/2.83 ( ( butlast_nat @ ( upt @ M2 @ N ) )
% 2.52/2.83 = ( upt @ M2 @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % butlast_upt
% 2.52/2.83 thf(fact_5219_sorted__list__of__set__greaterThanAtMost,axiom,
% 2.52/2.83 ! [I2: nat,J: nat] :
% 2.52/2.83 ( ( ord_less_eq_nat @ ( suc @ I2 ) @ J )
% 2.52/2.83 => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I2 @ J ) )
% 2.52/2.83 = ( cons_nat @ ( suc @ I2 ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I2 ) @ J ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % sorted_list_of_set_greaterThanAtMost
% 2.52/2.83 thf(fact_5220_greaterThanLessThan__upto,axiom,
% 2.52/2.83 ( set_or5832277885323065728an_int
% 2.52/2.83 = ( ^ [I4: int,J2: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I4 @ one_one_int ) @ ( minus_minus_int @ J2 @ one_one_int ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % greaterThanLessThan_upto
% 2.52/2.83 thf(fact_5221_quotient__of__number_I5_J,axiom,
% 2.52/2.83 ! [K: num] :
% 2.52/2.83 ( ( quotient_of @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 2.52/2.83 = ( product_Pair_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 2.52/2.83
% 2.52/2.83 % quotient_of_number(5)
% 2.52/2.83 thf(fact_5222_cppi,axiom,
% 2.52/2.83 ! [D: int,P2: int > $o,P3: int > $o,A3: set_int] :
% 2.52/2.83 ( ( ord_less_int @ zero_zero_int @ D )
% 2.52/2.83 => ( ? [Z5: int] :
% 2.52/2.83 ! [X3: int] :
% 2.52/2.83 ( ( ord_less_int @ Z5 @ X3 )
% 2.52/2.83 => ( ( P2 @ X3 )
% 2.52/2.83 = ( P3 @ X3 ) ) )
% 2.52/2.83 => ( ! [X3: int] :
% 2.52/2.83 ( ! [Xa2: int] :
% 2.52/2.83 ( ( member_int2 @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.52/2.83 => ! [Xb2: int] :
% 2.52/2.83 ( ( member_int2 @ Xb2 @ A3 )
% 2.52/2.83 => ( X3
% 2.52/2.83 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 2.52/2.83 => ( ( P2 @ X3 )
% 2.52/2.83 => ( P2 @ ( plus_plus_int @ X3 @ D ) ) ) )
% 2.52/2.83 => ( ! [X3: int,K2: int] :
% 2.52/2.83 ( ( P3 @ X3 )
% 2.52/2.83 = ( P3 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D ) ) ) )
% 2.52/2.83 => ( ( ? [X5: int] : ( P2 @ X5 ) )
% 2.52/2.83 = ( ? [X2: int] :
% 2.52/2.83 ( ( member_int2 @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.52/2.83 & ( P3 @ X2 ) )
% 2.52/2.83 | ? [X2: int] :
% 2.52/2.83 ( ( member_int2 @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.52/2.83 & ? [Y2: int] :
% 2.52/2.83 ( ( member_int2 @ Y2 @ A3 )
% 2.52/2.83 & ( P2 @ ( minus_minus_int @ Y2 @ X2 ) ) ) ) ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % cppi
% 2.52/2.83 thf(fact_5223_card__UNIV__unit,axiom,
% 2.52/2.83 ( ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit )
% 2.52/2.83 = one_one_nat ) ).
% 2.52/2.83
% 2.52/2.83 % card_UNIV_unit
% 2.52/2.83 thf(fact_5224_rat__one__code,axiom,
% 2.52/2.83 ( ( quotient_of @ one_one_rat )
% 2.52/2.83 = ( product_Pair_int_int @ one_one_int @ one_one_int ) ) ).
% 2.52/2.83
% 2.52/2.83 % rat_one_code
% 2.52/2.83 thf(fact_5225_rat__zero__code,axiom,
% 2.52/2.83 ( ( quotient_of @ zero_zero_rat )
% 2.52/2.83 = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 2.52/2.83
% 2.52/2.83 % rat_zero_code
% 2.52/2.83 thf(fact_5226_card__atLeastAtMost__int,axiom,
% 2.52/2.83 ! [L: int,U: int] :
% 2.52/2.83 ( ( finite_card_int @ ( set_or1266510415728281911st_int @ L @ U ) )
% 2.52/2.83 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ U @ L ) @ one_one_int ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % card_atLeastAtMost_int
% 2.52/2.83 thf(fact_5227_quotient__of__number_I4_J,axiom,
% 2.52/2.83 ( ( quotient_of @ ( uminus_uminus_rat @ one_one_rat ) )
% 2.52/2.83 = ( product_Pair_int_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ) ) ).
% 2.52/2.83
% 2.52/2.83 % quotient_of_number(4)
% 2.52/2.83 thf(fact_5228_quotient__of__number_I3_J,axiom,
% 2.52/2.83 ! [K: num] :
% 2.52/2.83 ( ( quotient_of @ ( numeral_numeral_rat @ K ) )
% 2.52/2.83 = ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) ) ).
% 2.52/2.83
% 2.52/2.83 % quotient_of_number(3)
% 2.52/2.83 thf(fact_5229_card__greaterThanLessThan__int,axiom,
% 2.52/2.83 ! [L: int,U: int] :
% 2.52/2.83 ( ( finite_card_int @ ( set_or5832277885323065728an_int @ L @ U ) )
% 2.52/2.83 = ( nat2 @ ( minus_minus_int @ U @ ( plus_plus_int @ L @ one_one_int ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % card_greaterThanLessThan_int
% 2.52/2.83 thf(fact_5230_sgn__rat__def,axiom,
% 2.52/2.83 ( sgn_sgn_rat
% 2.52/2.83 = ( ^ [A2: rat] : ( if_rat @ ( A2 = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ A2 ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % sgn_rat_def
% 2.52/2.83 thf(fact_5231_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 2.52/2.83 ! [L: int,U: int] :
% 2.52/2.83 ( ( set_or1266510415728281911st_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 2.52/2.83 = ( set_or6656581121297822940st_int @ L @ U ) ) ).
% 2.52/2.83
% 2.52/2.83 % atLeastPlusOneAtMost_greaterThanAtMost_int
% 2.52/2.83 thf(fact_5232_atLeastAtMost__upto,axiom,
% 2.52/2.83 ( set_or1266510415728281911st_int
% 2.52/2.83 = ( ^ [I4: int,J2: int] : ( set_int2 @ ( upto @ I4 @ J2 ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % atLeastAtMost_upto
% 2.52/2.83 thf(fact_5233_bset_I1_J,axiom,
% 2.52/2.83 ! [D: int,B3: set_int,P2: int > $o,Q2: int > $o] :
% 2.52/2.83 ( ! [X3: int] :
% 2.52/2.83 ( ! [Xa2: int] :
% 2.52/2.83 ( ( member_int2 @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.52/2.83 => ! [Xb2: int] :
% 2.52/2.83 ( ( member_int2 @ Xb2 @ B3 )
% 2.52/2.83 => ( X3
% 2.52/2.83 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 2.52/2.83 => ( ( P2 @ X3 )
% 2.52/2.83 => ( P2 @ ( minus_minus_int @ X3 @ D ) ) ) )
% 2.52/2.83 => ( ! [X3: int] :
% 2.52/2.83 ( ! [Xa2: int] :
% 2.52/2.83 ( ( member_int2 @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.52/2.83 => ! [Xb2: int] :
% 2.52/2.83 ( ( member_int2 @ Xb2 @ B3 )
% 2.52/2.83 => ( X3
% 2.52/2.83 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 2.52/2.83 => ( ( Q2 @ X3 )
% 2.52/2.83 => ( Q2 @ ( minus_minus_int @ X3 @ D ) ) ) )
% 2.52/2.83 => ! [X4: int] :
% 2.52/2.83 ( ! [Xa3: int] :
% 2.52/2.83 ( ( member_int2 @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.52/2.83 => ! [Xb3: int] :
% 2.52/2.83 ( ( member_int2 @ Xb3 @ B3 )
% 2.52/2.83 => ( X4
% 2.52/2.83 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 2.52/2.83 => ( ( ( P2 @ X4 )
% 2.52/2.83 & ( Q2 @ X4 ) )
% 2.52/2.83 => ( ( P2 @ ( minus_minus_int @ X4 @ D ) )
% 2.52/2.83 & ( Q2 @ ( minus_minus_int @ X4 @ D ) ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % bset(1)
% 2.52/2.83 thf(fact_5234_bset_I2_J,axiom,
% 2.52/2.83 ! [D: int,B3: set_int,P2: int > $o,Q2: int > $o] :
% 2.52/2.83 ( ! [X3: int] :
% 2.52/2.83 ( ! [Xa2: int] :
% 2.52/2.83 ( ( member_int2 @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.52/2.83 => ! [Xb2: int] :
% 2.52/2.83 ( ( member_int2 @ Xb2 @ B3 )
% 2.52/2.83 => ( X3
% 2.52/2.83 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 2.52/2.83 => ( ( P2 @ X3 )
% 2.52/2.83 => ( P2 @ ( minus_minus_int @ X3 @ D ) ) ) )
% 2.52/2.83 => ( ! [X3: int] :
% 2.52/2.83 ( ! [Xa2: int] :
% 2.52/2.83 ( ( member_int2 @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.52/2.83 => ! [Xb2: int] :
% 2.52/2.83 ( ( member_int2 @ Xb2 @ B3 )
% 2.52/2.83 => ( X3
% 2.52/2.83 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 2.52/2.83 => ( ( Q2 @ X3 )
% 2.52/2.83 => ( Q2 @ ( minus_minus_int @ X3 @ D ) ) ) )
% 2.52/2.83 => ! [X4: int] :
% 2.52/2.83 ( ! [Xa3: int] :
% 2.52/2.83 ( ( member_int2 @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.52/2.83 => ! [Xb3: int] :
% 2.52/2.83 ( ( member_int2 @ Xb3 @ B3 )
% 2.52/2.83 => ( X4
% 2.52/2.83 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 2.52/2.83 => ( ( ( P2 @ X4 )
% 2.52/2.83 | ( Q2 @ X4 ) )
% 2.52/2.83 => ( ( P2 @ ( minus_minus_int @ X4 @ D ) )
% 2.52/2.83 | ( Q2 @ ( minus_minus_int @ X4 @ D ) ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % bset(2)
% 2.52/2.83 thf(fact_5235_aset_I1_J,axiom,
% 2.52/2.83 ! [D: int,A3: set_int,P2: int > $o,Q2: int > $o] :
% 2.52/2.83 ( ! [X3: int] :
% 2.52/2.83 ( ! [Xa2: int] :
% 2.52/2.83 ( ( member_int2 @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.52/2.83 => ! [Xb2: int] :
% 2.52/2.83 ( ( member_int2 @ Xb2 @ A3 )
% 2.52/2.83 => ( X3
% 2.52/2.83 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 2.52/2.83 => ( ( P2 @ X3 )
% 2.52/2.83 => ( P2 @ ( plus_plus_int @ X3 @ D ) ) ) )
% 2.52/2.83 => ( ! [X3: int] :
% 2.52/2.83 ( ! [Xa2: int] :
% 2.52/2.83 ( ( member_int2 @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.52/2.83 => ! [Xb2: int] :
% 2.52/2.83 ( ( member_int2 @ Xb2 @ A3 )
% 2.52/2.83 => ( X3
% 2.52/2.83 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 2.52/2.83 => ( ( Q2 @ X3 )
% 2.52/2.83 => ( Q2 @ ( plus_plus_int @ X3 @ D ) ) ) )
% 2.52/2.83 => ! [X4: int] :
% 2.52/2.83 ( ! [Xa3: int] :
% 2.52/2.83 ( ( member_int2 @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.52/2.83 => ! [Xb3: int] :
% 2.52/2.83 ( ( member_int2 @ Xb3 @ A3 )
% 2.52/2.83 => ( X4
% 2.52/2.83 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 2.52/2.83 => ( ( ( P2 @ X4 )
% 2.52/2.83 & ( Q2 @ X4 ) )
% 2.52/2.83 => ( ( P2 @ ( plus_plus_int @ X4 @ D ) )
% 2.52/2.83 & ( Q2 @ ( plus_plus_int @ X4 @ D ) ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % aset(1)
% 2.52/2.83 thf(fact_5236_aset_I2_J,axiom,
% 2.52/2.83 ! [D: int,A3: set_int,P2: int > $o,Q2: int > $o] :
% 2.52/2.83 ( ! [X3: int] :
% 2.52/2.83 ( ! [Xa2: int] :
% 2.52/2.83 ( ( member_int2 @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.52/2.83 => ! [Xb2: int] :
% 2.52/2.83 ( ( member_int2 @ Xb2 @ A3 )
% 2.52/2.83 => ( X3
% 2.52/2.83 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 2.52/2.83 => ( ( P2 @ X3 )
% 2.52/2.83 => ( P2 @ ( plus_plus_int @ X3 @ D ) ) ) )
% 2.52/2.83 => ( ! [X3: int] :
% 2.52/2.83 ( ! [Xa2: int] :
% 2.52/2.83 ( ( member_int2 @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.52/2.83 => ! [Xb2: int] :
% 2.52/2.83 ( ( member_int2 @ Xb2 @ A3 )
% 2.52/2.83 => ( X3
% 2.52/2.83 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 2.52/2.83 => ( ( Q2 @ X3 )
% 2.52/2.83 => ( Q2 @ ( plus_plus_int @ X3 @ D ) ) ) )
% 2.52/2.83 => ! [X4: int] :
% 2.52/2.83 ( ! [Xa3: int] :
% 2.52/2.83 ( ( member_int2 @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.52/2.83 => ! [Xb3: int] :
% 2.52/2.83 ( ( member_int2 @ Xb3 @ A3 )
% 2.52/2.83 => ( X4
% 2.52/2.83 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 2.52/2.83 => ( ( ( P2 @ X4 )
% 2.52/2.83 | ( Q2 @ X4 ) )
% 2.52/2.83 => ( ( P2 @ ( plus_plus_int @ X4 @ D ) )
% 2.52/2.83 | ( Q2 @ ( plus_plus_int @ X4 @ D ) ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % aset(2)
% 2.52/2.83 thf(fact_5237_greaterThanAtMost__upto,axiom,
% 2.52/2.83 ( set_or6656581121297822940st_int
% 2.52/2.83 = ( ^ [I4: int,J2: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I4 @ one_one_int ) @ J2 ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % greaterThanAtMost_upto
% 2.52/2.83 thf(fact_5238_bset_I9_J,axiom,
% 2.52/2.83 ! [D2: int,D: int,B3: set_int,T3: int] :
% 2.52/2.83 ( ( dvd_dvd_int @ D2 @ D )
% 2.52/2.83 => ! [X4: int] :
% 2.52/2.83 ( ! [Xa3: int] :
% 2.52/2.83 ( ( member_int2 @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.52/2.83 => ! [Xb3: int] :
% 2.52/2.83 ( ( member_int2 @ Xb3 @ B3 )
% 2.52/2.83 => ( X4
% 2.52/2.83 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 2.52/2.83 => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X4 @ T3 ) )
% 2.52/2.83 => ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X4 @ D ) @ T3 ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % bset(9)
% 2.52/2.83 thf(fact_5239_bset_I10_J,axiom,
% 2.52/2.83 ! [D2: int,D: int,B3: set_int,T3: int] :
% 2.52/2.83 ( ( dvd_dvd_int @ D2 @ D )
% 2.52/2.83 => ! [X4: int] :
% 2.52/2.83 ( ! [Xa3: int] :
% 2.52/2.83 ( ( member_int2 @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.52/2.83 => ! [Xb3: int] :
% 2.52/2.83 ( ( member_int2 @ Xb3 @ B3 )
% 2.52/2.83 => ( X4
% 2.52/2.83 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 2.52/2.83 => ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X4 @ T3 ) )
% 2.52/2.83 => ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X4 @ D ) @ T3 ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % bset(10)
% 2.52/2.83 thf(fact_5240_aset_I9_J,axiom,
% 2.52/2.83 ! [D2: int,D: int,A3: set_int,T3: int] :
% 2.52/2.83 ( ( dvd_dvd_int @ D2 @ D )
% 2.52/2.83 => ! [X4: int] :
% 2.52/2.83 ( ! [Xa3: int] :
% 2.52/2.83 ( ( member_int2 @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.52/2.83 => ! [Xb3: int] :
% 2.52/2.83 ( ( member_int2 @ Xb3 @ A3 )
% 2.52/2.83 => ( X4
% 2.52/2.83 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 2.52/2.83 => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X4 @ T3 ) )
% 2.52/2.83 => ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( plus_plus_int @ X4 @ D ) @ T3 ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % aset(9)
% 2.52/2.83 thf(fact_5241_aset_I10_J,axiom,
% 2.52/2.83 ! [D2: int,D: int,A3: set_int,T3: int] :
% 2.52/2.83 ( ( dvd_dvd_int @ D2 @ D )
% 2.52/2.83 => ! [X4: int] :
% 2.52/2.83 ( ! [Xa3: int] :
% 2.52/2.83 ( ( member_int2 @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.52/2.83 => ! [Xb3: int] :
% 2.52/2.83 ( ( member_int2 @ Xb3 @ A3 )
% 2.52/2.83 => ( X4
% 2.52/2.83 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 2.52/2.83 => ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X4 @ T3 ) )
% 2.52/2.83 => ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( plus_plus_int @ X4 @ D ) @ T3 ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % aset(10)
% 2.52/2.83 thf(fact_5242_atLeastAtMostPlus1__int__conv,axiom,
% 2.52/2.83 ! [M2: int,N: int] :
% 2.52/2.83 ( ( ord_less_eq_int @ M2 @ ( plus_plus_int @ one_one_int @ N ) )
% 2.52/2.83 => ( ( set_or1266510415728281911st_int @ M2 @ ( plus_plus_int @ one_one_int @ N ) )
% 2.52/2.83 = ( insert_int2 @ ( plus_plus_int @ one_one_int @ N ) @ ( set_or1266510415728281911st_int @ M2 @ N ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % atLeastAtMostPlus1_int_conv
% 2.52/2.83 thf(fact_5243_periodic__finite__ex,axiom,
% 2.52/2.83 ! [D2: int,P2: int > $o] :
% 2.52/2.83 ( ( ord_less_int @ zero_zero_int @ D2 )
% 2.52/2.83 => ( ! [X3: int,K2: int] :
% 2.52/2.83 ( ( P2 @ X3 )
% 2.52/2.83 = ( P2 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D2 ) ) ) )
% 2.52/2.83 => ( ( ? [X5: int] : ( P2 @ X5 ) )
% 2.52/2.83 = ( ? [X2: int] :
% 2.52/2.83 ( ( member_int2 @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D2 ) )
% 2.52/2.83 & ( P2 @ X2 ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % periodic_finite_ex
% 2.52/2.83 thf(fact_5244_aset_I7_J,axiom,
% 2.52/2.83 ! [D: int,A3: set_int,T3: int] :
% 2.52/2.83 ( ( ord_less_int @ zero_zero_int @ D )
% 2.52/2.83 => ! [X4: int] :
% 2.52/2.83 ( ! [Xa3: int] :
% 2.52/2.83 ( ( member_int2 @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.52/2.83 => ! [Xb3: int] :
% 2.52/2.83 ( ( member_int2 @ Xb3 @ A3 )
% 2.52/2.83 => ( X4
% 2.52/2.83 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 2.52/2.83 => ( ( ord_less_int @ T3 @ X4 )
% 2.52/2.83 => ( ord_less_int @ T3 @ ( plus_plus_int @ X4 @ D ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % aset(7)
% 2.52/2.83 thf(fact_5245_aset_I5_J,axiom,
% 2.52/2.83 ! [D: int,T3: int,A3: set_int] :
% 2.52/2.83 ( ( ord_less_int @ zero_zero_int @ D )
% 2.52/2.83 => ( ( member_int2 @ T3 @ A3 )
% 2.52/2.83 => ! [X4: int] :
% 2.52/2.83 ( ! [Xa3: int] :
% 2.52/2.83 ( ( member_int2 @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.52/2.83 => ! [Xb3: int] :
% 2.52/2.83 ( ( member_int2 @ Xb3 @ A3 )
% 2.52/2.83 => ( X4
% 2.52/2.83 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 2.52/2.83 => ( ( ord_less_int @ X4 @ T3 )
% 2.52/2.83 => ( ord_less_int @ ( plus_plus_int @ X4 @ D ) @ T3 ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % aset(5)
% 2.52/2.83 thf(fact_5246_aset_I4_J,axiom,
% 2.52/2.83 ! [D: int,T3: int,A3: set_int] :
% 2.52/2.83 ( ( ord_less_int @ zero_zero_int @ D )
% 2.52/2.83 => ( ( member_int2 @ T3 @ A3 )
% 2.52/2.83 => ! [X4: int] :
% 2.52/2.83 ( ! [Xa3: int] :
% 2.52/2.83 ( ( member_int2 @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.52/2.83 => ! [Xb3: int] :
% 2.52/2.83 ( ( member_int2 @ Xb3 @ A3 )
% 2.52/2.83 => ( X4
% 2.52/2.83 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 2.52/2.83 => ( ( X4 != T3 )
% 2.52/2.83 => ( ( plus_plus_int @ X4 @ D )
% 2.52/2.83 != T3 ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % aset(4)
% 2.52/2.83 thf(fact_5247_aset_I3_J,axiom,
% 2.52/2.83 ! [D: int,T3: int,A3: set_int] :
% 2.52/2.83 ( ( ord_less_int @ zero_zero_int @ D )
% 2.52/2.83 => ( ( member_int2 @ ( plus_plus_int @ T3 @ one_one_int ) @ A3 )
% 2.52/2.83 => ! [X4: int] :
% 2.52/2.83 ( ! [Xa3: int] :
% 2.52/2.83 ( ( member_int2 @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.52/2.83 => ! [Xb3: int] :
% 2.52/2.83 ( ( member_int2 @ Xb3 @ A3 )
% 2.52/2.83 => ( X4
% 2.52/2.83 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 2.52/2.83 => ( ( X4 = T3 )
% 2.52/2.83 => ( ( plus_plus_int @ X4 @ D )
% 2.52/2.83 = T3 ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % aset(3)
% 2.52/2.83 thf(fact_5248_bset_I7_J,axiom,
% 2.52/2.83 ! [D: int,T3: int,B3: set_int] :
% 2.52/2.83 ( ( ord_less_int @ zero_zero_int @ D )
% 2.52/2.83 => ( ( member_int2 @ T3 @ B3 )
% 2.52/2.83 => ! [X4: int] :
% 2.52/2.83 ( ! [Xa3: int] :
% 2.52/2.83 ( ( member_int2 @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.52/2.83 => ! [Xb3: int] :
% 2.52/2.83 ( ( member_int2 @ Xb3 @ B3 )
% 2.52/2.83 => ( X4
% 2.52/2.83 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 2.52/2.83 => ( ( ord_less_int @ T3 @ X4 )
% 2.52/2.83 => ( ord_less_int @ T3 @ ( minus_minus_int @ X4 @ D ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % bset(7)
% 2.52/2.83 thf(fact_5249_bset_I5_J,axiom,
% 2.52/2.83 ! [D: int,B3: set_int,T3: int] :
% 2.52/2.83 ( ( ord_less_int @ zero_zero_int @ D )
% 2.52/2.83 => ! [X4: int] :
% 2.52/2.83 ( ! [Xa3: int] :
% 2.52/2.83 ( ( member_int2 @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.52/2.83 => ! [Xb3: int] :
% 2.52/2.83 ( ( member_int2 @ Xb3 @ B3 )
% 2.52/2.83 => ( X4
% 2.52/2.83 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 2.52/2.83 => ( ( ord_less_int @ X4 @ T3 )
% 2.52/2.83 => ( ord_less_int @ ( minus_minus_int @ X4 @ D ) @ T3 ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % bset(5)
% 2.52/2.83 thf(fact_5250_bset_I4_J,axiom,
% 2.52/2.83 ! [D: int,T3: int,B3: set_int] :
% 2.52/2.83 ( ( ord_less_int @ zero_zero_int @ D )
% 2.52/2.83 => ( ( member_int2 @ T3 @ B3 )
% 2.52/2.83 => ! [X4: int] :
% 2.52/2.83 ( ! [Xa3: int] :
% 2.52/2.83 ( ( member_int2 @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.52/2.83 => ! [Xb3: int] :
% 2.52/2.83 ( ( member_int2 @ Xb3 @ B3 )
% 2.52/2.83 => ( X4
% 2.52/2.83 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 2.52/2.83 => ( ( X4 != T3 )
% 2.52/2.83 => ( ( minus_minus_int @ X4 @ D )
% 2.52/2.83 != T3 ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % bset(4)
% 2.52/2.83 thf(fact_5251_bset_I3_J,axiom,
% 2.52/2.83 ! [D: int,T3: int,B3: set_int] :
% 2.52/2.83 ( ( ord_less_int @ zero_zero_int @ D )
% 2.52/2.83 => ( ( member_int2 @ ( minus_minus_int @ T3 @ one_one_int ) @ B3 )
% 2.52/2.83 => ! [X4: int] :
% 2.52/2.83 ( ! [Xa3: int] :
% 2.52/2.83 ( ( member_int2 @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.52/2.83 => ! [Xb3: int] :
% 2.52/2.83 ( ( member_int2 @ Xb3 @ B3 )
% 2.52/2.83 => ( X4
% 2.52/2.83 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 2.52/2.83 => ( ( X4 = T3 )
% 2.52/2.83 => ( ( minus_minus_int @ X4 @ D )
% 2.52/2.83 = T3 ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % bset(3)
% 2.52/2.83 thf(fact_5252_rat__sgn__code,axiom,
% 2.52/2.83 ! [P5: rat] :
% 2.52/2.83 ( ( quotient_of @ ( sgn_sgn_rat @ P5 ) )
% 2.52/2.83 = ( product_Pair_int_int @ ( sgn_sgn_int @ ( product_fst_int_int @ ( quotient_of @ P5 ) ) ) @ one_one_int ) ) ).
% 2.52/2.83
% 2.52/2.83 % rat_sgn_code
% 2.52/2.83 thf(fact_5253_simp__from__to,axiom,
% 2.52/2.83 ( set_or1266510415728281911st_int
% 2.52/2.83 = ( ^ [I4: int,J2: int] : ( if_set_int @ ( ord_less_int @ J2 @ I4 ) @ bot_bot_set_int @ ( insert_int2 @ I4 @ ( set_or1266510415728281911st_int @ ( plus_plus_int @ I4 @ one_one_int ) @ J2 ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % simp_from_to
% 2.52/2.83 thf(fact_5254_aset_I8_J,axiom,
% 2.52/2.83 ! [D: int,A3: set_int,T3: int] :
% 2.52/2.83 ( ( ord_less_int @ zero_zero_int @ D )
% 2.52/2.83 => ! [X4: int] :
% 2.52/2.83 ( ! [Xa3: int] :
% 2.52/2.83 ( ( member_int2 @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.52/2.83 => ! [Xb3: int] :
% 2.52/2.83 ( ( member_int2 @ Xb3 @ A3 )
% 2.52/2.83 => ( X4
% 2.52/2.83 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 2.52/2.83 => ( ( ord_less_eq_int @ T3 @ X4 )
% 2.52/2.83 => ( ord_less_eq_int @ T3 @ ( plus_plus_int @ X4 @ D ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % aset(8)
% 2.52/2.83 thf(fact_5255_aset_I6_J,axiom,
% 2.52/2.83 ! [D: int,T3: int,A3: set_int] :
% 2.52/2.83 ( ( ord_less_int @ zero_zero_int @ D )
% 2.52/2.83 => ( ( member_int2 @ ( plus_plus_int @ T3 @ one_one_int ) @ A3 )
% 2.52/2.83 => ! [X4: int] :
% 2.52/2.83 ( ! [Xa3: int] :
% 2.52/2.83 ( ( member_int2 @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.52/2.83 => ! [Xb3: int] :
% 2.52/2.83 ( ( member_int2 @ Xb3 @ A3 )
% 2.52/2.83 => ( X4
% 2.52/2.83 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 2.52/2.83 => ( ( ord_less_eq_int @ X4 @ T3 )
% 2.52/2.83 => ( ord_less_eq_int @ ( plus_plus_int @ X4 @ D ) @ T3 ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % aset(6)
% 2.52/2.83 thf(fact_5256_bset_I8_J,axiom,
% 2.52/2.83 ! [D: int,T3: int,B3: set_int] :
% 2.52/2.83 ( ( ord_less_int @ zero_zero_int @ D )
% 2.52/2.83 => ( ( member_int2 @ ( minus_minus_int @ T3 @ one_one_int ) @ B3 )
% 2.52/2.83 => ! [X4: int] :
% 2.52/2.83 ( ! [Xa3: int] :
% 2.52/2.83 ( ( member_int2 @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.52/2.83 => ! [Xb3: int] :
% 2.52/2.83 ( ( member_int2 @ Xb3 @ B3 )
% 2.52/2.83 => ( X4
% 2.52/2.83 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 2.52/2.83 => ( ( ord_less_eq_int @ T3 @ X4 )
% 2.52/2.83 => ( ord_less_eq_int @ T3 @ ( minus_minus_int @ X4 @ D ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % bset(8)
% 2.52/2.83 thf(fact_5257_bset_I6_J,axiom,
% 2.52/2.83 ! [D: int,B3: set_int,T3: int] :
% 2.52/2.83 ( ( ord_less_int @ zero_zero_int @ D )
% 2.52/2.83 => ! [X4: int] :
% 2.52/2.83 ( ! [Xa3: int] :
% 2.52/2.83 ( ( member_int2 @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.52/2.83 => ! [Xb3: int] :
% 2.52/2.83 ( ( member_int2 @ Xb3 @ B3 )
% 2.52/2.83 => ( X4
% 2.52/2.83 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 2.52/2.83 => ( ( ord_less_eq_int @ X4 @ T3 )
% 2.52/2.83 => ( ord_less_eq_int @ ( minus_minus_int @ X4 @ D ) @ T3 ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % bset(6)
% 2.52/2.83 thf(fact_5258_cpmi,axiom,
% 2.52/2.83 ! [D: int,P2: int > $o,P3: int > $o,B3: set_int] :
% 2.52/2.83 ( ( ord_less_int @ zero_zero_int @ D )
% 2.52/2.83 => ( ? [Z5: int] :
% 2.52/2.83 ! [X3: int] :
% 2.52/2.83 ( ( ord_less_int @ X3 @ Z5 )
% 2.52/2.83 => ( ( P2 @ X3 )
% 2.52/2.83 = ( P3 @ X3 ) ) )
% 2.52/2.83 => ( ! [X3: int] :
% 2.52/2.83 ( ! [Xa2: int] :
% 2.52/2.83 ( ( member_int2 @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.52/2.83 => ! [Xb2: int] :
% 2.52/2.83 ( ( member_int2 @ Xb2 @ B3 )
% 2.52/2.83 => ( X3
% 2.52/2.83 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 2.52/2.83 => ( ( P2 @ X3 )
% 2.52/2.83 => ( P2 @ ( minus_minus_int @ X3 @ D ) ) ) )
% 2.52/2.83 => ( ! [X3: int,K2: int] :
% 2.52/2.83 ( ( P3 @ X3 )
% 2.52/2.83 = ( P3 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D ) ) ) )
% 2.52/2.83 => ( ( ? [X5: int] : ( P2 @ X5 ) )
% 2.52/2.83 = ( ? [X2: int] :
% 2.52/2.83 ( ( member_int2 @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.52/2.83 & ( P3 @ X2 ) )
% 2.52/2.83 | ? [X2: int] :
% 2.52/2.83 ( ( member_int2 @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 2.52/2.83 & ? [Y2: int] :
% 2.52/2.83 ( ( member_int2 @ Y2 @ B3 )
% 2.52/2.83 & ( P2 @ ( plus_plus_int @ Y2 @ X2 ) ) ) ) ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % cpmi
% 2.52/2.83 thf(fact_5259_quotient__of__int,axiom,
% 2.52/2.83 ! [A: int] :
% 2.52/2.83 ( ( quotient_of @ ( of_int @ A ) )
% 2.52/2.83 = ( product_Pair_int_int @ A @ one_one_int ) ) ).
% 2.52/2.83
% 2.52/2.83 % quotient_of_int
% 2.52/2.83 thf(fact_5260_Frct__code__post_I4_J,axiom,
% 2.52/2.83 ! [K: num] :
% 2.52/2.83 ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) )
% 2.52/2.83 = ( numeral_numeral_rat @ K ) ) ).
% 2.52/2.83
% 2.52/2.83 % Frct_code_post(4)
% 2.52/2.83 thf(fact_5261_Frct__code__post_I5_J,axiom,
% 2.52/2.83 ! [K: num] :
% 2.52/2.83 ( ( frct @ ( product_Pair_int_int @ one_one_int @ ( numeral_numeral_int @ K ) ) )
% 2.52/2.83 = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % Frct_code_post(5)
% 2.52/2.83 thf(fact_5262_all__nat__less,axiom,
% 2.52/2.83 ! [N: nat,P2: nat > $o] :
% 2.52/2.83 ( ( ! [M3: nat] :
% 2.52/2.83 ( ( ord_less_eq_nat @ M3 @ N )
% 2.52/2.83 => ( P2 @ M3 ) ) )
% 2.52/2.83 = ( ! [X2: nat] :
% 2.52/2.83 ( ( member_nat2 @ X2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 2.52/2.83 => ( P2 @ X2 ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % all_nat_less
% 2.52/2.83 thf(fact_5263_ex__nat__less,axiom,
% 2.52/2.83 ! [N: nat,P2: nat > $o] :
% 2.52/2.83 ( ( ? [M3: nat] :
% 2.52/2.83 ( ( ord_less_eq_nat @ M3 @ N )
% 2.52/2.83 & ( P2 @ M3 ) ) )
% 2.52/2.83 = ( ? [X2: nat] :
% 2.52/2.83 ( ( member_nat2 @ X2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 2.52/2.83 & ( P2 @ X2 ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % ex_nat_less
% 2.52/2.83 thf(fact_5264_atLeastAtMost__upt,axiom,
% 2.52/2.83 ( set_or1269000886237332187st_nat
% 2.52/2.83 = ( ^ [N3: nat,M3: nat] : ( set_nat2 @ ( upt @ N3 @ ( suc @ M3 ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % atLeastAtMost_upt
% 2.52/2.83 thf(fact_5265_Frct__code__post_I3_J,axiom,
% 2.52/2.83 ( ( frct @ ( product_Pair_int_int @ one_one_int @ one_one_int ) )
% 2.52/2.83 = one_one_rat ) ).
% 2.52/2.83
% 2.52/2.83 % Frct_code_post(3)
% 2.52/2.83 thf(fact_5266_zero__rat__def,axiom,
% 2.52/2.83 ( zero_zero_rat
% 2.52/2.83 = ( abs_Rat @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % zero_rat_def
% 2.52/2.83 thf(fact_5267_one__rat__def,axiom,
% 2.52/2.83 ( one_one_rat
% 2.52/2.83 = ( abs_Rat @ ( product_Pair_int_int @ one_one_int @ one_one_int ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % one_rat_def
% 2.52/2.83 thf(fact_5268_zero__rat_Otransfer,axiom,
% 2.52/2.83 pcr_rat @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ zero_zero_rat ).
% 2.52/2.83
% 2.52/2.83 % zero_rat.transfer
% 2.52/2.83 thf(fact_5269_image__Suc__atMost,axiom,
% 2.52/2.83 ! [N: nat] :
% 2.52/2.83 ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) )
% 2.52/2.83 = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % image_Suc_atMost
% 2.52/2.83 thf(fact_5270_image__Suc__lessThan,axiom,
% 2.52/2.83 ! [N: nat] :
% 2.52/2.83 ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) )
% 2.52/2.83 = ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ).
% 2.52/2.83
% 2.52/2.83 % image_Suc_lessThan
% 2.52/2.83 thf(fact_5271_one__rat_Otransfer,axiom,
% 2.52/2.83 pcr_rat @ ( product_Pair_int_int @ one_one_int @ one_one_int ) @ one_one_rat ).
% 2.52/2.83
% 2.52/2.83 % one_rat.transfer
% 2.52/2.83 thf(fact_5272_sorted__list__of__set__range,axiom,
% 2.52/2.83 ! [M2: nat,N: nat] :
% 2.52/2.83 ( ( linord2614967742042102400et_nat @ ( set_or4665077453230672383an_nat @ M2 @ N ) )
% 2.52/2.83 = ( upt @ M2 @ N ) ) ).
% 2.52/2.83
% 2.52/2.83 % sorted_list_of_set_range
% 2.52/2.83 thf(fact_5273_ex__nat__less__eq,axiom,
% 2.52/2.83 ! [N: nat,P2: nat > $o] :
% 2.52/2.83 ( ( ? [M3: nat] :
% 2.52/2.83 ( ( ord_less_nat @ M3 @ N )
% 2.52/2.83 & ( P2 @ M3 ) ) )
% 2.52/2.83 = ( ? [X2: nat] :
% 2.52/2.83 ( ( member_nat2 @ X2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 2.52/2.83 & ( P2 @ X2 ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % ex_nat_less_eq
% 2.52/2.83 thf(fact_5274_all__nat__less__eq,axiom,
% 2.52/2.83 ! [N: nat,P2: nat > $o] :
% 2.52/2.83 ( ( ! [M3: nat] :
% 2.52/2.83 ( ( ord_less_nat @ M3 @ N )
% 2.52/2.83 => ( P2 @ M3 ) ) )
% 2.52/2.83 = ( ! [X2: nat] :
% 2.52/2.83 ( ( member_nat2 @ X2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 2.52/2.83 => ( P2 @ X2 ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % all_nat_less_eq
% 2.52/2.83 thf(fact_5275_atLeastLessThan__upt,axiom,
% 2.52/2.83 ( set_or4665077453230672383an_nat
% 2.52/2.83 = ( ^ [I4: nat,J2: nat] : ( set_nat2 @ ( upt @ I4 @ J2 ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % atLeastLessThan_upt
% 2.52/2.83 thf(fact_5276_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 2.52/2.83 ! [L: int,U: int] :
% 2.52/2.83 ( ( set_or4662586982721622107an_int @ L @ ( plus_plus_int @ U @ one_one_int ) )
% 2.52/2.83 = ( set_or1266510415728281911st_int @ L @ U ) ) ).
% 2.52/2.83
% 2.52/2.83 % atLeastLessThanPlusOne_atLeastAtMost_int
% 2.52/2.83 thf(fact_5277_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 2.52/2.83 ! [L: int,U: int] :
% 2.52/2.83 ( ( set_or4662586982721622107an_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 2.52/2.83 = ( set_or5832277885323065728an_int @ L @ U ) ) ).
% 2.52/2.83
% 2.52/2.83 % atLeastPlusOneLessThan_greaterThanLessThan_int
% 2.52/2.83 thf(fact_5278_atLeastLessThan__upto,axiom,
% 2.52/2.83 ( set_or4662586982721622107an_int
% 2.52/2.83 = ( ^ [I4: int,J2: int] : ( set_int2 @ ( upto @ I4 @ ( minus_minus_int @ J2 @ one_one_int ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % atLeastLessThan_upto
% 2.52/2.83 thf(fact_5279_bool__assn__proper_I4_J,axiom,
% 2.52/2.83 ! [P2: produc3658429121746597890et_nat > $o,Q2: produc3658429121746597890et_nat > $o] :
% 2.52/2.83 ( ( proper @ P2 )
% 2.52/2.83 => ( ( proper @ Q2 )
% 2.52/2.83 => ( proper
% 2.52/2.83 @ ^ [H: produc3658429121746597890et_nat] :
% 2.52/2.83 ( ( P2 @ H )
% 2.52/2.83 & ( Q2 @ H ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % bool_assn_proper(4)
% 2.52/2.83 thf(fact_5280_bool__assn__proper_I3_J,axiom,
% 2.52/2.83 ! [P2: produc3658429121746597890et_nat > $o,Q2: produc3658429121746597890et_nat > $o] :
% 2.52/2.83 ( ( proper @ P2 )
% 2.52/2.83 => ( ( proper @ Q2 )
% 2.52/2.83 => ( proper
% 2.52/2.83 @ ^ [H: produc3658429121746597890et_nat] :
% 2.52/2.83 ( ( P2 @ H )
% 2.52/2.83 | ( Q2 @ H ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % bool_assn_proper(3)
% 2.52/2.83 thf(fact_5281_bool__assn__proper_I2_J,axiom,
% 2.52/2.83 ( proper
% 2.52/2.83 @ ^ [Uu2: produc3658429121746597890et_nat] : $false ) ).
% 2.52/2.83
% 2.52/2.83 % bool_assn_proper(2)
% 2.52/2.83 thf(fact_5282_tl__upt,axiom,
% 2.52/2.83 ! [M2: nat,N: nat] :
% 2.52/2.83 ( ( tl_nat @ ( upt @ M2 @ N ) )
% 2.52/2.83 = ( upt @ ( suc @ M2 ) @ N ) ) ).
% 2.52/2.83
% 2.52/2.83 % tl_upt
% 2.52/2.83 thf(fact_5283_bool__assn__proper_I5_J,axiom,
% 2.52/2.83 ! [P2: produc3658429121746597890et_nat > $o] :
% 2.52/2.83 ( ( proper @ P2 )
% 2.52/2.83 => ( proper
% 2.52/2.83 @ ^ [H: produc3658429121746597890et_nat] :
% 2.52/2.83 ( ( in_range @ H )
% 2.52/2.83 & ~ ( P2 @ H ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % bool_assn_proper(5)
% 2.52/2.83 thf(fact_5284_bot__assn__def,axiom,
% 2.52/2.83 ( bot_bot_assn
% 2.52/2.83 = ( abs_assn
% 2.52/2.83 @ ^ [Uu2: produc3658429121746597890et_nat] : $false ) ) ).
% 2.52/2.83
% 2.52/2.83 % bot_assn_def
% 2.52/2.83 thf(fact_5285_sup__assn__def,axiom,
% 2.52/2.83 ( sup_sup_assn
% 2.52/2.83 = ( ^ [P: assn,Q: assn] :
% 2.52/2.83 ( abs_assn
% 2.52/2.83 @ ^ [H: produc3658429121746597890et_nat] :
% 2.52/2.83 ( ( rep_assn @ P @ H )
% 2.52/2.83 | ( rep_assn @ Q @ H ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % sup_assn_def
% 2.52/2.83 thf(fact_5286_inf__assn__def,axiom,
% 2.52/2.83 ( inf_inf_assn
% 2.52/2.83 = ( ^ [P: assn,Q: assn] :
% 2.52/2.83 ( abs_assn
% 2.52/2.83 @ ^ [H: produc3658429121746597890et_nat] :
% 2.52/2.83 ( ( rep_assn @ P @ H )
% 2.52/2.83 & ( rep_assn @ Q @ H ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % inf_assn_def
% 2.52/2.83 thf(fact_5287_map__add__upt,axiom,
% 2.52/2.83 ! [N: nat,M2: nat] :
% 2.52/2.83 ( ( map_nat_nat
% 2.52/2.83 @ ^ [I4: nat] : ( plus_plus_nat @ I4 @ N )
% 2.52/2.83 @ ( upt @ zero_zero_nat @ M2 ) )
% 2.52/2.83 = ( upt @ N @ ( plus_plus_nat @ M2 @ N ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % map_add_upt
% 2.52/2.83 thf(fact_5288_uminus__assn__def,axiom,
% 2.52/2.83 ( uminus_uminus_assn
% 2.52/2.83 = ( ^ [P: assn] :
% 2.52/2.83 ( abs_assn
% 2.52/2.83 @ ^ [H: produc3658429121746597890et_nat] :
% 2.52/2.83 ( ( in_range @ H )
% 2.52/2.83 & ~ ( rep_assn @ P @ H ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % uminus_assn_def
% 2.52/2.83 thf(fact_5289_map__decr__upt,axiom,
% 2.52/2.83 ! [M2: nat,N: nat] :
% 2.52/2.83 ( ( map_nat_nat
% 2.52/2.83 @ ^ [N3: nat] : ( minus_minus_nat @ N3 @ ( suc @ zero_zero_nat ) )
% 2.52/2.83 @ ( upt @ ( suc @ M2 ) @ ( suc @ N ) ) )
% 2.52/2.83 = ( upt @ M2 @ N ) ) ).
% 2.52/2.83
% 2.52/2.83 % map_decr_upt
% 2.52/2.83 thf(fact_5290_fact__div__fact,axiom,
% 2.52/2.83 ! [N: nat,M2: nat] :
% 2.52/2.83 ( ( ord_less_eq_nat @ N @ M2 )
% 2.52/2.83 => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M2 ) @ ( semiri1408675320244567234ct_nat @ N ) )
% 2.52/2.83 = ( groups708209901874060359at_nat
% 2.52/2.83 @ ^ [X2: nat] : X2
% 2.52/2.83 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M2 ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % fact_div_fact
% 2.52/2.83 thf(fact_5291_choose__rising__sum_I2_J,axiom,
% 2.52/2.83 ! [N: nat,M2: nat] :
% 2.52/2.83 ( ( groups3542108847815614940at_nat
% 2.52/2.83 @ ^ [J2: nat] : ( binomial @ ( plus_plus_nat @ N @ J2 ) @ N )
% 2.52/2.83 @ ( set_ord_atMost_nat @ M2 ) )
% 2.52/2.83 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M2 ) @ one_one_nat ) @ M2 ) ) ).
% 2.52/2.83
% 2.52/2.83 % choose_rising_sum(2)
% 2.52/2.83 thf(fact_5292_choose__rising__sum_I1_J,axiom,
% 2.52/2.83 ! [N: nat,M2: nat] :
% 2.52/2.83 ( ( groups3542108847815614940at_nat
% 2.52/2.83 @ ^ [J2: nat] : ( binomial @ ( plus_plus_nat @ N @ J2 ) @ N )
% 2.52/2.83 @ ( set_ord_atMost_nat @ M2 ) )
% 2.52/2.83 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M2 ) @ one_one_nat ) @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % choose_rising_sum(1)
% 2.52/2.83 thf(fact_5293_sum__power2,axiom,
% 2.52/2.83 ! [K: nat] :
% 2.52/2.83 ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 2.52/2.83 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 2.52/2.83
% 2.52/2.83 % sum_power2
% 2.52/2.83 thf(fact_5294_Sum__Ico__nat,axiom,
% 2.52/2.83 ! [M2: nat,N: nat] :
% 2.52/2.83 ( ( groups3542108847815614940at_nat
% 2.52/2.83 @ ^ [X2: nat] : X2
% 2.52/2.83 @ ( set_or4665077453230672383an_nat @ M2 @ N ) )
% 2.52/2.83 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( times_times_nat @ M2 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % Sum_Ico_nat
% 2.52/2.83 thf(fact_5295_Sum__Icc__nat,axiom,
% 2.52/2.83 ! [M2: nat,N: nat] :
% 2.52/2.83 ( ( groups3542108847815614940at_nat
% 2.52/2.83 @ ^ [X2: nat] : X2
% 2.52/2.83 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 2.52/2.83 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N @ ( plus_plus_nat @ N @ one_one_nat ) ) @ ( times_times_nat @ M2 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % Sum_Icc_nat
% 2.52/2.83 thf(fact_5296_binomial__r__part__sum,axiom,
% 2.52/2.83 ! [M2: nat] :
% 2.52/2.83 ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M2 ) )
% 2.52/2.83 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % binomial_r_part_sum
% 2.52/2.83 thf(fact_5297_choose__linear__sum,axiom,
% 2.52/2.83 ! [N: nat] :
% 2.52/2.83 ( ( groups3542108847815614940at_nat
% 2.52/2.83 @ ^ [I4: nat] : ( times_times_nat @ I4 @ ( binomial @ N @ I4 ) )
% 2.52/2.83 @ ( set_ord_atMost_nat @ N ) )
% 2.52/2.83 = ( times_times_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % choose_linear_sum
% 2.52/2.83 thf(fact_5298_divmod__step__nat__def,axiom,
% 2.52/2.83 ( unique5026877609467782581ep_nat
% 2.52/2.83 = ( ^ [L3: num] :
% 2.52/2.83 ( produc2626176000494625587at_nat
% 2.52/2.83 @ ^ [Q6: nat,R4: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L3 ) @ R4 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q6 ) @ one_one_nat ) @ ( minus_minus_nat @ R4 @ ( numeral_numeral_nat @ L3 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q6 ) @ R4 ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % divmod_step_nat_def
% 2.52/2.83 thf(fact_5299_divmod__step__int__def,axiom,
% 2.52/2.83 ( unique5024387138958732305ep_int
% 2.52/2.83 = ( ^ [L3: num] :
% 2.52/2.83 ( produc4245557441103728435nt_int
% 2.52/2.83 @ ^ [Q6: int,R4: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L3 ) @ R4 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q6 ) @ one_one_int ) @ ( minus_minus_int @ R4 @ ( numeral_numeral_int @ L3 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q6 ) @ R4 ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % divmod_step_int_def
% 2.52/2.83 thf(fact_5300_Sum__Icc__int,axiom,
% 2.52/2.83 ! [M2: int,N: int] :
% 2.52/2.83 ( ( ord_less_eq_int @ M2 @ N )
% 2.52/2.83 => ( ( groups4538972089207619220nt_int
% 2.52/2.83 @ ^ [X2: int] : X2
% 2.52/2.83 @ ( set_or1266510415728281911st_int @ M2 @ N ) )
% 2.52/2.83 = ( divide_divide_int @ ( minus_minus_int @ ( times_times_int @ N @ ( plus_plus_int @ N @ one_one_int ) ) @ ( times_times_int @ M2 @ ( minus_minus_int @ M2 @ one_one_int ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % Sum_Icc_int
% 2.52/2.83 thf(fact_5301_normalize__def,axiom,
% 2.52/2.83 ( normalize
% 2.52/2.83 = ( ^ [P6: product_prod_int_int] :
% 2.52/2.83 ( if_Pro3027730157355071871nt_int @ ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ P6 ) ) @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P6 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P6 ) @ ( product_snd_int_int @ P6 ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P6 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P6 ) @ ( product_snd_int_int @ P6 ) ) ) )
% 2.52/2.83 @ ( if_Pro3027730157355071871nt_int
% 2.52/2.83 @ ( ( product_snd_int_int @ P6 )
% 2.52/2.83 = zero_zero_int )
% 2.52/2.83 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 2.52/2.83 @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P6 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P6 ) @ ( product_snd_int_int @ P6 ) ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P6 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P6 ) @ ( product_snd_int_int @ P6 ) ) ) ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % normalize_def
% 2.52/2.83 thf(fact_5302_remdups__upt,axiom,
% 2.52/2.83 ! [M2: nat,N: nat] :
% 2.52/2.83 ( ( remdups_nat @ ( upt @ M2 @ N ) )
% 2.52/2.83 = ( upt @ M2 @ N ) ) ).
% 2.52/2.83
% 2.52/2.83 % remdups_upt
% 2.52/2.83 thf(fact_5303_gcd__1__int,axiom,
% 2.52/2.83 ! [M2: int] :
% 2.52/2.83 ( ( gcd_gcd_int @ M2 @ one_one_int )
% 2.52/2.83 = one_one_int ) ).
% 2.52/2.83
% 2.52/2.83 % gcd_1_int
% 2.52/2.83 thf(fact_5304_gcd__1__nat,axiom,
% 2.52/2.83 ! [M2: nat] :
% 2.52/2.83 ( ( gcd_gcd_nat @ M2 @ one_one_nat )
% 2.52/2.83 = one_one_nat ) ).
% 2.52/2.83
% 2.52/2.83 % gcd_1_nat
% 2.52/2.83 thf(fact_5305_sort__upt,axiom,
% 2.52/2.83 ! [M2: nat,N: nat] :
% 2.52/2.83 ( ( linord738340561235409698at_nat
% 2.52/2.83 @ ^ [X2: nat] : X2
% 2.52/2.83 @ ( upt @ M2 @ N ) )
% 2.52/2.83 = ( upt @ M2 @ N ) ) ).
% 2.52/2.83
% 2.52/2.83 % sort_upt
% 2.52/2.83 thf(fact_5306_sort__upto,axiom,
% 2.52/2.83 ! [I2: int,J: int] :
% 2.52/2.83 ( ( linord1735203802627413978nt_int
% 2.52/2.83 @ ^ [X2: int] : X2
% 2.52/2.83 @ ( upto @ I2 @ J ) )
% 2.52/2.83 = ( upto @ I2 @ J ) ) ).
% 2.52/2.83
% 2.52/2.83 % sort_upto
% 2.52/2.83 thf(fact_5307_rat__inverse__code,axiom,
% 2.52/2.83 ! [P5: rat] :
% 2.52/2.83 ( ( quotient_of @ ( inverse_inverse_rat @ P5 ) )
% 2.52/2.83 = ( produc4245557441103728435nt_int
% 2.52/2.83 @ ^ [A2: int,B2: int] : ( if_Pro3027730157355071871nt_int @ ( A2 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ ( times_times_int @ ( sgn_sgn_int @ A2 ) @ B2 ) @ ( abs_abs_int @ A2 ) ) )
% 2.52/2.83 @ ( quotient_of @ P5 ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % rat_inverse_code
% 2.52/2.83 thf(fact_5308_inverse__rat_Oabs__eq,axiom,
% 2.52/2.83 ! [X: product_prod_int_int] :
% 2.52/2.83 ( ( ratrel @ X @ X )
% 2.52/2.83 => ( ( inverse_inverse_rat @ ( abs_Rat @ X ) )
% 2.52/2.83 = ( abs_Rat
% 2.52/2.83 @ ( if_Pro3027730157355071871nt_int
% 2.52/2.83 @ ( ( product_fst_int_int @ X )
% 2.52/2.83 = zero_zero_int )
% 2.52/2.83 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 2.52/2.83 @ ( product_Pair_int_int @ ( product_snd_int_int @ X ) @ ( product_fst_int_int @ X ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % inverse_rat.abs_eq
% 2.52/2.83 thf(fact_5309_divmod__step__integer__def,axiom,
% 2.52/2.83 ( unique4921790084139445826nteger
% 2.52/2.83 = ( ^ [L3: num] :
% 2.52/2.83 ( produc6916734918728496179nteger
% 2.52/2.83 @ ^ [Q6: code_integer,R4: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L3 ) @ R4 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q6 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R4 @ ( numera6620942414471956472nteger @ L3 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q6 ) @ R4 ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % divmod_step_integer_def
% 2.52/2.83 thf(fact_5310_inverse__rat_Otransfer,axiom,
% 2.52/2.83 ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat
% 2.52/2.83 @ ^ [X2: product_prod_int_int] :
% 2.52/2.83 ( if_Pro3027730157355071871nt_int
% 2.52/2.83 @ ( ( product_fst_int_int @ X2 )
% 2.52/2.83 = zero_zero_int )
% 2.52/2.83 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 2.52/2.83 @ ( product_Pair_int_int @ ( product_snd_int_int @ X2 ) @ ( product_fst_int_int @ X2 ) ) )
% 2.52/2.83 @ inverse_inverse_rat ) ).
% 2.52/2.83
% 2.52/2.83 % inverse_rat.transfer
% 2.52/2.83 thf(fact_5311_atLeastPlusOneLessThan__greaterThanLessThan__integer,axiom,
% 2.52/2.83 ! [L: code_integer,U: code_integer] :
% 2.52/2.83 ( ( set_or8404916559141939852nteger @ ( plus_p5714425477246183910nteger @ L @ one_one_Code_integer ) @ U )
% 2.52/2.83 = ( set_or4266950643985792945nteger @ L @ U ) ) ).
% 2.52/2.83
% 2.52/2.83 % atLeastPlusOneLessThan_greaterThanLessThan_integer
% 2.52/2.83 thf(fact_5312_atLeastLessThanPlusOne__atLeastAtMost__integer,axiom,
% 2.52/2.83 ! [L: code_integer,U: code_integer] :
% 2.52/2.83 ( ( set_or8404916559141939852nteger @ L @ ( plus_p5714425477246183910nteger @ U @ one_one_Code_integer ) )
% 2.52/2.83 = ( set_or189985376899183464nteger @ L @ U ) ) ).
% 2.52/2.83
% 2.52/2.83 % atLeastLessThanPlusOne_atLeastAtMost_integer
% 2.52/2.83 thf(fact_5313_atLeastPlusOneAtMost__greaterThanAtMost__integer,axiom,
% 2.52/2.83 ! [L: code_integer,U: code_integer] :
% 2.52/2.83 ( ( set_or189985376899183464nteger @ ( plus_p5714425477246183910nteger @ L @ one_one_Code_integer ) @ U )
% 2.52/2.83 = ( set_or2715278749043346189nteger @ L @ U ) ) ).
% 2.52/2.83
% 2.52/2.83 % atLeastPlusOneAtMost_greaterThanAtMost_integer
% 2.52/2.83 thf(fact_5314_sgn__integer__code,axiom,
% 2.52/2.83 ( sgn_sgn_Code_integer
% 2.52/2.83 = ( ^ [K4: code_integer] : ( if_Code_integer @ ( K4 = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K4 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % sgn_integer_code
% 2.52/2.83 thf(fact_5315_one__rat_Orsp,axiom,
% 2.52/2.83 ratrel @ ( product_Pair_int_int @ one_one_int @ one_one_int ) @ ( product_Pair_int_int @ one_one_int @ one_one_int ) ).
% 2.52/2.83
% 2.52/2.83 % one_rat.rsp
% 2.52/2.83 thf(fact_5316_zero__rat_Orsp,axiom,
% 2.52/2.83 ratrel @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ).
% 2.52/2.83
% 2.52/2.83 % zero_rat.rsp
% 2.52/2.83 thf(fact_5317_one__integer_Orsp,axiom,
% 2.52/2.83 one_one_int = one_one_int ).
% 2.52/2.83
% 2.52/2.83 % one_integer.rsp
% 2.52/2.83 thf(fact_5318_one__natural_Orsp,axiom,
% 2.52/2.83 one_one_nat = one_one_nat ).
% 2.52/2.83
% 2.52/2.83 % one_natural.rsp
% 2.52/2.83 thf(fact_5319_integer__of__int__code,axiom,
% 2.52/2.83 ( code_integer_of_int
% 2.52/2.83 = ( ^ [K4: int] :
% 2.52/2.83 ( if_Code_integer @ ( ord_less_int @ K4 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K4 ) ) )
% 2.52/2.83 @ ( if_Code_integer @ ( K4 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 2.52/2.83 @ ( if_Code_integer
% 2.52/2.83 @ ( ( modulo_modulo_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 2.52/2.83 = zero_zero_int )
% 2.52/2.83 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 2.52/2.83 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % integer_of_int_code
% 2.52/2.83 thf(fact_5320_integer__of__num_I3_J,axiom,
% 2.52/2.83 ! [N: num] :
% 2.52/2.83 ( ( code_integer_of_num @ ( bit1 @ N ) )
% 2.52/2.83 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) @ one_one_Code_integer ) ) ).
% 2.52/2.83
% 2.52/2.83 % integer_of_num(3)
% 2.52/2.83 thf(fact_5321_Fract_Orsp,axiom,
% 2.52/2.83 ( bNF_re157797125943740599nt_int
% 2.52/2.83 @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 2.52/2.83 @ ( bNF_re6250860962936578807nt_int
% 2.52/2.83 @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 2.52/2.83 @ ratrel )
% 2.52/2.83 @ ^ [A2: int,B2: int] : ( if_Pro3027730157355071871nt_int @ ( B2 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A2 @ B2 ) )
% 2.52/2.83 @ ^ [A2: int,B2: int] : ( if_Pro3027730157355071871nt_int @ ( B2 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A2 @ B2 ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % Fract.rsp
% 2.52/2.83 thf(fact_5322_one__integer__def,axiom,
% 2.52/2.83 ( one_one_Code_integer
% 2.52/2.83 = ( code_integer_of_int @ one_one_int ) ) ).
% 2.52/2.83
% 2.52/2.83 % one_integer_def
% 2.52/2.83 thf(fact_5323_integer__of__num__triv_I1_J,axiom,
% 2.52/2.83 ( ( code_integer_of_num @ one )
% 2.52/2.83 = one_one_Code_integer ) ).
% 2.52/2.83
% 2.52/2.83 % integer_of_num_triv(1)
% 2.52/2.83 thf(fact_5324_FI__def,axiom,
% 2.52/2.83 ( fi
% 2.52/2.83 = ( ^ [M3: list_P8527749157015355191n_assn,P6: assn,Q6: assn,Up: assn,Uq: assn,F3: assn] :
% 2.52/2.83 ( ! [X2: produc6575502325842934193n_assn] :
% 2.52/2.83 ( ( member7957490590177025114n_assn @ X2 @ ( set_Pr1139785259514867910n_assn @ M3 ) )
% 2.52/2.83 => ( produc7274209992780475162assn_o @ entails @ X2 ) )
% 2.52/2.83 => ( entails @ ( times_times_assn @ ( times_times_assn @ ( foldr_assn_assn @ times_times_assn @ ( map_Pr8991440229025900053n_assn @ produc9167289414957590229n_assn @ M3 ) @ one_one_assn ) @ P6 ) @ Up ) @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ ( foldr_assn_assn @ times_times_assn @ ( map_Pr8991440229025900053n_assn @ produc2051961928117032727n_assn @ M3 ) @ one_one_assn ) @ Q6 ) @ Uq ) @ F3 ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % FI_def
% 2.52/2.83 thf(fact_5325_inverse__rat_Orsp,axiom,
% 2.52/2.83 ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel
% 2.52/2.83 @ ^ [X2: product_prod_int_int] :
% 2.52/2.83 ( if_Pro3027730157355071871nt_int
% 2.52/2.83 @ ( ( product_fst_int_int @ X2 )
% 2.52/2.83 = zero_zero_int )
% 2.52/2.83 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 2.52/2.83 @ ( product_Pair_int_int @ ( product_snd_int_int @ X2 ) @ ( product_fst_int_int @ X2 ) ) )
% 2.52/2.83 @ ^ [X2: product_prod_int_int] :
% 2.52/2.83 ( if_Pro3027730157355071871nt_int
% 2.52/2.83 @ ( ( product_fst_int_int @ X2 )
% 2.52/2.83 = zero_zero_int )
% 2.52/2.83 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 2.52/2.83 @ ( product_Pair_int_int @ ( product_snd_int_int @ X2 ) @ ( product_fst_int_int @ X2 ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % inverse_rat.rsp
% 2.52/2.83 thf(fact_5326_FI__RESULT__def,axiom,
% 2.52/2.83 ( fI_RESULT
% 2.52/2.83 = ( ^ [M5: list_P8527749157015355191n_assn,UP: assn,UQ: assn,F: assn] :
% 2.52/2.83 ( ! [X2: produc6575502325842934193n_assn] :
% 2.52/2.83 ( ( member7957490590177025114n_assn @ X2 @ ( set_Pr1139785259514867910n_assn @ M5 ) )
% 2.52/2.83 => ( produc7274209992780475162assn_o @ entails @ X2 ) )
% 2.52/2.83 => ( entails @ ( times_times_assn @ ( foldr_assn_assn @ times_times_assn @ ( map_Pr8991440229025900053n_assn @ produc9167289414957590229n_assn @ M5 ) @ one_one_assn ) @ UP ) @ ( times_times_assn @ ( times_times_assn @ ( foldr_assn_assn @ times_times_assn @ ( map_Pr8991440229025900053n_assn @ produc2051961928117032727n_assn @ M5 ) @ one_one_assn ) @ UQ ) @ F ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % FI_RESULT_def
% 2.52/2.83 thf(fact_5327_num__of__integer__code,axiom,
% 2.52/2.83 ( code_num_of_integer
% 2.52/2.83 = ( ^ [K4: code_integer] :
% 2.52/2.83 ( if_num @ ( ord_le3102999989581377725nteger @ K4 @ one_one_Code_integer ) @ one
% 2.52/2.83 @ ( produc7336495610019696514er_num
% 2.52/2.83 @ ^ [L3: code_integer,J2: code_integer] : ( if_num @ ( J2 = zero_z3403309356797280102nteger ) @ ( plus_plus_num @ ( code_num_of_integer @ L3 ) @ ( code_num_of_integer @ L3 ) ) @ ( plus_plus_num @ ( plus_plus_num @ ( code_num_of_integer @ L3 ) @ ( code_num_of_integer @ L3 ) ) @ one ) )
% 2.52/2.83 @ ( code_divmod_integer @ K4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % num_of_integer_code
% 2.52/2.83 thf(fact_5328_int__of__integer__code,axiom,
% 2.52/2.83 ( code_int_of_integer
% 2.52/2.83 = ( ^ [K4: code_integer] :
% 2.52/2.83 ( if_int @ ( ord_le6747313008572928689nteger @ K4 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K4 ) ) )
% 2.52/2.83 @ ( if_int @ ( K4 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 2.52/2.83 @ ( produc1553301316500091796er_int
% 2.52/2.83 @ ^ [L3: code_integer,J2: code_integer] : ( if_int @ ( J2 = zero_z3403309356797280102nteger ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L3 ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L3 ) ) @ one_one_int ) )
% 2.52/2.83 @ ( code_divmod_integer @ K4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % int_of_integer_code
% 2.52/2.83 thf(fact_5329_bit__cut__integer__code,axiom,
% 2.52/2.83 ( code_bit_cut_integer
% 2.52/2.83 = ( ^ [K4: code_integer] :
% 2.52/2.83 ( if_Pro5737122678794959658eger_o @ ( K4 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 2.52/2.83 @ ( produc9125791028180074456eger_o
% 2.52/2.83 @ ^ [R4: code_integer,S4: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K4 ) @ R4 @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R4 ) @ S4 ) ) @ ( S4 = one_one_Code_integer ) )
% 2.52/2.83 @ ( code_divmod_abs @ K4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % bit_cut_integer_code
% 2.52/2.83 thf(fact_5330_nat__of__integer__code,axiom,
% 2.52/2.83 ( code_nat_of_integer
% 2.52/2.83 = ( ^ [K4: code_integer] :
% 2.52/2.83 ( if_nat @ ( ord_le3102999989581377725nteger @ K4 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 2.52/2.83 @ ( produc1555791787009142072er_nat
% 2.52/2.83 @ ^ [L3: code_integer,J2: code_integer] : ( if_nat @ ( J2 = zero_z3403309356797280102nteger ) @ ( plus_plus_nat @ ( code_nat_of_integer @ L3 ) @ ( code_nat_of_integer @ L3 ) ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( code_nat_of_integer @ L3 ) @ ( code_nat_of_integer @ L3 ) ) @ one_one_nat ) )
% 2.52/2.83 @ ( code_divmod_integer @ K4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % nat_of_integer_code
% 2.52/2.83 thf(fact_5331_one__integer_Orep__eq,axiom,
% 2.52/2.83 ( ( code_int_of_integer @ one_one_Code_integer )
% 2.52/2.83 = one_one_int ) ).
% 2.52/2.83
% 2.52/2.83 % one_integer.rep_eq
% 2.52/2.83 thf(fact_5332_divmod__integer__code,axiom,
% 2.52/2.83 ( code_divmod_integer
% 2.52/2.83 = ( ^ [K4: code_integer,L3: code_integer] :
% 2.52/2.83 ( if_Pro6119634080678213985nteger @ ( K4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 2.52/2.83 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ L3 )
% 2.52/2.83 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K4 ) @ ( code_divmod_abs @ K4 @ L3 )
% 2.52/2.83 @ ( produc6916734918728496179nteger
% 2.52/2.83 @ ^ [R4: code_integer,S4: code_integer] : ( if_Pro6119634080678213985nteger @ ( S4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R4 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R4 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ L3 @ S4 ) ) )
% 2.52/2.83 @ ( code_divmod_abs @ K4 @ L3 ) ) )
% 2.52/2.83 @ ( if_Pro6119634080678213985nteger @ ( L3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K4 )
% 2.52/2.83 @ ( produc6499014454317279255nteger @ uminus1351360451143612070nteger
% 2.52/2.83 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ K4 @ zero_z3403309356797280102nteger ) @ ( code_divmod_abs @ K4 @ L3 )
% 2.52/2.83 @ ( produc6916734918728496179nteger
% 2.52/2.83 @ ^ [R4: code_integer,S4: code_integer] : ( if_Pro6119634080678213985nteger @ ( S4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R4 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R4 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ L3 ) @ S4 ) ) )
% 2.52/2.83 @ ( code_divmod_abs @ K4 @ L3 ) ) ) ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % divmod_integer_code
% 2.52/2.83 thf(fact_5333_divmod__integer__eq__cases,axiom,
% 2.52/2.83 ( code_divmod_integer
% 2.52/2.83 = ( ^ [K4: code_integer,L3: code_integer] :
% 2.52/2.83 ( if_Pro6119634080678213985nteger @ ( K4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 2.52/2.83 @ ( if_Pro6119634080678213985nteger @ ( L3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K4 )
% 2.52/2.83 @ ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ produc6499014454317279255nteger @ times_3573771949741848930nteger ) @ sgn_sgn_Code_integer @ L3
% 2.52/2.83 @ ( if_Pro6119634080678213985nteger
% 2.52/2.83 @ ( ( sgn_sgn_Code_integer @ K4 )
% 2.52/2.83 = ( sgn_sgn_Code_integer @ L3 ) )
% 2.52/2.83 @ ( code_divmod_abs @ K4 @ L3 )
% 2.52/2.83 @ ( produc6916734918728496179nteger
% 2.52/2.83 @ ^ [R4: code_integer,S4: code_integer] : ( if_Pro6119634080678213985nteger @ ( S4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R4 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R4 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ L3 ) @ S4 ) ) )
% 2.52/2.83 @ ( code_divmod_abs @ K4 @ L3 ) ) ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % divmod_integer_eq_cases
% 2.52/2.83 thf(fact_5334_card__length__sum__list,axiom,
% 2.52/2.83 ! [M2: nat,N2: nat] :
% 2.52/2.83 ( ( finite_card_list_nat
% 2.52/2.83 @ ( collect_list_nat
% 2.52/2.83 @ ^ [L3: list_nat] :
% 2.52/2.83 ( ( ( size_size_list_nat @ L3 )
% 2.52/2.83 = M2 )
% 2.52/2.83 & ( ( groups4561878855575611511st_nat @ L3 )
% 2.52/2.83 = N2 ) ) ) )
% 2.52/2.83 = ( binomial @ ( minus_minus_nat @ ( plus_plus_nat @ N2 @ M2 ) @ one_one_nat ) @ N2 ) ) ).
% 2.52/2.83
% 2.52/2.83 % card_length_sum_list
% 2.52/2.83 thf(fact_5335_card__length__sum__list__rec,axiom,
% 2.52/2.83 ! [M2: nat,N2: nat] :
% 2.52/2.83 ( ( ord_less_eq_nat @ one_one_nat @ M2 )
% 2.52/2.83 => ( ( finite_card_list_nat
% 2.52/2.83 @ ( collect_list_nat
% 2.52/2.83 @ ^ [L3: list_nat] :
% 2.52/2.83 ( ( ( size_size_list_nat @ L3 )
% 2.52/2.83 = M2 )
% 2.52/2.83 & ( ( groups4561878855575611511st_nat @ L3 )
% 2.52/2.83 = N2 ) ) ) )
% 2.52/2.83 = ( plus_plus_nat
% 2.52/2.83 @ ( finite_card_list_nat
% 2.52/2.83 @ ( collect_list_nat
% 2.52/2.83 @ ^ [L3: list_nat] :
% 2.52/2.83 ( ( ( size_size_list_nat @ L3 )
% 2.52/2.83 = ( minus_minus_nat @ M2 @ one_one_nat ) )
% 2.52/2.83 & ( ( groups4561878855575611511st_nat @ L3 )
% 2.52/2.83 = N2 ) ) ) )
% 2.52/2.83 @ ( finite_card_list_nat
% 2.52/2.83 @ ( collect_list_nat
% 2.52/2.83 @ ^ [L3: list_nat] :
% 2.52/2.83 ( ( ( size_size_list_nat @ L3 )
% 2.52/2.83 = M2 )
% 2.52/2.83 & ( ( plus_plus_nat @ ( groups4561878855575611511st_nat @ L3 ) @ one_one_nat )
% 2.52/2.83 = N2 ) ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % card_length_sum_list_rec
% 2.52/2.83 thf(fact_5336_rat__number__expand_I5_J,axiom,
% 2.52/2.83 ! [K: num] :
% 2.52/2.83 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) )
% 2.52/2.83 = ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 2.52/2.83
% 2.52/2.83 % rat_number_expand(5)
% 2.52/2.83 thf(fact_5337_Fract__of__int__eq,axiom,
% 2.52/2.83 ! [K: int] :
% 2.52/2.83 ( ( fract @ K @ one_one_int )
% 2.52/2.83 = ( ring_1_of_int_rat @ K ) ) ).
% 2.52/2.83
% 2.52/2.83 % Fract_of_int_eq
% 2.52/2.83 thf(fact_5338_eq__rat_I2_J,axiom,
% 2.52/2.83 ! [A: int] :
% 2.52/2.83 ( ( fract @ A @ zero_zero_int )
% 2.52/2.83 = ( fract @ zero_zero_int @ one_one_int ) ) ).
% 2.52/2.83
% 2.52/2.83 % eq_rat(2)
% 2.52/2.83 thf(fact_5339_Fract__of__nat__eq,axiom,
% 2.52/2.83 ! [K: nat] :
% 2.52/2.83 ( ( fract @ ( semiri1314217659103216013at_int @ K ) @ one_one_int )
% 2.52/2.83 = ( semiri681578069525770553at_rat @ K ) ) ).
% 2.52/2.83
% 2.52/2.83 % Fract_of_nat_eq
% 2.52/2.83 thf(fact_5340_One__rat__def,axiom,
% 2.52/2.83 ( one_one_rat
% 2.52/2.83 = ( fract @ one_one_int @ one_one_int ) ) ).
% 2.52/2.83
% 2.52/2.83 % One_rat_def
% 2.52/2.83 thf(fact_5341_Zero__rat__def,axiom,
% 2.52/2.83 ( zero_zero_rat
% 2.52/2.83 = ( fract @ zero_zero_int @ one_one_int ) ) ).
% 2.52/2.83
% 2.52/2.83 % Zero_rat_def
% 2.52/2.83 thf(fact_5342_Fract__add__one,axiom,
% 2.52/2.83 ! [N: int,M2: int] :
% 2.52/2.83 ( ( N != zero_zero_int )
% 2.52/2.83 => ( ( fract @ ( plus_plus_int @ M2 @ N ) @ N )
% 2.52/2.83 = ( plus_plus_rat @ ( fract @ M2 @ N ) @ one_one_rat ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % Fract_add_one
% 2.52/2.83 thf(fact_5343_rat__number__collapse_I3_J,axiom,
% 2.52/2.83 ! [W: num] :
% 2.52/2.83 ( ( fract @ ( numeral_numeral_int @ W ) @ one_one_int )
% 2.52/2.83 = ( numeral_numeral_rat @ W ) ) ).
% 2.52/2.83
% 2.52/2.83 % rat_number_collapse(3)
% 2.52/2.83 thf(fact_5344_rat__number__expand_I3_J,axiom,
% 2.52/2.83 ( numeral_numeral_rat
% 2.52/2.83 = ( ^ [K4: num] : ( fract @ ( numeral_numeral_int @ K4 ) @ one_one_int ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % rat_number_expand(3)
% 2.52/2.83 thf(fact_5345_one__le__Fract__iff,axiom,
% 2.52/2.83 ! [B: int,A: int] :
% 2.52/2.83 ( ( ord_less_int @ zero_zero_int @ B )
% 2.52/2.83 => ( ( ord_less_eq_rat @ one_one_rat @ ( fract @ A @ B ) )
% 2.52/2.83 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % one_le_Fract_iff
% 2.52/2.83 thf(fact_5346_Fract__le__one__iff,axiom,
% 2.52/2.83 ! [B: int,A: int] :
% 2.52/2.83 ( ( ord_less_int @ zero_zero_int @ B )
% 2.52/2.83 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ one_one_rat )
% 2.52/2.83 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % Fract_le_one_iff
% 2.52/2.83 thf(fact_5347_Fract_Oabs__eq,axiom,
% 2.52/2.83 ( fract
% 2.52/2.83 = ( ^ [Xa4: int,X2: int] : ( abs_Rat @ ( if_Pro3027730157355071871nt_int @ ( X2 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ Xa4 @ X2 ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % Fract.abs_eq
% 2.52/2.83 thf(fact_5348_rat__floor__lemma,axiom,
% 2.52/2.83 ! [A: int,B: int] :
% 2.52/2.83 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( divide_divide_int @ A @ B ) ) @ ( fract @ A @ B ) )
% 2.52/2.83 & ( ord_less_rat @ ( fract @ A @ B ) @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % rat_floor_lemma
% 2.52/2.83 thf(fact_5349_one__less__Fract__iff,axiom,
% 2.52/2.83 ! [B: int,A: int] :
% 2.52/2.83 ( ( ord_less_int @ zero_zero_int @ B )
% 2.52/2.83 => ( ( ord_less_rat @ one_one_rat @ ( fract @ A @ B ) )
% 2.52/2.83 = ( ord_less_int @ B @ A ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % one_less_Fract_iff
% 2.52/2.83 thf(fact_5350_Fract__less__one__iff,axiom,
% 2.52/2.83 ! [B: int,A: int] :
% 2.52/2.83 ( ( ord_less_int @ zero_zero_int @ B )
% 2.52/2.83 => ( ( ord_less_rat @ ( fract @ A @ B ) @ one_one_rat )
% 2.52/2.83 = ( ord_less_int @ A @ B ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % Fract_less_one_iff
% 2.52/2.83 thf(fact_5351_rat__number__collapse_I5_J,axiom,
% 2.52/2.83 ( ( fract @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 2.52/2.83 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 2.52/2.83
% 2.52/2.83 % rat_number_collapse(5)
% 2.52/2.83 thf(fact_5352_Fract_Otransfer,axiom,
% 2.52/2.83 ( bNF_re3461391660133120880nt_rat
% 2.52/2.83 @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 2.52/2.83 @ ( bNF_re2214769303045360666nt_rat
% 2.52/2.83 @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 2.52/2.83 @ pcr_rat )
% 2.52/2.83 @ ^ [A2: int,B2: int] : ( if_Pro3027730157355071871nt_int @ ( B2 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A2 @ B2 ) )
% 2.52/2.83 @ fract ) ).
% 2.52/2.83
% 2.52/2.83 % Fract.transfer
% 2.52/2.83 thf(fact_5353_rat__number__collapse_I4_J,axiom,
% 2.52/2.83 ! [W: num] :
% 2.52/2.83 ( ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ one_one_int )
% 2.52/2.83 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % rat_number_collapse(4)
% 2.52/2.83 thf(fact_5354_floor__rat__def,axiom,
% 2.52/2.83 ( archim3151403230148437115or_rat
% 2.52/2.83 = ( ^ [X2: rat] :
% 2.52/2.83 ( the_int
% 2.52/2.83 @ ^ [Z3: int] :
% 2.52/2.83 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z3 ) @ X2 )
% 2.52/2.83 & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z3 @ one_one_int ) ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % floor_rat_def
% 2.52/2.83 thf(fact_5355_abs__division__segment,axiom,
% 2.52/2.83 ! [K: int] :
% 2.52/2.83 ( ( abs_abs_int @ ( euclid3395696857347342551nt_int @ K ) )
% 2.52/2.83 = one_one_int ) ).
% 2.52/2.83
% 2.52/2.83 % abs_division_segment
% 2.52/2.83 thf(fact_5356_division__segment__nat__def,axiom,
% 2.52/2.83 ( euclid3398187327856392827nt_nat
% 2.52/2.83 = ( ^ [N3: nat] : one_one_nat ) ) ).
% 2.52/2.83
% 2.52/2.83 % division_segment_nat_def
% 2.52/2.83 thf(fact_5357_division__segment__int__def,axiom,
% 2.52/2.83 ( euclid3395696857347342551nt_int
% 2.52/2.83 = ( ^ [K4: int] : ( if_int @ ( ord_less_eq_int @ zero_zero_int @ K4 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % division_segment_int_def
% 2.52/2.83 thf(fact_5358_inverse__rat__def,axiom,
% 2.52/2.83 ( inverse_inverse_rat
% 2.52/2.83 = ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat
% 2.52/2.83 @ ^ [X2: product_prod_int_int] :
% 2.52/2.83 ( if_Pro3027730157355071871nt_int
% 2.52/2.83 @ ( ( product_fst_int_int @ X2 )
% 2.52/2.83 = zero_zero_int )
% 2.52/2.83 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 2.52/2.83 @ ( product_Pair_int_int @ ( product_snd_int_int @ X2 ) @ ( product_fst_int_int @ X2 ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % inverse_rat_def
% 2.52/2.83 thf(fact_5359_num__of__nat__One,axiom,
% 2.52/2.83 ! [N: nat] :
% 2.52/2.83 ( ( ord_less_eq_nat @ N @ one_one_nat )
% 2.52/2.83 => ( ( num_of_nat @ N )
% 2.52/2.83 = one ) ) ).
% 2.52/2.83
% 2.52/2.83 % num_of_nat_One
% 2.52/2.83 thf(fact_5360_one__int_Otransfer,axiom,
% 2.52/2.83 pcr_int @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ one_one_int ).
% 2.52/2.83
% 2.52/2.83 % one_int.transfer
% 2.52/2.83 thf(fact_5361_one__int__def,axiom,
% 2.52/2.83 ( one_one_int
% 2.52/2.83 = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % one_int_def
% 2.52/2.83 thf(fact_5362_integer__of__nat__1,axiom,
% 2.52/2.83 ( ( code_integer_of_nat @ one_one_nat )
% 2.52/2.83 = one_one_Code_integer ) ).
% 2.52/2.83
% 2.52/2.83 % integer_of_nat_1
% 2.52/2.83 thf(fact_5363_list__all__iff__all__interval__int,axiom,
% 2.52/2.83 ! [P2: int > $o,I2: int,J: int] :
% 2.52/2.83 ( ( list_all_int @ P2 @ ( upto @ I2 @ J ) )
% 2.52/2.83 = ( all_interval_int @ P2 @ I2 @ J ) ) ).
% 2.52/2.83
% 2.52/2.83 % list_all_iff_all_interval_int
% 2.52/2.83 thf(fact_5364_list__ex__iff__not__all__inverval__int,axiom,
% 2.52/2.83 ! [P2: int > $o,I2: int,J: int] :
% 2.52/2.83 ( ( list_ex_int @ P2 @ ( upto @ I2 @ J ) )
% 2.52/2.83 = ( ~ ( all_interval_int @ ( comp_o_o_int @ (~) @ P2 ) @ I2 @ J ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % list_ex_iff_not_all_inverval_int
% 2.52/2.83 thf(fact_5365_all__interval__int__def,axiom,
% 2.52/2.83 ( all_interval_int
% 2.52/2.83 = ( ^ [P: int > $o,I4: int,J2: int] :
% 2.52/2.83 ! [X2: int] :
% 2.52/2.83 ( ( member_int2 @ X2 @ ( set_or1266510415728281911st_int @ I4 @ J2 ) )
% 2.52/2.83 => ( P @ X2 ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % all_interval_int_def
% 2.52/2.83 thf(fact_5366_unit__factor__simps_I2_J,axiom,
% 2.52/2.83 ! [N: nat] :
% 2.52/2.83 ( ( unit_f2748546683901255202or_nat @ ( suc @ N ) )
% 2.52/2.83 = one_one_nat ) ).
% 2.52/2.83
% 2.52/2.83 % unit_factor_simps(2)
% 2.52/2.83 thf(fact_5367_unit__factor__nat__def,axiom,
% 2.52/2.83 ( unit_f2748546683901255202or_nat
% 2.52/2.83 = ( ^ [N3: nat] : ( if_nat @ ( N3 = zero_zero_nat ) @ zero_zero_nat @ one_one_nat ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % unit_factor_nat_def
% 2.52/2.83 thf(fact_5368_list__all__iff__all__interval__nat,axiom,
% 2.52/2.83 ! [P2: nat > $o,I2: nat,J: nat] :
% 2.52/2.83 ( ( list_all_nat @ P2 @ ( upt @ I2 @ J ) )
% 2.52/2.83 = ( all_interval_nat @ P2 @ I2 @ J ) ) ).
% 2.52/2.83
% 2.52/2.83 % list_all_iff_all_interval_nat
% 2.52/2.83 thf(fact_5369_list__ex__iff__not__all__inverval__nat,axiom,
% 2.52/2.83 ! [P2: nat > $o,I2: nat,J: nat] :
% 2.52/2.83 ( ( list_ex_nat @ P2 @ ( upt @ I2 @ J ) )
% 2.52/2.83 = ( ~ ( all_interval_nat @ ( comp_o_o_nat @ (~) @ P2 ) @ I2 @ J ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % list_ex_iff_not_all_inverval_nat
% 2.52/2.83 thf(fact_5370_Gcd__nat__eq__one,axiom,
% 2.52/2.83 ! [N2: set_nat] :
% 2.52/2.83 ( ( member_nat2 @ one_one_nat @ N2 )
% 2.52/2.83 => ( ( gcd_Gcd_nat @ N2 )
% 2.52/2.83 = one_one_nat ) ) ).
% 2.52/2.83
% 2.52/2.83 % Gcd_nat_eq_one
% 2.52/2.83 thf(fact_5371_Lcm__nat__empty,axiom,
% 2.52/2.83 ( ( gcd_Lcm_nat @ bot_bot_set_nat )
% 2.52/2.83 = one_one_nat ) ).
% 2.52/2.83
% 2.52/2.83 % Lcm_nat_empty
% 2.52/2.83 thf(fact_5372_all__interval__nat__def,axiom,
% 2.52/2.83 ( all_interval_nat
% 2.52/2.83 = ( ^ [P: nat > $o,I4: nat,J2: nat] :
% 2.52/2.83 ! [X2: nat] :
% 2.52/2.83 ( ( member_nat2 @ X2 @ ( set_or4665077453230672383an_nat @ I4 @ J2 ) )
% 2.52/2.83 => ( P @ X2 ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % all_interval_nat_def
% 2.52/2.83 thf(fact_5373_lcm__1__iff__int,axiom,
% 2.52/2.83 ! [M2: int,N: int] :
% 2.52/2.83 ( ( ( gcd_lcm_int @ M2 @ N )
% 2.52/2.83 = one_one_int )
% 2.52/2.83 = ( ( ( M2 = one_one_int )
% 2.52/2.83 | ( M2
% 2.52/2.83 = ( uminus_uminus_int @ one_one_int ) ) )
% 2.52/2.83 & ( ( N = one_one_int )
% 2.52/2.83 | ( N
% 2.52/2.83 = ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % lcm_1_iff_int
% 2.52/2.83 thf(fact_5374_Lcm__nat__set__eq__fold,axiom,
% 2.52/2.83 ! [Xs: list_nat] :
% 2.52/2.83 ( ( gcd_Lcm_nat @ ( set_nat2 @ Xs ) )
% 2.52/2.83 = ( fold_nat_nat @ gcd_lcm_nat @ Xs @ one_one_nat ) ) ).
% 2.52/2.83
% 2.52/2.83 % Lcm_nat_set_eq_fold
% 2.52/2.83 thf(fact_5375_Lcm__int__set__eq__fold,axiom,
% 2.52/2.83 ! [Xs: list_int] :
% 2.52/2.83 ( ( gcd_Lcm_int @ ( set_int2 @ Xs ) )
% 2.52/2.83 = ( fold_int_int @ gcd_lcm_int @ Xs @ one_one_int ) ) ).
% 2.52/2.83
% 2.52/2.83 % Lcm_int_set_eq_fold
% 2.52/2.83 thf(fact_5376_Lcm__nat__def,axiom,
% 2.52/2.83 ( gcd_Lcm_nat
% 2.52/2.83 = ( ^ [M5: set_nat] : ( if_nat @ ( finite_finite_nat @ M5 ) @ ( lattic7826324295020591184_F_nat @ gcd_lcm_nat @ one_one_nat @ M5 ) @ zero_zero_nat ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % Lcm_nat_def
% 2.52/2.83 thf(fact_5377_coprime__diff__one__right__nat,axiom,
% 2.52/2.83 ! [N: nat] :
% 2.52/2.83 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.52/2.83 => ( algebr934650988132801477me_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % coprime_diff_one_right_nat
% 2.52/2.83 thf(fact_5378_coprime__common__divisor__nat,axiom,
% 2.52/2.83 ! [A: nat,B: nat,X: nat] :
% 2.52/2.83 ( ( algebr934650988132801477me_nat @ A @ B )
% 2.52/2.83 => ( ( dvd_dvd_nat @ X @ A )
% 2.52/2.83 => ( ( dvd_dvd_nat @ X @ B )
% 2.52/2.83 => ( X = one_one_nat ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % coprime_common_divisor_nat
% 2.52/2.83 thf(fact_5379_coprime__diff__one__left__nat,axiom,
% 2.52/2.83 ! [N: nat] :
% 2.52/2.83 ( ( ord_less_nat @ zero_zero_nat @ N )
% 2.52/2.83 => ( algebr934650988132801477me_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ N ) ) ).
% 2.52/2.83
% 2.52/2.83 % coprime_diff_one_left_nat
% 2.52/2.83 thf(fact_5380_in__range_Osimps,axiom,
% 2.52/2.83 ! [H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 2.52/2.83 ( ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As2 ) )
% 2.52/2.83 = ( ! [X2: nat] :
% 2.52/2.83 ( ( member_nat2 @ X2 @ As2 )
% 2.52/2.83 => ( ord_less_nat @ X2 @ ( lim_Product_unit @ H2 ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % in_range.simps
% 2.52/2.83 thf(fact_5381_coprime__common__divisor__int,axiom,
% 2.52/2.83 ! [A: int,B: int,X: int] :
% 2.52/2.83 ( ( algebr932160517623751201me_int @ A @ B )
% 2.52/2.83 => ( ( dvd_dvd_int @ X @ A )
% 2.52/2.83 => ( ( dvd_dvd_int @ X @ B )
% 2.52/2.83 => ( ( abs_abs_int @ X )
% 2.52/2.83 = one_one_int ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % coprime_common_divisor_int
% 2.52/2.83 thf(fact_5382_in__range_Oelims_I3_J,axiom,
% 2.52/2.83 ! [X: produc3658429121746597890et_nat] :
% 2.52/2.83 ( ~ ( in_range @ X )
% 2.52/2.83 => ~ ! [H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.52/2.83 ( ( X
% 2.52/2.83 = ( produc7507926704131184380et_nat @ H3 @ As ) )
% 2.52/2.83 => ! [X3: nat] :
% 2.52/2.83 ( ( member_nat2 @ X3 @ As )
% 2.52/2.83 => ( ord_less_nat @ X3 @ ( lim_Product_unit @ H3 ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % in_range.elims(3)
% 2.52/2.83 thf(fact_5383_in__range_Oelims_I2_J,axiom,
% 2.52/2.83 ! [X: produc3658429121746597890et_nat] :
% 2.52/2.83 ( ( in_range @ X )
% 2.52/2.83 => ~ ! [H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.52/2.83 ( ( X
% 2.52/2.83 = ( produc7507926704131184380et_nat @ H3 @ As ) )
% 2.52/2.83 => ~ ! [X4: nat] :
% 2.52/2.83 ( ( member_nat2 @ X4 @ As )
% 2.52/2.83 => ( ord_less_nat @ X4 @ ( lim_Product_unit @ H3 ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % in_range.elims(2)
% 2.52/2.83 thf(fact_5384_in__range_Oelims_I1_J,axiom,
% 2.52/2.83 ! [X: produc3658429121746597890et_nat,Y: $o] :
% 2.52/2.83 ( ( ( in_range @ X )
% 2.52/2.83 = Y )
% 2.52/2.83 => ~ ! [H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.52/2.83 ( ( X
% 2.52/2.83 = ( produc7507926704131184380et_nat @ H3 @ As ) )
% 2.52/2.83 => ( Y
% 2.52/2.83 = ( ~ ! [X2: nat] :
% 2.52/2.83 ( ( member_nat2 @ X2 @ As )
% 2.52/2.83 => ( ord_less_nat @ X2 @ ( lim_Product_unit @ H3 ) ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % in_range.elims(1)
% 2.52/2.83 thf(fact_5385_one__int_Orsp,axiom,
% 2.52/2.83 intrel @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ).
% 2.52/2.83
% 2.52/2.83 % one_int.rsp
% 2.52/2.83 thf(fact_5386_wait__rule,axiom,
% 2.52/2.83 ! [N: nat] :
% 2.52/2.83 ( hoare_8945653483474564448t_unit @ one_one_assn @ ( heap_Time_wait @ N )
% 2.52/2.83 @ ^ [Uu2: product_unit] : one_one_assn ) ).
% 2.52/2.83
% 2.52/2.83 % wait_rule
% 2.52/2.83 thf(fact_5387_inf__unit__def,axiom,
% 2.52/2.83 ( inf_inf_Product_unit
% 2.52/2.83 = ( ^ [Uu3: product_unit,Uv: product_unit] : product_Unity ) ) ).
% 2.52/2.83
% 2.52/2.83 % inf_unit_def
% 2.52/2.83 thf(fact_5388_assert_H__rule,axiom,
% 2.52/2.83 ! [P2: assn,Phi: $o] :
% 2.52/2.83 ( ! [H3: produc3658429121746597890et_nat] :
% 2.52/2.83 ( ( rep_assn @ P2 @ H3 )
% 2.52/2.83 => Phi )
% 2.52/2.83 => ( hoare_8945653483474564448t_unit @ P2 @ ( refine_Imp_assert @ Phi )
% 2.52/2.83 @ ^ [Uu2: product_unit] : P2 ) ) ).
% 2.52/2.83
% 2.52/2.83 % assert'_rule
% 2.52/2.83 thf(fact_5389_natural__zero__minus__one,axiom,
% 2.52/2.83 ( ( minus_7197305767214868737atural @ zero_z2226904508553997617atural @ one_one_Code_natural )
% 2.52/2.83 = zero_z2226904508553997617atural ) ).
% 2.52/2.83
% 2.52/2.83 % natural_zero_minus_one
% 2.52/2.83 thf(fact_5390_log_Oelims,axiom,
% 2.52/2.83 ! [X: code_natural,Xa: code_natural,Y: code_natural] :
% 2.52/2.83 ( ( ( log @ X @ Xa )
% 2.52/2.83 = Y )
% 2.52/2.83 => ( ( ( ( ord_le1926595141338095240atural @ X @ one_one_Code_natural )
% 2.52/2.83 | ( ord_le5570908160329646204atural @ Xa @ X ) )
% 2.52/2.83 => ( Y = one_one_Code_natural ) )
% 2.52/2.83 & ( ~ ( ( ord_le1926595141338095240atural @ X @ one_one_Code_natural )
% 2.52/2.83 | ( ord_le5570908160329646204atural @ Xa @ X ) )
% 2.52/2.83 => ( Y
% 2.52/2.83 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( log @ X @ ( divide5121882707175180666atural @ Xa @ X ) ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % log.elims
% 2.52/2.83 thf(fact_5391_log_Osimps,axiom,
% 2.52/2.83 ( log
% 2.52/2.83 = ( ^ [B2: code_natural,I4: code_natural] :
% 2.52/2.83 ( if_Code_natural
% 2.52/2.83 @ ( ( ord_le1926595141338095240atural @ B2 @ one_one_Code_natural )
% 2.52/2.83 | ( ord_le5570908160329646204atural @ I4 @ B2 ) )
% 2.52/2.83 @ one_one_Code_natural
% 2.52/2.83 @ ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( log @ B2 @ ( divide5121882707175180666atural @ I4 @ B2 ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % log.simps
% 2.52/2.83 thf(fact_5392_next_Osimps,axiom,
% 2.52/2.83 ! [V2: code_natural,W: code_natural] :
% 2.52/2.83 ( ( next @ ( produc3574140220909816553atural @ V2 @ W ) )
% 2.52/2.83 = ( produc6639722614265839536atural @ ( plus_p4538020629002901425atural @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ V2 @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ V2 @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( plus_p4538020629002901425atural @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ W @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ W @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ one_one_Code_natural ) ) @ one_one_Code_natural ) @ ( produc3574140220909816553atural @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ V2 @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ V2 @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ W @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ W @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % next.simps
% 2.52/2.83 thf(fact_5393_Random_Orange__def,axiom,
% 2.52/2.83 ( range
% 2.52/2.83 = ( ^ [K4: code_natural] :
% 2.52/2.83 ( produc5538323210962509403atural
% 2.52/2.83 @ ( iterat8892046348760725948atural @ ( log @ ( numera5444537566228673987atural @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ K4 )
% 2.52/2.83 @ ^ [L3: code_natural] :
% 2.52/2.83 ( produc5538323210962509403atural @ next
% 2.52/2.83 @ ^ [V3: code_natural] : ( produc6639722614265839536atural @ ( plus_p4538020629002901425atural @ V3 @ ( times_2397367101498566445atural @ L3 @ ( numera5444537566228673987atural @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 2.52/2.83 @ one_one_Code_natural )
% 2.52/2.83 @ ^ [V3: code_natural] : ( produc6639722614265839536atural @ ( modulo8411746178871703098atural @ V3 @ K4 ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % Random.range_def
% 2.52/2.83 thf(fact_5394_inc__shift__def,axiom,
% 2.52/2.83 ( inc_shift
% 2.52/2.83 = ( ^ [V3: code_natural,K4: code_natural] : ( if_Code_natural @ ( V3 = K4 ) @ one_one_Code_natural @ ( plus_p4538020629002901425atural @ K4 @ one_one_Code_natural ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % inc_shift_def
% 2.52/2.83 thf(fact_5395_log_Opelims,axiom,
% 2.52/2.83 ! [X: code_natural,Xa: code_natural,Y: code_natural] :
% 2.52/2.83 ( ( ( log @ X @ Xa )
% 2.52/2.83 = Y )
% 2.52/2.83 => ( ( accp_P8126237942716283194atural @ log_rel @ ( produc3574140220909816553atural @ X @ Xa ) )
% 2.52/2.83 => ~ ( ( ( ( ( ord_le1926595141338095240atural @ X @ one_one_Code_natural )
% 2.52/2.83 | ( ord_le5570908160329646204atural @ Xa @ X ) )
% 2.52/2.83 => ( Y = one_one_Code_natural ) )
% 2.52/2.83 & ( ~ ( ( ord_le1926595141338095240atural @ X @ one_one_Code_natural )
% 2.52/2.83 | ( ord_le5570908160329646204atural @ Xa @ X ) )
% 2.52/2.83 => ( Y
% 2.52/2.83 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( log @ X @ ( divide5121882707175180666atural @ Xa @ X ) ) ) ) ) )
% 2.52/2.83 => ~ ( accp_P8126237942716283194atural @ log_rel @ ( produc3574140220909816553atural @ X @ Xa ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % log.pelims
% 2.52/2.83 thf(fact_5396_one__natural__def,axiom,
% 2.52/2.83 ( one_one_Code_natural
% 2.52/2.83 = ( code_natural_of_nat @ one_one_nat ) ) ).
% 2.52/2.83
% 2.52/2.83 % one_natural_def
% 2.52/2.83 thf(fact_5397_Suc__natural__minus__one,axiom,
% 2.52/2.83 ! [N: code_natural] :
% 2.52/2.83 ( ( minus_7197305767214868737atural @ ( code_Suc @ N ) @ one_one_Code_natural )
% 2.52/2.83 = N ) ).
% 2.52/2.83
% 2.52/2.83 % Suc_natural_minus_one
% 2.52/2.83 thf(fact_5398_Code__Numeral_Osub__code_I9_J,axiom,
% 2.52/2.83 ! [M2: num,N: num] :
% 2.52/2.83 ( ( code_sub @ ( bit0 @ M2 ) @ ( bit1 @ N ) )
% 2.52/2.83 = ( minus_8373710615458151222nteger @ ( code_dup @ ( code_sub @ M2 @ N ) ) @ one_one_Code_integer ) ) ).
% 2.52/2.83
% 2.52/2.83 % Code_Numeral.sub_code(9)
% 2.52/2.83 thf(fact_5399_Code__Numeral_Osub__code_I8_J,axiom,
% 2.52/2.83 ! [M2: num,N: num] :
% 2.52/2.83 ( ( code_sub @ ( bit1 @ M2 ) @ ( bit0 @ N ) )
% 2.52/2.83 = ( plus_p5714425477246183910nteger @ ( code_dup @ ( code_sub @ M2 @ N ) ) @ one_one_Code_integer ) ) ).
% 2.52/2.83
% 2.52/2.83 % Code_Numeral.sub_code(8)
% 2.52/2.83 thf(fact_5400_Int_Osub__code_I9_J,axiom,
% 2.52/2.83 ! [M2: num,N: num] :
% 2.52/2.83 ( ( sub @ ( bit0 @ M2 ) @ ( bit1 @ N ) )
% 2.52/2.83 = ( minus_minus_int @ ( dup @ ( sub @ M2 @ N ) ) @ one_one_int ) ) ).
% 2.52/2.83
% 2.52/2.83 % Int.sub_code(9)
% 2.52/2.83 thf(fact_5401_Int_Osub__code_I8_J,axiom,
% 2.52/2.83 ! [M2: num,N: num] :
% 2.52/2.83 ( ( sub @ ( bit1 @ M2 ) @ ( bit0 @ N ) )
% 2.52/2.83 = ( plus_plus_int @ ( dup @ ( sub @ M2 @ N ) ) @ one_one_int ) ) ).
% 2.52/2.83
% 2.52/2.83 % Int.sub_code(8)
% 2.52/2.83 thf(fact_5402_Fract__def,axiom,
% 2.52/2.83 ( fract
% 2.52/2.83 = ( map_fu7831380289885515383nt_rat @ id_int @ ( map_fu3424225382358772769nt_rat @ id_int @ abs_Rat )
% 2.52/2.83 @ ^ [A2: int,B2: int] : ( if_Pro3027730157355071871nt_int @ ( B2 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A2 @ B2 ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % Fract_def
% 2.52/2.83 thf(fact_5403_in__range_Opelims_I3_J,axiom,
% 2.52/2.83 ! [X: produc3658429121746597890et_nat] :
% 2.52/2.83 ( ~ ( in_range @ X )
% 2.52/2.83 => ( ( accp_P5801069581201407417et_nat @ in_range_rel @ X )
% 2.52/2.83 => ~ ! [H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.52/2.83 ( ( X
% 2.52/2.83 = ( produc7507926704131184380et_nat @ H3 @ As ) )
% 2.52/2.83 => ( ( accp_P5801069581201407417et_nat @ in_range_rel @ ( produc7507926704131184380et_nat @ H3 @ As ) )
% 2.52/2.83 => ! [X3: nat] :
% 2.52/2.83 ( ( member_nat2 @ X3 @ As )
% 2.52/2.83 => ( ord_less_nat @ X3 @ ( lim_Product_unit @ H3 ) ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % in_range.pelims(3)
% 2.52/2.83 thf(fact_5404_in__range_Opelims_I1_J,axiom,
% 2.52/2.83 ! [X: produc3658429121746597890et_nat,Y: $o] :
% 2.52/2.83 ( ( ( in_range @ X )
% 2.52/2.83 = Y )
% 2.52/2.83 => ( ( accp_P5801069581201407417et_nat @ in_range_rel @ X )
% 2.52/2.83 => ~ ! [H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.52/2.83 ( ( X
% 2.52/2.83 = ( produc7507926704131184380et_nat @ H3 @ As ) )
% 2.52/2.83 => ( ( Y
% 2.52/2.83 = ( ! [X2: nat] :
% 2.52/2.83 ( ( member_nat2 @ X2 @ As )
% 2.52/2.83 => ( ord_less_nat @ X2 @ ( lim_Product_unit @ H3 ) ) ) ) )
% 2.52/2.83 => ~ ( accp_P5801069581201407417et_nat @ in_range_rel @ ( produc7507926704131184380et_nat @ H3 @ As ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % in_range.pelims(1)
% 2.52/2.83 thf(fact_5405_in__range_Opelims_I2_J,axiom,
% 2.52/2.83 ! [X: produc3658429121746597890et_nat] :
% 2.52/2.83 ( ( in_range @ X )
% 2.52/2.83 => ( ( accp_P5801069581201407417et_nat @ in_range_rel @ X )
% 2.52/2.83 => ~ ! [H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.52/2.83 ( ( X
% 2.52/2.83 = ( produc7507926704131184380et_nat @ H3 @ As ) )
% 2.52/2.83 => ( ( accp_P5801069581201407417et_nat @ in_range_rel @ ( produc7507926704131184380et_nat @ H3 @ As ) )
% 2.52/2.83 => ~ ! [X4: nat] :
% 2.52/2.83 ( ( member_nat2 @ X4 @ As )
% 2.52/2.83 => ( ord_less_nat @ X4 @ ( lim_Product_unit @ H3 ) ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % in_range.pelims(2)
% 2.52/2.83 thf(fact_5406_one__assn__raw_Opelims_I3_J,axiom,
% 2.52/2.83 ! [X: produc3658429121746597890et_nat] :
% 2.52/2.83 ( ~ ( one_assn_raw @ X )
% 2.52/2.83 => ( ( accp_P5801069581201407417et_nat @ one_assn_raw_rel @ X )
% 2.52/2.83 => ~ ! [H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.52/2.83 ( ( X
% 2.52/2.83 = ( produc7507926704131184380et_nat @ H3 @ As ) )
% 2.52/2.83 => ( ( accp_P5801069581201407417et_nat @ one_assn_raw_rel @ ( produc7507926704131184380et_nat @ H3 @ As ) )
% 2.52/2.83 => ( As = bot_bot_set_nat ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % one_assn_raw.pelims(3)
% 2.52/2.83 thf(fact_5407_one__assn__raw_Opelims_I2_J,axiom,
% 2.52/2.83 ! [X: produc3658429121746597890et_nat] :
% 2.52/2.83 ( ( one_assn_raw @ X )
% 2.52/2.83 => ( ( accp_P5801069581201407417et_nat @ one_assn_raw_rel @ X )
% 2.52/2.83 => ~ ! [H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.52/2.83 ( ( X
% 2.52/2.83 = ( produc7507926704131184380et_nat @ H3 @ As ) )
% 2.52/2.83 => ( ( accp_P5801069581201407417et_nat @ one_assn_raw_rel @ ( produc7507926704131184380et_nat @ H3 @ As ) )
% 2.52/2.83 => ( As != bot_bot_set_nat ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % one_assn_raw.pelims(2)
% 2.52/2.83 thf(fact_5408_one__assn__raw_Opelims_I1_J,axiom,
% 2.52/2.83 ! [X: produc3658429121746597890et_nat,Y: $o] :
% 2.52/2.83 ( ( ( one_assn_raw @ X )
% 2.52/2.83 = Y )
% 2.52/2.83 => ( ( accp_P5801069581201407417et_nat @ one_assn_raw_rel @ X )
% 2.52/2.83 => ~ ! [H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 2.52/2.83 ( ( X
% 2.52/2.83 = ( produc7507926704131184380et_nat @ H3 @ As ) )
% 2.52/2.83 => ( ( Y
% 2.52/2.83 = ( As = bot_bot_set_nat ) )
% 2.52/2.83 => ~ ( accp_P5801069581201407417et_nat @ one_assn_raw_rel @ ( produc7507926704131184380et_nat @ H3 @ As ) ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % one_assn_raw.pelims(1)
% 2.52/2.83 thf(fact_5409_Restr__natLeq,axiom,
% 2.52/2.83 ! [N: nat] :
% 2.52/2.83 ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 2.52/2.83 @ ( produc457027306803732586at_nat
% 2.52/2.83 @ ( collect_nat
% 2.52/2.83 @ ^ [X2: nat] : ( ord_less_nat @ X2 @ N ) )
% 2.52/2.83 @ ^ [Uu2: nat] :
% 2.52/2.83 ( collect_nat
% 2.52/2.83 @ ^ [X2: nat] : ( ord_less_nat @ X2 @ N ) ) ) )
% 2.52/2.83 = ( collec3392354462482085612at_nat
% 2.52/2.83 @ ( produc6081775807080527818_nat_o
% 2.52/2.83 @ ^ [X2: nat,Y2: nat] :
% 2.52/2.83 ( ( ord_less_nat @ X2 @ N )
% 2.52/2.83 & ( ord_less_nat @ Y2 @ N )
% 2.52/2.83 & ( ord_less_eq_nat @ X2 @ Y2 ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % Restr_natLeq
% 2.52/2.83 thf(fact_5410_Restr__natLeq2,axiom,
% 2.52/2.83 ! [N: nat] :
% 2.52/2.83 ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 2.52/2.83 @ ( produc457027306803732586at_nat @ ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N )
% 2.52/2.83 @ ^ [Uu2: nat] : ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N ) ) )
% 2.52/2.83 = ( collec3392354462482085612at_nat
% 2.52/2.83 @ ( produc6081775807080527818_nat_o
% 2.52/2.83 @ ^ [X2: nat,Y2: nat] :
% 2.52/2.83 ( ( ord_less_nat @ X2 @ N )
% 2.52/2.83 & ( ord_less_nat @ Y2 @ N )
% 2.52/2.83 & ( ord_less_eq_nat @ X2 @ Y2 ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % Restr_natLeq2
% 2.52/2.83 thf(fact_5411_one__integer__code,axiom,
% 2.52/2.83 ( one_one_Code_integer
% 2.52/2.83 = ( code_Pos @ one ) ) ).
% 2.52/2.83
% 2.52/2.83 % one_integer_code
% 2.52/2.83 thf(fact_5412_one__natural_Orep__eq,axiom,
% 2.52/2.83 ( ( code_nat_of_natural @ one_one_Code_natural )
% 2.52/2.83 = one_one_nat ) ).
% 2.52/2.83
% 2.52/2.83 % one_natural.rep_eq
% 2.52/2.83 thf(fact_5413_nat__of__num__code_I1_J,axiom,
% 2.52/2.83 ( ( nat_of_num @ one )
% 2.52/2.83 = one_one_nat ) ).
% 2.52/2.83
% 2.52/2.83 % nat_of_num_code(1)
% 2.52/2.83 thf(fact_5414_one__int__code,axiom,
% 2.52/2.83 ( one_one_int
% 2.52/2.83 = ( pos @ one ) ) ).
% 2.52/2.83
% 2.52/2.83 % one_int_code
% 2.52/2.83 thf(fact_5415_one__natural_Otransfer,axiom,
% 2.52/2.83 code_pcr_natural @ one_one_nat @ one_one_Code_natural ).
% 2.52/2.83
% 2.52/2.83 % one_natural.transfer
% 2.52/2.83 thf(fact_5416_one__integer_Otransfer,axiom,
% 2.52/2.83 code_pcr_integer @ one_one_int @ one_one_Code_integer ).
% 2.52/2.83
% 2.52/2.83 % one_integer.transfer
% 2.52/2.83 thf(fact_5417_rat_Odomain__par,axiom,
% 2.52/2.83 ! [DR1: int > $o,DR2: int > $o,P22: product_prod_int_int > $o] :
% 2.52/2.83 ( ( ( domainp_int_int
% 2.52/2.83 @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 ) )
% 2.52/2.83 = DR1 )
% 2.52/2.83 => ( ( ( domainp_int_int
% 2.52/2.83 @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 ) )
% 2.52/2.83 = DR2 )
% 2.52/2.83 => ( ( bNF_re8699439704749558557nt_o_o
% 2.52/2.83 @ ( basic_4387203522000727145nt_int
% 2.52/2.83 @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 2.52/2.83 @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 ) )
% 2.52/2.83 @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 2.52/2.83 @ P22
% 2.52/2.83 @ ^ [X2: product_prod_int_int] : ( ratrel @ X2 @ X2 ) )
% 2.52/2.83 => ( ( domain9213661015745956397nt_rat @ pcr_rat )
% 2.52/2.83 = ( inf_in3604695632404883862_int_o @ ( basic_1567116559311922317nt_int @ DR1 @ DR2 ) @ P22 ) ) ) ) ) ).
% 2.52/2.83
% 2.52/2.83 % rat.domain_par
% 2.52/2.83
% 2.52/2.83 % Helper facts (29)
% 2.52/2.83 thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 2.52/2.83 ! [X: int,Y: int] :
% 2.52/2.83 ( ( if_int @ $false @ X @ Y )
% 2.52/2.83 = Y ) ).
% 2.52/2.83
% 2.52/2.83 thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 2.52/2.83 ! [X: int,Y: int] :
% 2.52/2.83 ( ( if_int @ $true @ X @ Y )
% 2.52/2.83 = X ) ).
% 2.52/2.83
% 2.52/2.83 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 2.52/2.83 ! [X: nat,Y: nat] :
% 2.52/2.83 ( ( if_nat @ $false @ X @ Y )
% 2.52/2.83 = Y ) ).
% 2.52/2.83
% 2.52/2.83 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 2.52/2.83 ! [X: nat,Y: nat] :
% 2.52/2.83 ( ( if_nat @ $true @ X @ Y )
% 2.52/2.83 = X ) ).
% 2.52/2.83
% 2.52/2.83 thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 2.52/2.83 ! [X: num,Y: num] :
% 2.52/2.83 ( ( if_num @ $false @ X @ Y )
% 2.52/2.83 = Y ) ).
% 2.52/2.83
% 2.52/2.83 thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 2.52/2.83 ! [X: num,Y: num] :
% 2.52/2.83 ( ( if_num @ $true @ X @ Y )
% 2.52/2.83 = X ) ).
% 2.52/2.83
% 2.52/2.83 thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 2.52/2.83 ! [X: rat,Y: rat] :
% 2.52/2.83 ( ( if_rat @ $false @ X @ Y )
% 2.52/2.83 = Y ) ).
% 2.52/2.83
% 2.52/2.83 thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 2.52/2.83 ! [X: rat,Y: rat] :
% 2.52/2.83 ( ( if_rat @ $true @ X @ Y )
% 2.52/2.83 = X ) ).
% 2.52/2.83
% 2.52/2.83 thf(help_If_2_1_If_001t__Assertions__Oassn_T,axiom,
% 2.52/2.83 ! [X: assn,Y: assn] :
% 2.52/2.83 ( ( if_assn @ $false @ X @ Y )
% 2.52/2.83 = Y ) ).
% 2.52/2.83
% 2.52/2.83 thf(help_If_1_1_If_001t__Assertions__Oassn_T,axiom,
% 2.52/2.83 ! [X: assn,Y: assn] :
% 2.52/2.83 ( ( if_assn @ $true @ X @ Y )
% 2.52/2.83 = X ) ).
% 2.52/2.83
% 2.52/2.83 thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 2.52/2.83 ! [X: code_integer,Y: code_integer] :
% 2.52/2.83 ( ( if_Code_integer @ $false @ X @ Y )
% 2.52/2.83 = Y ) ).
% 2.52/2.83
% 2.52/2.83 thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 2.52/2.83 ! [X: code_integer,Y: code_integer] :
% 2.52/2.83 ( ( if_Code_integer @ $true @ X @ Y )
% 2.52/2.83 = X ) ).
% 2.52/2.83
% 2.52/2.83 thf(help_If_2_1_If_001t__Code____Numeral__Onatural_T,axiom,
% 2.52/2.83 ! [X: code_natural,Y: code_natural] :
% 2.52/2.83 ( ( if_Code_natural @ $false @ X @ Y )
% 2.52/2.83 = Y ) ).
% 2.52/2.83
% 2.52/2.83 thf(help_If_1_1_If_001t__Code____Numeral__Onatural_T,axiom,
% 2.52/2.83 ! [X: code_natural,Y: code_natural] :
% 2.52/2.83 ( ( if_Code_natural @ $true @ X @ Y )
% 2.52/2.83 = X ) ).
% 2.52/2.83
% 2.52/2.83 thf(help_If_2_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 2.52/2.83 ! [X: set_int,Y: set_int] :
% 2.52/2.83 ( ( if_set_int @ $false @ X @ Y )
% 2.52/2.83 = Y ) ).
% 2.52/2.83
% 2.52/2.83 thf(help_If_1_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 2.52/2.83 ! [X: set_int,Y: set_int] :
% 2.52/2.83 ( ( if_set_int @ $true @ X @ Y )
% 2.52/2.83 = X ) ).
% 2.52/2.83
% 2.52/2.83 thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 2.52/2.83 ! [X: list_int,Y: list_int] :
% 2.52/2.83 ( ( if_list_int @ $false @ X @ Y )
% 2.52/2.83 = Y ) ).
% 2.52/2.83
% 2.52/2.83 thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 2.52/2.83 ! [X: list_int,Y: list_int] :
% 2.52/2.83 ( ( if_list_int @ $true @ X @ Y )
% 2.52/2.83 = X ) ).
% 2.52/2.83
% 2.52/2.83 thf(help_If_2_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 2.52/2.83 ! [X: list_nat,Y: list_nat] :
% 2.52/2.83 ( ( if_list_nat @ $false @ X @ Y )
% 2.52/2.83 = Y ) ).
% 2.52/2.83
% 2.52/2.83 thf(help_If_1_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 2.52/2.83 ! [X: list_nat,Y: list_nat] :
% 2.52/2.83 ( ( if_list_nat @ $true @ X @ Y )
% 2.52/2.83 = X ) ).
% 2.52/2.83
% 2.52/2.83 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 2.52/2.83 ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 2.52/2.83 ( ( if_Pro3027730157355071871nt_int @ $false @ X @ Y )
% 2.52/2.83 = Y ) ).
% 2.52/2.83
% 2.52/2.83 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 2.52/2.83 ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 2.52/2.83 ( ( if_Pro3027730157355071871nt_int @ $true @ X @ Y )
% 2.52/2.83 = X ) ).
% 2.52/2.83
% 2.52/2.83 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 2.52/2.84 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 2.52/2.84 ( ( if_Pro6206227464963214023at_nat @ $false @ X @ Y )
% 2.52/2.84 = Y ) ).
% 2.52/2.84
% 2.52/2.84 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 2.52/2.84 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 2.52/2.84 ( ( if_Pro6206227464963214023at_nat @ $true @ X @ Y )
% 2.52/2.84 = X ) ).
% 2.52/2.84
% 2.52/2.84 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 2.52/2.84 ! [X: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 2.52/2.84 ( ( if_Pro5737122678794959658eger_o @ $false @ X @ Y )
% 2.52/2.84 = Y ) ).
% 2.52/2.84
% 2.52/2.84 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 2.52/2.84 ! [X: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 2.52/2.84 ( ( if_Pro5737122678794959658eger_o @ $true @ X @ Y )
% 2.52/2.84 = X ) ).
% 2.52/2.84
% 2.52/2.84 thf(help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 2.52/2.84 ! [P2: $o] :
% 2.52/3.48 ( ( P2 = $true )
% 2.52/3.48 | ( P2 = $false ) ) ).
% 2.52/3.48
% 2.52/3.48 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 2.52/3.48 ! [X: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 2.52/3.48 ( ( if_Pro6119634080678213985nteger @ $false @ X @ Y )
% 2.52/3.48 = Y ) ).
% 2.52/3.48
% 2.52/3.48 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 2.52/3.48 ! [X: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 2.52/3.48 ( ( if_Pro6119634080678213985nteger @ $true @ X @ Y )
% 2.52/3.48 = X ) ).
% 2.52/3.48
% 2.52/3.48 % Conjectures (1)
% 2.52/3.48 thf(conj_0,conjecture,
% 2.52/3.48 fI_QUERY @ p @ q @ f ).
% 2.52/3.48
% 2.52/3.48 %------------------------------------------------------------------------------
% 2.52/3.48 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.Nr1HNAV9G8/cvc5---1.0.5_4940.p...
% 2.52/3.48 (declare-sort $$unsorted 0)
% 2.52/3.48 (declare-sort tptp.list_P362550909693114634et_nat 0)
% 2.52/3.48 (declare-sort tptp.produc3251403909973641504n_assn 0)
% 2.52/3.48 (declare-sort tptp.produc2732055786443039994et_nat 0)
% 2.52/3.48 (declare-sort tptp.produc6691681559177096800n_assn 0)
% 2.52/3.48 (declare-sort tptp.produc858023921370090807n_assn 0)
% 2.52/3.48 (declare-sort tptp.list_P2321686559999237006et_nat 0)
% 2.52/3.48 (declare-sort tptp.produc6280221377895650458st_nat 0)
% 2.52/3.48 (declare-sort tptp.produc4920635200459206554st_int 0)
% 2.52/3.48 (declare-sort tptp.produc3272579373640082088n_assn 0)
% 2.52/3.48 (declare-sort tptp.produc4944321512348556200n_assn 0)
% 2.52/3.48 (declare-sort tptp.produc4530688714081574576n_assn 0)
% 2.52/3.48 (declare-sort tptp.produc3925858234332021118et_nat 0)
% 2.52/3.48 (declare-sort tptp.produc337509097454979815n_assn 0)
% 2.52/3.48 (declare-sort tptp.produc6155704871766690142st_nat 0)
% 2.52/3.48 (declare-sort tptp.produc141556263843406102st_int 0)
% 2.52/3.48 (declare-sort tptp.list_P28140577958321773n_assn 0)
% 2.52/3.48 (declare-sort tptp.produc4787317212837456354st_nat 0)
% 2.52/3.48 (declare-sort tptp.produc5847166148257158298st_int 0)
% 2.52/3.48 (declare-sort tptp.produc5074578776457504922st_nat 0)
% 2.52/3.48 (declare-sort tptp.produc6134427711877206866st_int 0)
% 2.52/3.48 (declare-sort tptp.produc8368264342088597808st_nat 0)
% 2.52/3.48 (declare-sort tptp.produc5625914783551145028st_int 0)
% 2.52/3.48 (declare-sort tptp.produc6654255674790325574st_nat 0)
% 2.52/3.48 (declare-sort tptp.produc4164172529858598818st_int 0)
% 2.52/3.48 (declare-sort tptp.produc2555908794901494476n_assn 0)
% 2.52/3.48 (declare-sort tptp.produc8582807064127716720n_assn 0)
% 2.52/3.48 (declare-sort tptp.produc6197004810343482825et_nat 0)
% 2.52/3.48 (declare-sort tptp.list_P7985473006766602707_nat_o 0)
% 2.52/3.48 (declare-sort tptp.produc5835291356934675326atural 0)
% 2.52/3.48 (declare-sort tptp.set_Pr4532377907799695533_nat_o 0)
% 2.52/3.48 (declare-sort tptp.list_P9062070895058802706et_nat 0)
% 2.52/3.48 (declare-sort tptp.list_P2911967483291296064sn_nat 0)
% 2.52/3.48 (declare-sort tptp.list_P421884338359569308sn_int 0)
% 2.52/3.48 (declare-sort tptp.list_P7711101519850957926n_assn 0)
% 2.52/3.48 (declare-sort tptp.list_P1495281457390866698n_assn 0)
% 2.52/3.48 (declare-sort tptp.produc3658429121746597890et_nat 0)
% 2.52/3.48 (declare-sort tptp.produc254973753779126261st_nat 0)
% 2.52/3.48 (declare-sort tptp.produc5834231552977413017st_int 0)
% 2.52/3.48 (declare-sort tptp.list_l6351802567095793725n_assn 0)
% 2.52/3.48 (declare-sort tptp.option7057359848497031415n_assn 0)
% 2.52/3.48 (declare-sort tptp.produc1828647624359046049st_nat 0)
% 2.52/3.48 (declare-sort tptp.produc8561936516282095101st_int 0)
% 2.52/3.48 (declare-sort tptp.produc3676724955757786621st_nat 0)
% 2.52/3.48 (declare-sort tptp.produc1186641810826059865st_int 0)
% 2.52/3.48 (declare-sort tptp.list_P8527749157015355191n_assn 0)
% 2.52/3.48 (declare-sort tptp.set_Pr5949110396991348497n_assn 0)
% 2.52/3.48 (declare-sort tptp.produc7822875418678951345atural 0)
% 2.52/3.48 (declare-sort tptp.produc8923325533196201883nteger 0)
% 2.52/3.48 (declare-sort tptp.list_h2745205591237434579t_unit 0)
% 2.52/3.48 (declare-sort tptp.list_P6011104703257516679at_nat 0)
% 2.52/3.48 (declare-sort tptp.list_P3521021558325789923at_int 0)
% 2.52/3.48 (declare-sort tptp.list_P8198026277950538467nt_nat 0)
% 2.52/3.48 (declare-sort tptp.list_P5707943133018811711nt_int 0)
% 2.52/3.48 (declare-sort tptp.set_Pr1261947904930325089at_nat 0)
% 2.52/3.48 (declare-sort tptp.set_Pr958786334691620121nt_int 0)
% 2.52/3.48 (declare-sort tptp.produc6575502325842934193n_assn 0)
% 2.52/3.48 (declare-sort tptp.produc6271795597528267376eger_o 0)
% 2.52/3.48 (declare-sort tptp.heap_T5738788834812785303t_unit 0)
% 2.52/3.48 (declare-sort tptp.heap_e7401611519738050253t_unit 0)
% 2.52/3.48 (declare-sort tptp.product_prod_nat_nat 0)
% 2.52/3.48 (declare-sort tptp.product_prod_nat_int 0)
% 2.52/3.48 (declare-sort tptp.product_prod_int_nat 0)
% 2.52/3.48 (declare-sort tptp.product_prod_int_int 0)
% 2.52/3.48 (declare-sort tptp.list_nat_nat 0)
% 2.52/3.48 (declare-sort tptp.list_int_nat 0)
% 2.52/3.48 (declare-sort tptp.list_list_nat 0)
% 2.52/3.48 (declare-sort tptp.list_list_int 0)
% 2.52/3.48 (declare-sort tptp.set_list_nat 0)
% 2.52/3.48 (declare-sort tptp.set_list_int 0)
% 2.52/3.48 (declare-sort tptp.list_set_nat 0)
% 2.52/3.48 (declare-sort tptp.set_Code_integer 0)
% 2.52/3.48 (declare-sort tptp.list_Product_unit 0)
% 2.52/3.48 (declare-sort tptp.set_Product_unit 0)
% 2.52/3.48 (declare-sort tptp.list_assn 0)
% 2.52/3.48 (declare-sort tptp.option_nat 0)
% 2.52/3.48 (declare-sort tptp.option_int 0)
% 2.52/3.48 (declare-sort tptp.list_nat 0)
% 2.52/3.48 (declare-sort tptp.list_int 0)
% 2.52/3.48 (declare-sort tptp.set_nat 0)
% 2.52/3.48 (declare-sort tptp.set_int 0)
% 2.52/3.48 (declare-sort tptp.code_natural 0)
% 2.52/3.48 (declare-sort tptp.code_integer 0)
% 2.52/3.48 (declare-sort tptp.product_unit 0)
% 2.52/3.48 (declare-sort tptp.typerep 0)
% 2.52/3.48 (declare-sort tptp.assn 0)
% 2.52/3.48 (declare-sort tptp.rat 0)
% 2.52/3.48 (declare-sort tptp.num 0)
% 2.52/3.48 (declare-sort tptp.nat 0)
% 2.52/3.48 (declare-sort tptp.int 0)
% 2.52/3.48 (declare-fun tptp.archim3151403230148437115or_rat (tptp.rat) tptp.int)
% 2.52/3.48 (declare-fun tptp.abs_assn ((-> tptp.produc3658429121746597890et_nat Bool)) tptp.assn)
% 2.52/3.48 (declare-fun tptp.rep_assn (tptp.assn tptp.produc3658429121746597890et_nat) Bool)
% 2.52/3.48 (declare-fun tptp.entails (tptp.assn tptp.assn) Bool)
% 2.52/3.48 (declare-fun tptp.entailst (tptp.assn tptp.assn) Bool)
% 2.52/3.48 (declare-fun tptp.in_range (tptp.produc3658429121746597890et_nat) Bool)
% 2.52/3.48 (declare-fun tptp.in_range_rel (tptp.produc3658429121746597890et_nat tptp.produc3658429121746597890et_nat) Bool)
% 2.52/3.48 (declare-fun tptp.is_pure_assn (tptp.assn) Bool)
% 2.52/3.48 (declare-fun tptp.one_assn_raw (tptp.produc3658429121746597890et_nat) Bool)
% 2.52/3.48 (declare-fun tptp.one_assn_raw_rel (tptp.produc3658429121746597890et_nat tptp.produc3658429121746597890et_nat) Bool)
% 2.52/3.48 (declare-fun tptp.proper ((-> tptp.produc3658429121746597890et_nat Bool)) Bool)
% 2.52/3.48 (declare-fun tptp.pure_assn (Bool) tptp.assn)
% 2.52/3.48 (declare-fun tptp.pure_a825153325127701367it_nat (Bool tptp.produc3658429121746597890et_nat) Bool)
% 2.52/3.48 (declare-fun tptp.relH (tptp.set_nat tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit) Bool)
% 2.52/3.48 (declare-fun tptp.times_assn_raw ((-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat) Bool)
% 2.52/3.48 (declare-fun tptp.times_assn_raw_rel (tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat) Bool)
% 2.52/3.48 (declare-fun tptp.wand_assn (tptp.assn tptp.assn) tptp.assn)
% 2.52/3.48 (declare-fun tptp.wand_raw ((-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat) Bool)
% 2.52/3.48 (declare-fun tptp.wand_raw_rel (tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat) Bool)
% 2.52/3.48 (declare-fun tptp.fi (tptp.list_P8527749157015355191n_assn tptp.assn tptp.assn tptp.assn tptp.assn tptp.assn) Bool)
% 2.52/3.48 (declare-fun tptp.fI_QUERY (tptp.assn tptp.assn tptp.assn) Bool)
% 2.52/3.48 (declare-fun tptp.fI_RESULT (tptp.list_P8527749157015355191n_assn tptp.assn tptp.assn tptp.assn) Bool)
% 2.52/3.48 (declare-fun tptp.sln () tptp.assn)
% 2.52/3.48 (declare-fun tptp.bNF_Ca8665028551170535155natLeq () tptp.set_Pr1261947904930325089at_nat)
% 2.52/3.48 (declare-fun tptp.bNF_re157797125943740599nt_int ((-> tptp.int tptp.int Bool) (-> (-> tptp.int tptp.product_prod_int_int) (-> tptp.int tptp.product_prod_int_int) Bool) (-> tptp.int tptp.int tptp.product_prod_int_int) (-> tptp.int tptp.int tptp.product_prod_int_int)) Bool)
% 2.52/3.48 (declare-fun tptp.bNF_re3461391660133120880nt_rat ((-> tptp.int tptp.int Bool) (-> (-> tptp.int tptp.product_prod_int_int) (-> tptp.int tptp.rat) Bool) (-> tptp.int tptp.int tptp.product_prod_int_int) (-> tptp.int tptp.int tptp.rat)) Bool)
% 2.52/3.48 (declare-fun tptp.bNF_re6250860962936578807nt_int ((-> tptp.int tptp.int Bool) (-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) (-> tptp.int tptp.product_prod_int_int) (-> tptp.int tptp.product_prod_int_int)) Bool)
% 2.52/3.48 (declare-fun tptp.bNF_re2214769303045360666nt_rat ((-> tptp.int tptp.int Bool) (-> tptp.product_prod_int_int tptp.rat Bool) (-> tptp.int tptp.product_prod_int_int) (-> tptp.int tptp.rat)) Bool)
% 2.52/3.48 (declare-fun tptp.bNF_re8699439704749558557nt_o_o ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) (-> Bool Bool Bool) (-> tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool)) Bool)
% 2.52/3.48 (declare-fun tptp.bNF_re7145576690424134365nt_int ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int tptp.product_prod_int_int) (-> tptp.product_prod_int_int tptp.product_prod_int_int)) Bool)
% 2.52/3.48 (declare-fun tptp.bNF_re8279943556446156061nt_rat ((-> tptp.product_prod_int_int tptp.rat Bool) (-> tptp.product_prod_int_int tptp.rat Bool) (-> tptp.product_prod_int_int tptp.product_prod_int_int) (-> tptp.rat tptp.rat)) Bool)
% 2.52/3.48 (declare-fun tptp.basic_1567116559311922317nt_int ((-> tptp.int Bool) (-> tptp.int Bool) tptp.product_prod_int_int) Bool)
% 2.52/3.48 (declare-fun tptp.basic_4387203522000727145nt_int ((-> tptp.int tptp.int Bool) (-> tptp.int tptp.int Bool) tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 2.52/3.48 (declare-fun tptp.binomial (tptp.nat tptp.nat) tptp.nat)
% 2.52/3.48 (declare-fun tptp.bit_and_int_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 2.52/3.48 (declare-fun tptp.bit_or_not_num_neg (tptp.num tptp.num) tptp.num)
% 2.52/3.48 (declare-fun tptp.bit_ri7632146776885996613nteger (tptp.code_integer) tptp.code_integer)
% 2.52/3.48 (declare-fun tptp.bit_ri7919022796975470100ot_int (tptp.int) tptp.int)
% 2.52/3.48 (declare-fun tptp.bit_ri6519982836138164636nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 2.52/3.48 (declare-fun tptp.bit_ri631733984087533419it_int (tptp.nat tptp.int) tptp.int)
% 2.52/3.48 (declare-fun tptp.bit_se3949692690581998587nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 2.52/3.48 (declare-fun tptp.bit_se2773287842338716102atural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 2.52/3.48 (declare-fun tptp.bit_se725231765392027082nd_int (tptp.int tptp.int) tptp.int)
% 2.52/3.48 (declare-fun tptp.bit_se727722235901077358nd_nat (tptp.nat tptp.nat) tptp.nat)
% 2.52/3.48 (declare-fun tptp.bit_se3928097537394005634nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 2.52/3.48 (declare-fun tptp.bit_se2751692689150723149atural (tptp.nat tptp.code_natural) tptp.code_natural)
% 2.52/3.48 (declare-fun tptp.bit_se8568078237143864401it_int (tptp.nat tptp.int) tptp.int)
% 2.52/3.48 (declare-fun tptp.bit_se8570568707652914677it_nat (tptp.nat tptp.nat) tptp.nat)
% 2.52/3.48 (declare-fun tptp.bit_se1345352211410354436nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 2.52/3.48 (declare-fun tptp.bit_se168947363167071951atural (tptp.nat tptp.code_natural) tptp.code_natural)
% 2.52/3.48 (declare-fun tptp.bit_se2159334234014336723it_int (tptp.nat tptp.int) tptp.int)
% 2.52/3.48 (declare-fun tptp.bit_se2161824704523386999it_nat (tptp.nat tptp.nat) tptp.nat)
% 2.52/3.48 (declare-fun tptp.bit_se2119862282449309892nteger (tptp.nat) tptp.code_integer)
% 2.52/3.48 (declare-fun tptp.bit_se943457434206027407atural (tptp.nat) tptp.code_natural)
% 2.52/3.48 (declare-fun tptp.bit_se2000444600071755411sk_int (tptp.nat) tptp.int)
% 2.52/3.48 (declare-fun tptp.bit_se2002935070580805687sk_nat (tptp.nat) tptp.nat)
% 2.52/3.48 (declare-fun tptp.bit_se1080825931792720795nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 2.52/3.48 (declare-fun tptp.bit_se9127793120404214118atural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 2.52/3.48 (declare-fun tptp.bit_se1409905431419307370or_int (tptp.int tptp.int) tptp.int)
% 2.52/3.48 (declare-fun tptp.bit_se1412395901928357646or_nat (tptp.nat tptp.nat) tptp.nat)
% 2.52/3.48 (declare-fun tptp.bit_se7788150548672797655nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 2.52/3.48 (declare-fun tptp.bit_se6611745700429515170atural (tptp.nat tptp.code_natural) tptp.code_natural)
% 2.52/3.48 (declare-fun tptp.bit_se545348938243370406it_int (tptp.nat tptp.int) tptp.int)
% 2.52/3.48 (declare-fun tptp.bit_se547839408752420682it_nat (tptp.nat tptp.nat) tptp.nat)
% 2.52/3.48 (declare-fun tptp.bit_se2793503036327961859nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 2.52/3.48 (declare-fun tptp.bit_se1617098188084679374atural (tptp.nat tptp.code_natural) tptp.code_natural)
% 2.52/3.48 (declare-fun tptp.bit_se7879613467334960850it_int (tptp.nat tptp.int) tptp.int)
% 2.52/3.48 (declare-fun tptp.bit_se7882103937844011126it_nat (tptp.nat tptp.nat) tptp.nat)
% 2.52/3.48 (declare-fun tptp.bit_se1745604003318907178nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 2.52/3.48 (declare-fun tptp.bit_se569199155075624693atural (tptp.nat tptp.code_natural) tptp.code_natural)
% 2.52/3.48 (declare-fun tptp.bit_se2923211474154528505it_int (tptp.nat tptp.int) tptp.int)
% 2.52/3.48 (declare-fun tptp.bit_se2925701944663578781it_nat (tptp.nat tptp.nat) tptp.nat)
% 2.52/3.48 (declare-fun tptp.bit_se8260200283734997820nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 2.52/3.48 (declare-fun tptp.bit_se7083795435491715335atural (tptp.nat tptp.code_natural) tptp.code_natural)
% 2.52/3.48 (declare-fun tptp.bit_se4203085406695923979it_int (tptp.nat tptp.int) tptp.int)
% 2.52/3.48 (declare-fun tptp.bit_se4205575877204974255it_nat (tptp.nat tptp.nat) tptp.nat)
% 2.52/3.48 (declare-fun tptp.bit_se3222712562003087583nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 2.52/3.48 (declare-fun tptp.bit_se2046307713759805098atural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 2.52/3.48 (declare-fun tptp.bit_se6526347334894502574or_int (tptp.int tptp.int) tptp.int)
% 2.52/3.48 (declare-fun tptp.bit_se6528837805403552850or_nat (tptp.nat tptp.nat) tptp.nat)
% 2.52/3.48 (declare-fun tptp.bit_se9216721137139052372nteger (tptp.code_integer tptp.nat) Bool)
% 2.52/3.48 (declare-fun tptp.bit_se8040316288895769887atural (tptp.code_natural tptp.nat) Bool)
% 2.52/3.48 (declare-fun tptp.bit_se1146084159140164899it_int (tptp.int tptp.nat) Bool)
% 2.52/3.48 (declare-fun tptp.bit_se1148574629649215175it_nat (tptp.nat tptp.nat) Bool)
% 2.52/3.48 (declare-fun tptp.boolea1849928419393854478_int_o ((-> (-> tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool) tptp.product_prod_int_int Bool) (-> (-> tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool) tptp.product_prod_int_int Bool) (-> (-> tptp.product_prod_int_int Bool) tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool)) Bool)
% 2.52/3.48 (declare-fun tptp.boolea5875918072483028530a_assn ((-> tptp.assn tptp.assn tptp.assn) (-> tptp.assn tptp.assn tptp.assn) (-> tptp.assn tptp.assn) tptp.assn tptp.assn) Bool)
% 2.52/3.48 (declare-fun tptp.boolea5643492148547655015nteger ((-> tptp.code_integer tptp.code_integer tptp.code_integer) (-> tptp.code_integer tptp.code_integer tptp.code_integer) (-> tptp.code_integer tptp.code_integer) tptp.code_integer tptp.code_integer) Bool)
% 2.52/3.48 (declare-fun tptp.boolea5469654029284665142ra_int ((-> tptp.int tptp.int tptp.int) (-> tptp.int tptp.int tptp.int) (-> tptp.int tptp.int) tptp.int tptp.int) Bool)
% 2.52/3.48 (declare-fun tptp.boolea5824373010784320748et_int ((-> tptp.set_int tptp.set_int tptp.set_int) (-> tptp.set_int tptp.set_int tptp.set_int) (-> tptp.set_int tptp.set_int) tptp.set_int tptp.set_int) Bool)
% 2.52/3.48 (declare-fun tptp.boolea778851993438741648et_nat ((-> tptp.set_nat tptp.set_nat tptp.set_nat) (-> tptp.set_nat tptp.set_nat tptp.set_nat) (-> tptp.set_nat tptp.set_nat) tptp.set_nat tptp.set_nat) Bool)
% 2.52/3.48 (declare-fun tptp.boolea949959532490082519at_nat ((-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) (-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) (-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 2.52/3.48 (declare-fun tptp.boolea3191171876098928227t_unit ((-> tptp.set_Product_unit tptp.set_Product_unit tptp.set_Product_unit) (-> tptp.set_Product_unit tptp.set_Product_unit tptp.set_Product_unit) (-> tptp.set_Product_unit tptp.set_Product_unit) tptp.set_Product_unit tptp.set_Product_unit) Bool)
% 2.52/3.48 (declare-fun tptp.boolea2445317508997433345nteger ((-> tptp.code_integer tptp.code_integer tptp.code_integer) (-> tptp.code_integer tptp.code_integer tptp.code_integer) (-> tptp.code_integer tptp.code_integer) tptp.code_integer tptp.code_integer (-> tptp.code_integer tptp.code_integer tptp.code_integer)) Bool)
% 2.52/3.48 (declare-fun tptp.boolea8527374999097803216ff_int ((-> tptp.int tptp.int tptp.int) (-> tptp.int tptp.int tptp.int) (-> tptp.int tptp.int) tptp.int tptp.int (-> tptp.int tptp.int tptp.int)) Bool)
% 2.52/3.48 (declare-fun tptp.code_Pos (tptp.num) tptp.code_integer)
% 2.52/3.48 (declare-fun tptp.code_Suc (tptp.code_natural) tptp.code_natural)
% 2.52/3.49 (declare-fun tptp.code_bit_cut_integer (tptp.code_integer) tptp.produc6271795597528267376eger_o)
% 2.52/3.49 (declare-fun tptp.code_divmod_abs (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 2.52/3.49 (declare-fun tptp.code_divmod_integer (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 2.52/3.49 (declare-fun tptp.code_dup (tptp.code_integer) tptp.code_integer)
% 2.52/3.49 (declare-fun tptp.code_int_of_integer (tptp.code_integer) tptp.int)
% 2.52/3.49 (declare-fun tptp.code_integer_of_int (tptp.int) tptp.code_integer)
% 2.52/3.49 (declare-fun tptp.code_integer_of_nat (tptp.nat) tptp.code_integer)
% 2.52/3.49 (declare-fun tptp.code_integer_of_num (tptp.num) tptp.code_integer)
% 2.52/3.49 (declare-fun tptp.code_nat_of_integer (tptp.code_integer) tptp.nat)
% 2.52/3.49 (declare-fun tptp.code_nat_of_natural (tptp.code_natural) tptp.nat)
% 2.52/3.49 (declare-fun tptp.code_natural_of_nat (tptp.nat) tptp.code_natural)
% 2.52/3.49 (declare-fun tptp.code_num_of_integer (tptp.code_integer) tptp.num)
% 2.52/3.49 (declare-fun tptp.code_pcr_integer (tptp.int tptp.code_integer) Bool)
% 2.52/3.49 (declare-fun tptp.code_pcr_natural (tptp.nat tptp.code_natural) Bool)
% 2.52/3.49 (declare-fun tptp.code_sub (tptp.num tptp.num) tptp.code_integer)
% 2.52/3.49 (declare-fun tptp.adjust_div (tptp.product_prod_int_int) tptp.int)
% 2.52/3.49 (declare-fun tptp.adjust_mod (tptp.int tptp.int) tptp.int)
% 2.52/3.49 (declare-fun tptp.eucl_rel_int (tptp.int tptp.int tptp.product_prod_int_int) Bool)
% 2.52/3.49 (declare-fun tptp.unique3479559517661332726nteger (tptp.num tptp.num) tptp.produc8923325533196201883nteger)
% 2.52/3.49 (declare-fun tptp.unique5052692396658037445od_int (tptp.num tptp.num) tptp.product_prod_int_int)
% 2.52/3.49 (declare-fun tptp.unique5055182867167087721od_nat (tptp.num tptp.num) tptp.product_prod_nat_nat)
% 2.52/3.49 (declare-fun tptp.unique4921790084139445826nteger (tptp.num tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 2.52/3.49 (declare-fun tptp.unique5024387138958732305ep_int (tptp.num tptp.product_prod_int_int) tptp.product_prod_int_int)
% 2.52/3.49 (declare-fun tptp.unique5026877609467782581ep_nat (tptp.num tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 2.52/3.49 (declare-fun tptp.euclid3395696857347342551nt_int (tptp.int) tptp.int)
% 2.52/3.49 (declare-fun tptp.euclid3398187327856392827nt_nat (tptp.nat) tptp.nat)
% 2.52/3.49 (declare-fun tptp.semiri1408675320244567234ct_nat (tptp.nat) tptp.nat)
% 2.52/3.49 (declare-fun tptp.inverse_inverse_rat (tptp.rat) tptp.rat)
% 2.52/3.49 (declare-fun tptp.finite_card_int (tptp.set_int) tptp.nat)
% 2.52/3.49 (declare-fun tptp.finite_card_list_nat (tptp.set_list_nat) tptp.nat)
% 2.52/3.49 (declare-fun tptp.finite410649719033368117t_unit (tptp.set_Product_unit) tptp.nat)
% 2.52/3.49 (declare-fun tptp.finite_finite_int (tptp.set_int) Bool)
% 2.52/3.49 (declare-fun tptp.finite3922522038869484883st_int (tptp.set_list_int) Bool)
% 2.52/3.49 (declare-fun tptp.finite8100373058378681591st_nat (tptp.set_list_nat) Bool)
% 2.52/3.49 (declare-fun tptp.finite_finite_nat (tptp.set_nat) Bool)
% 2.52/3.49 (declare-fun tptp.finite6177210948735845034at_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 2.52/3.49 (declare-fun tptp.comp_C8797469213163452608nteger ((-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) (-> tptp.code_integer tptp.code_integer tptp.code_integer) tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 2.52/3.49 (declare-fun tptp.comp_o_o_int ((-> Bool Bool) (-> tptp.int Bool) tptp.int) Bool)
% 2.52/3.49 (declare-fun tptp.comp_o_o_nat ((-> Bool Bool) (-> tptp.nat Bool) tptp.nat) Bool)
% 2.52/3.49 (declare-fun tptp.comp_C1593894019821074884nteger ((-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) (-> tptp.code_integer tptp.code_integer) tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 2.52/3.49 (declare-fun tptp.id_int (tptp.int) tptp.int)
% 2.52/3.49 (declare-fun tptp.map_fu7831380289885515383nt_rat ((-> tptp.int tptp.int) (-> (-> tptp.int tptp.product_prod_int_int) tptp.int tptp.rat) (-> tptp.int tptp.int tptp.product_prod_int_int) tptp.int tptp.int) tptp.rat)
% 2.52/3.49 (declare-fun tptp.map_fu3424225382358772769nt_rat ((-> tptp.int tptp.int) (-> tptp.product_prod_int_int tptp.rat) (-> tptp.int tptp.product_prod_int_int) tptp.int) tptp.rat)
% 2.52/3.49 (declare-fun tptp.map_fu5673905371560938248nt_rat ((-> tptp.rat tptp.product_prod_int_int) (-> tptp.product_prod_int_int tptp.rat) (-> tptp.product_prod_int_int tptp.product_prod_int_int) tptp.rat) tptp.rat)
% 2.52/3.49 (declare-fun tptp.gcd_Gcd_nat (tptp.set_nat) tptp.nat)
% 2.52/3.49 (declare-fun tptp.gcd_Lcm_int (tptp.set_int) tptp.int)
% 2.52/3.49 (declare-fun tptp.gcd_Lcm_nat (tptp.set_nat) tptp.nat)
% 2.52/3.49 (declare-fun tptp.bezw (tptp.nat tptp.nat) tptp.product_prod_int_int)
% 2.52/3.49 (declare-fun tptp.bezw_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 2.52/3.49 (declare-fun tptp.gcd_gcd_int (tptp.int tptp.int) tptp.int)
% 2.52/3.49 (declare-fun tptp.gcd_gcd_nat (tptp.nat tptp.nat) tptp.nat)
% 2.52/3.49 (declare-fun tptp.gcd_lcm_int (tptp.int tptp.int) tptp.int)
% 2.52/3.49 (declare-fun tptp.gcd_lcm_nat (tptp.nat tptp.nat) tptp.nat)
% 2.52/3.49 (declare-fun tptp.abel_s3861158783995384302_int_o ((-> (-> tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool) tptp.product_prod_int_int Bool)) Bool)
% 2.52/3.49 (declare-fun tptp.abel_semigroup_assn ((-> tptp.assn tptp.assn tptp.assn)) Bool)
% 2.52/3.49 (declare-fun tptp.abel_s8772020223019846471nteger ((-> tptp.code_integer tptp.code_integer tptp.code_integer)) Bool)
% 2.52/3.49 (declare-fun tptp.abel_s7595615374776563986atural ((-> tptp.code_natural tptp.code_natural tptp.code_natural)) Bool)
% 2.52/3.49 (declare-fun tptp.abel_semigroup_int ((-> tptp.int tptp.int tptp.int)) Bool)
% 2.52/3.49 (declare-fun tptp.abel_semigroup_nat ((-> tptp.nat tptp.nat tptp.nat)) Bool)
% 2.52/3.49 (declare-fun tptp.abel_semigroup_rat ((-> tptp.rat tptp.rat tptp.rat)) Bool)
% 2.52/3.49 (declare-fun tptp.abel_s3907380067910933104et_nat ((-> tptp.set_nat tptp.set_nat tptp.set_nat)) Bool)
% 2.52/3.49 (declare-fun tptp.abel_s1357164767337380599at_nat ((-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat)) Bool)
% 2.52/3.49 (declare-fun tptp.abs_abs_Code_integer (tptp.code_integer) tptp.code_integer)
% 2.52/3.49 (declare-fun tptp.abs_abs_int (tptp.int) tptp.int)
% 2.52/3.49 (declare-fun tptp.abs_abs_rat (tptp.rat) tptp.rat)
% 2.52/3.49 (declare-fun tptp.comm_m5839176995973721103_int_o ((-> (-> tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool) tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool)) Bool)
% 2.52/3.49 (declare-fun tptp.comm_monoid_assn ((-> tptp.assn tptp.assn tptp.assn) tptp.assn) Bool)
% 2.52/3.49 (declare-fun tptp.comm_m1654649897431166824nteger ((-> tptp.code_integer tptp.code_integer tptp.code_integer) tptp.code_integer) Bool)
% 2.52/3.49 (declare-fun tptp.comm_m478245049187884339atural ((-> tptp.code_natural tptp.code_natural tptp.code_natural) tptp.code_natural) Bool)
% 2.52/3.49 (declare-fun tptp.comm_monoid_int ((-> tptp.int tptp.int tptp.int) tptp.int) Bool)
% 2.52/3.49 (declare-fun tptp.comm_monoid_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat) Bool)
% 2.52/3.49 (declare-fun tptp.comm_monoid_rat ((-> tptp.rat tptp.rat tptp.rat) tptp.rat) Bool)
% 2.52/3.49 (declare-fun tptp.comm_monoid_set_int ((-> tptp.set_int tptp.set_int tptp.set_int) tptp.set_int) Bool)
% 2.52/3.49 (declare-fun tptp.comm_monoid_set_nat ((-> tptp.set_nat tptp.set_nat tptp.set_nat) tptp.set_nat) Bool)
% 2.52/3.49 (declare-fun tptp.comm_m5709050211238513046at_nat ((-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat) Bool)
% 2.52/3.49 (declare-fun tptp.comm_m7591727228438362018t_unit ((-> tptp.set_Product_unit tptp.set_Product_unit tptp.set_Product_unit) tptp.set_Product_unit) Bool)
% 2.52/3.49 (declare-fun tptp.minus_711738161318947805_int_o ((-> tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 2.52/3.49 (declare-fun tptp.minus_minus_assn (tptp.assn tptp.assn) tptp.assn)
% 2.52/3.49 (declare-fun tptp.minus_8373710615458151222nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 2.52/3.49 (declare-fun tptp.minus_7197305767214868737atural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 2.52/3.49 (declare-fun tptp.minus_minus_int (tptp.int tptp.int) tptp.int)
% 2.52/3.49 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat)
% 2.52/3.49 (declare-fun tptp.minus_minus_rat (tptp.rat tptp.rat) tptp.rat)
% 2.52/3.49 (declare-fun tptp.minus_minus_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 2.52/3.49 (declare-fun tptp.minus_minus_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 2.52/3.49 (declare-fun tptp.minus_1356011639430497352at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 2.52/3.49 (declare-fun tptp.monoid6910981727789844035_int_o ((-> (-> tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool) tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool)) Bool)
% 2.52/3.49 (declare-fun tptp.monoid_assn ((-> tptp.assn tptp.assn tptp.assn) tptp.assn) Bool)
% 2.52/3.49 (declare-fun tptp.monoid_Code_integer ((-> tptp.code_integer tptp.code_integer tptp.code_integer) tptp.code_integer) Bool)
% 2.52/3.49 (declare-fun tptp.monoid_Code_natural ((-> tptp.code_natural tptp.code_natural tptp.code_natural) tptp.code_natural) Bool)
% 2.52/3.49 (declare-fun tptp.monoid_int ((-> tptp.int tptp.int tptp.int) tptp.int) Bool)
% 2.52/3.49 (declare-fun tptp.monoid_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat) Bool)
% 2.52/3.49 (declare-fun tptp.monoid_rat ((-> tptp.rat tptp.rat tptp.rat) tptp.rat) Bool)
% 2.52/3.49 (declare-fun tptp.monoid_set_int ((-> tptp.set_int tptp.set_int tptp.set_int) tptp.set_int) Bool)
% 2.52/3.49 (declare-fun tptp.monoid_set_nat ((-> tptp.set_nat tptp.set_nat tptp.set_nat) tptp.set_nat) Bool)
% 2.52/3.49 (declare-fun tptp.monoid1519094961268053602at_nat ((-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat) Bool)
% 2.52/3.49 (declare-fun tptp.monoid202360481972076142t_unit ((-> tptp.set_Product_unit tptp.set_Product_unit tptp.set_Product_unit) tptp.set_Product_unit) Bool)
% 2.52/3.49 (declare-fun tptp.one_one_assn () tptp.assn)
% 2.52/3.49 (declare-fun tptp.one_one_Code_integer () tptp.code_integer)
% 2.52/3.49 (declare-fun tptp.one_one_Code_natural () tptp.code_natural)
% 2.52/3.49 (declare-fun tptp.one_one_int () tptp.int)
% 2.52/3.49 (declare-fun tptp.one_one_nat () tptp.nat)
% 2.52/3.49 (declare-fun tptp.one_one_rat () tptp.rat)
% 2.52/3.49 (declare-fun tptp.plus_p5714425477246183910nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 2.52/3.49 (declare-fun tptp.plus_p4538020629002901425atural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 2.52/3.49 (declare-fun tptp.plus_plus_int (tptp.int tptp.int) tptp.int)
% 2.52/3.49 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 2.52/3.49 (declare-fun tptp.plus_plus_num (tptp.num tptp.num) tptp.num)
% 2.52/3.49 (declare-fun tptp.plus_plus_rat (tptp.rat tptp.rat) tptp.rat)
% 2.52/3.49 (declare-fun tptp.semigr8095932293087610038_int_o ((-> (-> tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool) tptp.product_prod_int_int Bool)) Bool)
% 2.52/3.49 (declare-fun tptp.semigroup_assn ((-> tptp.assn tptp.assn tptp.assn)) Bool)
% 2.52/3.49 (declare-fun tptp.semigr7036097719740861967nteger ((-> tptp.code_integer tptp.code_integer tptp.code_integer)) Bool)
% 2.52/3.49 (declare-fun tptp.semigr5859692871497579482atural ((-> tptp.code_natural tptp.code_natural tptp.code_natural)) Bool)
% 2.52/3.49 (declare-fun tptp.semigroup_int ((-> tptp.int tptp.int tptp.int)) Bool)
% 2.52/3.49 (declare-fun tptp.semigroup_nat ((-> tptp.nat tptp.nat tptp.nat)) Bool)
% 2.52/3.49 (declare-fun tptp.semigroup_rat ((-> tptp.rat tptp.rat tptp.rat)) Bool)
% 2.52/3.49 (declare-fun tptp.semigroup_set_nat ((-> tptp.set_nat tptp.set_nat tptp.set_nat)) Bool)
% 2.52/3.49 (declare-fun tptp.semigr3814207799437385263at_nat ((-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat)) Bool)
% 2.52/3.49 (declare-fun tptp.sgn_sgn_Code_integer (tptp.code_integer) tptp.code_integer)
% 2.52/3.49 (declare-fun tptp.sgn_sgn_int (tptp.int) tptp.int)
% 2.52/3.49 (declare-fun tptp.sgn_sgn_rat (tptp.rat) tptp.rat)
% 2.52/3.49 (declare-fun tptp.times_times_assn (tptp.assn tptp.assn) tptp.assn)
% 2.52/3.49 (declare-fun tptp.times_3573771949741848930nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 2.52/3.49 (declare-fun tptp.times_2397367101498566445atural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 2.52/3.49 (declare-fun tptp.times_times_int (tptp.int tptp.int) tptp.int)
% 2.52/3.49 (declare-fun tptp.times_times_nat (tptp.nat tptp.nat) tptp.nat)
% 2.52/3.49 (declare-fun tptp.times_times_num (tptp.num tptp.num) tptp.num)
% 2.52/3.49 (declare-fun tptp.times_times_rat (tptp.rat tptp.rat) tptp.rat)
% 2.52/3.49 (declare-fun tptp.uminus7117520113953359693_int_o ((-> tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 2.52/3.49 (declare-fun tptp.uminus_uminus_assn (tptp.assn) tptp.assn)
% 2.52/3.49 (declare-fun tptp.uminus1351360451143612070nteger (tptp.code_integer) tptp.code_integer)
% 2.52/3.49 (declare-fun tptp.uminus_uminus_int (tptp.int) tptp.int)
% 2.52/3.49 (declare-fun tptp.uminus_uminus_rat (tptp.rat) tptp.rat)
% 2.52/3.49 (declare-fun tptp.uminus1532241313380277803et_int (tptp.set_int) tptp.set_int)
% 2.52/3.49 (declare-fun tptp.uminus5710092332889474511et_nat (tptp.set_nat) tptp.set_nat)
% 2.52/3.49 (declare-fun tptp.uminus6524753893492686040at_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 2.52/3.49 (declare-fun tptp.uminus5944136376168626660t_unit (tptp.set_Product_unit) tptp.set_Product_unit)
% 2.52/3.49 (declare-fun tptp.zero_z3403309356797280102nteger () tptp.code_integer)
% 2.52/3.49 (declare-fun tptp.zero_z2226904508553997617atural () tptp.code_natural)
% 2.52/3.49 (declare-fun tptp.zero_zero_int () tptp.int)
% 2.52/3.49 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 2.52/3.49 (declare-fun tptp.zero_zero_rat () tptp.rat)
% 2.52/3.49 (declare-fun tptp.groups4538972089207619220nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 2.52/3.49 (declare-fun tptp.groups3542108847815614940at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 2.52/3.49 (declare-fun tptp.groups708209901874060359at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 2.52/3.49 (declare-fun tptp.groups4561878855575611511st_nat (tptp.list_nat) tptp.nat)
% 2.52/3.49 (declare-fun tptp.nO_MAT8252062027627875367nteger (tptp.code_integer tptp.code_integer) Bool)
% 2.52/3.49 (declare-fun tptp.nO_MAT2693162092599435762nteger (tptp.code_natural tptp.code_integer) Bool)
% 2.52/3.49 (declare-fun tptp.nO_MAT4469370267861770177al_int (tptp.code_natural tptp.int) Bool)
% 2.52/3.49 (declare-fun tptp.nO_MAT9066612773553876470nteger (tptp.int tptp.code_integer) Bool)
% 2.52/3.49 (declare-fun tptp.nO_MAT7890207925310593985atural (tptp.int tptp.code_natural) Bool)
% 2.52/3.49 (declare-fun tptp.nO_MATCH_int_int (tptp.int tptp.int) Bool)
% 2.52/3.49 (declare-fun tptp.nO_MATCH_int_nat (tptp.int tptp.nat) Bool)
% 2.52/3.49 (declare-fun tptp.nO_MATCH_int_rat (tptp.int tptp.rat) Bool)
% 2.52/3.49 (declare-fun tptp.nO_MAT8694959213317031834nteger (tptp.nat tptp.code_integer) Bool)
% 2.52/3.49 (declare-fun tptp.nO_MAT7518554365073749349atural (tptp.nat tptp.code_natural) Bool)
% 2.52/3.49 (declare-fun tptp.nO_MATCH_nat_int (tptp.nat tptp.int) Bool)
% 2.52/3.49 (declare-fun tptp.nO_MATCH_nat_nat (tptp.nat tptp.nat) Bool)
% 2.52/3.49 (declare-fun tptp.nO_MATCH_nat_rat (tptp.nat tptp.rat) Bool)
% 2.52/3.49 (declare-fun tptp.nO_MAT243659986023775650nteger (tptp.rat tptp.code_integer) Bool)
% 2.52/3.49 (declare-fun tptp.nO_MATCH_rat_int (tptp.rat tptp.int) Bool)
% 2.52/3.49 (declare-fun tptp.nO_MATCH_rat_rat (tptp.rat tptp.rat) Bool)
% 2.52/3.49 (declare-fun tptp.the_int ((-> tptp.int Bool)) tptp.int)
% 2.52/3.49 (declare-fun tptp.arrays_Product_unit (tptp.heap_e7401611519738050253t_unit tptp.typerep tptp.nat) tptp.list_nat)
% 2.52/3.49 (declare-fun tptp.lim_Product_unit (tptp.heap_e7401611519738050253t_unit) tptp.nat)
% 2.52/3.49 (declare-fun tptp.refs_Product_unit (tptp.heap_e7401611519738050253t_unit tptp.typerep tptp.nat) tptp.nat)
% 2.52/3.49 (declare-fun tptp.heap_Time_wait (tptp.nat) tptp.heap_T5738788834812785303t_unit)
% 2.52/3.49 (declare-fun tptp.hoare_8945653483474564448t_unit (tptp.assn tptp.heap_T5738788834812785303t_unit (-> tptp.product_unit tptp.assn)) Bool)
% 2.52/3.49 (declare-fun tptp.if_assn (Bool tptp.assn tptp.assn) tptp.assn)
% 2.52/3.49 (declare-fun tptp.if_Code_integer (Bool tptp.code_integer tptp.code_integer) tptp.code_integer)
% 2.52/3.49 (declare-fun tptp.if_Code_natural (Bool tptp.code_natural tptp.code_natural) tptp.code_natural)
% 2.52/3.49 (declare-fun tptp.if_int (Bool tptp.int tptp.int) tptp.int)
% 2.52/3.49 (declare-fun tptp.if_list_int (Bool tptp.list_int tptp.list_int) tptp.list_int)
% 2.52/3.49 (declare-fun tptp.if_list_nat (Bool tptp.list_nat tptp.list_nat) tptp.list_nat)
% 2.52/3.49 (declare-fun tptp.if_nat (Bool tptp.nat tptp.nat) tptp.nat)
% 2.52/3.49 (declare-fun tptp.if_num (Bool tptp.num tptp.num) tptp.num)
% 2.52/3.49 (declare-fun tptp.if_Pro5737122678794959658eger_o (Bool tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o) tptp.produc6271795597528267376eger_o)
% 2.52/3.49 (declare-fun tptp.if_Pro6119634080678213985nteger (Bool tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 2.52/3.49 (declare-fun tptp.if_Pro3027730157355071871nt_int (Bool tptp.product_prod_int_int tptp.product_prod_int_int) tptp.product_prod_int_int)
% 2.52/3.49 (declare-fun tptp.if_Pro6206227464963214023at_nat (Bool tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 2.52/3.49 (declare-fun tptp.if_rat (Bool tptp.rat tptp.rat) tptp.rat)
% 2.52/3.49 (declare-fun tptp.if_set_int (Bool tptp.set_int tptp.set_int) tptp.set_int)
% 2.52/3.49 (declare-fun tptp.abs_Integ (tptp.product_prod_nat_nat) tptp.int)
% 2.52/3.49 (declare-fun tptp.pos (tptp.num) tptp.int)
% 2.52/3.49 (declare-fun tptp.dup (tptp.int) tptp.int)
% 2.52/3.49 (declare-fun tptp.intrel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 2.52/3.49 (declare-fun tptp.nat2 (tptp.int) tptp.nat)
% 2.52/3.49 (declare-fun tptp.pcr_int (tptp.product_prod_nat_nat tptp.int) Bool)
% 2.52/3.49 (declare-fun tptp.ring_1_of_int_rat (tptp.int) tptp.rat)
% 2.52/3.49 (declare-fun tptp.sub (tptp.num tptp.num) tptp.int)
% 2.52/3.49 (declare-fun tptp.inf_in3604695632404883862_int_o ((-> tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 2.52/3.49 (declare-fun tptp.inf_inf_o (Bool Bool) Bool)
% 2.52/3.49 (declare-fun tptp.inf_inf_assn (tptp.assn tptp.assn) tptp.assn)
% 2.52/3.49 (declare-fun tptp.inf_inf_int (tptp.int tptp.int) tptp.int)
% 2.52/3.49 (declare-fun tptp.inf_inf_nat (tptp.nat tptp.nat) tptp.nat)
% 2.52/3.49 (declare-fun tptp.inf_inf_Product_unit (tptp.product_unit tptp.product_unit) tptp.product_unit)
% 2.52/3.49 (declare-fun tptp.inf_inf_rat (tptp.rat tptp.rat) tptp.rat)
% 2.52/3.49 (declare-fun tptp.inf_in1906310914598751387_nat_o (tptp.set_Pr4532377907799695533_nat_o tptp.set_Pr4532377907799695533_nat_o) tptp.set_Pr4532377907799695533_nat_o)
% 2.52/3.49 (declare-fun tptp.inf_inf_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 2.52/3.49 (declare-fun tptp.inf_inf_set_list_nat (tptp.set_list_nat tptp.set_list_nat) tptp.set_list_nat)
% 2.52/3.49 (declare-fun tptp.inf_inf_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 2.52/3.49 (declare-fun tptp.inf_in2572325071724192079at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 2.52/3.49 (declare-fun tptp.inf_in4660618365625256667t_unit (tptp.set_Product_unit tptp.set_Product_unit) tptp.set_Product_unit)
% 2.52/3.49 (declare-fun tptp.semila1175464891343163876_int_o ((-> (-> tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool) tptp.product_prod_int_int Bool)) Bool)
% 2.52/3.49 (declare-fun tptp.semilattice_assn ((-> tptp.assn tptp.assn tptp.assn)) Bool)
% 2.52/3.49 (declare-fun tptp.semilattice_int ((-> tptp.int tptp.int tptp.int)) Bool)
% 2.52/3.49 (declare-fun tptp.semilattice_nat ((-> tptp.nat tptp.nat tptp.nat)) Bool)
% 2.52/3.49 (declare-fun tptp.semilattice_set_nat ((-> tptp.set_nat tptp.set_nat tptp.set_nat)) Bool)
% 2.52/3.49 (declare-fun tptp.semila6306352305301525377at_nat ((-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat)) Bool)
% 2.52/3.49 (declare-fun tptp.semila6538661356715008162_int_o ((-> (-> tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool) tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool)) Bool)
% 2.52/3.49 (declare-fun tptp.semila5388846958306562758r_assn ((-> tptp.assn tptp.assn tptp.assn) tptp.assn) Bool)
% 2.52/3.49 (declare-fun tptp.semila6106414119144251899nteger ((-> tptp.code_integer tptp.code_integer tptp.code_integer) tptp.code_integer) Bool)
% 2.52/3.49 (declare-fun tptp.semila9079005292280841162tr_int ((-> tptp.int tptp.int tptp.int) tptp.int) Bool)
% 2.52/3.49 (declare-fun tptp.semila6287294981380917632et_int ((-> tptp.set_int tptp.set_int tptp.set_int) tptp.set_int) Bool)
% 2.52/3.49 (declare-fun tptp.semila1241773964035338532et_nat ((-> tptp.set_nat tptp.set_nat tptp.set_nat) tptp.set_nat) Bool)
% 2.52/3.49 (declare-fun tptp.semila858173770281612099at_nat ((-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat) Bool)
% 2.52/3.49 (declare-fun tptp.semila7638931295954862799t_unit ((-> tptp.set_Product_unit tptp.set_Product_unit tptp.set_Product_unit) tptp.set_Product_unit) Bool)
% 2.52/3.49 (declare-fun tptp.semila8052717425514686422_int_o ((-> (-> tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool) tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool) (-> (-> tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool) Bool) (-> (-> tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool) Bool)) Bool)
% 2.52/3.49 (declare-fun tptp.semila8603258263270017530r_assn ((-> tptp.assn tptp.assn tptp.assn) tptp.assn (-> tptp.assn tptp.assn Bool) (-> tptp.assn tptp.assn Bool)) Bool)
% 2.52/3.49 (declare-fun tptp.semila1667268886620078168et_nat ((-> tptp.set_nat tptp.set_nat tptp.set_nat) tptp.set_nat (-> tptp.set_nat tptp.set_nat Bool) (-> tptp.set_nat tptp.set_nat Bool)) Bool)
% 2.52/3.49 (declare-fun tptp.semila4918476307565957903at_nat ((-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat (-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool) (-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)) Bool)
% 2.52/3.49 (declare-fun tptp.semila4423693302617054363t_unit ((-> tptp.set_Product_unit tptp.set_Product_unit tptp.set_Product_unit) tptp.set_Product_unit (-> tptp.set_Product_unit tptp.set_Product_unit Bool) (-> tptp.set_Product_unit tptp.set_Product_unit Bool)) Bool)
% 2.52/3.49 (declare-fun tptp.sup_su8463660629351352368_int_o ((-> tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 2.52/3.49 (declare-fun tptp.sup_sup_assn (tptp.assn tptp.assn) tptp.assn)
% 2.52/3.49 (declare-fun tptp.sup_sup_int (tptp.int tptp.int) tptp.int)
% 2.52/3.49 (declare-fun tptp.sup_sup_nat (tptp.nat tptp.nat) tptp.nat)
% 2.52/3.49 (declare-fun tptp.sup_sup_rat (tptp.rat tptp.rat) tptp.rat)
% 2.52/3.49 (declare-fun tptp.sup_sup_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 2.52/3.49 (declare-fun tptp.sup_sup_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 2.52/3.49 (declare-fun tptp.sup_su6327502436637775413at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 2.52/3.49 (declare-fun tptp.sup_su793286257634532545t_unit (tptp.set_Product_unit tptp.set_Product_unit) tptp.set_Product_unit)
% 2.52/3.49 (declare-fun tptp.lattic7826324295020591184_F_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat tptp.set_nat) tptp.nat)
% 2.52/3.49 (declare-fun tptp.all_interval_int ((-> tptp.int Bool) tptp.int tptp.int) Bool)
% 2.52/3.49 (declare-fun tptp.all_interval_nat ((-> tptp.nat Bool) tptp.nat tptp.nat) Bool)
% 2.52/3.49 (declare-fun tptp.append_int (tptp.list_int tptp.list_int) tptp.list_int)
% 2.52/3.49 (declare-fun tptp.append_nat (tptp.list_nat tptp.list_nat) tptp.list_nat)
% 2.52/3.49 (declare-fun tptp.bind_int_int (tptp.list_int (-> tptp.int tptp.list_int)) tptp.list_int)
% 2.52/3.49 (declare-fun tptp.bind_int_nat (tptp.list_int (-> tptp.int tptp.list_nat)) tptp.list_nat)
% 2.52/3.49 (declare-fun tptp.bind_i4941608653131063484n_assn (tptp.list_int (-> tptp.int tptp.list_P8527749157015355191n_assn)) tptp.list_P8527749157015355191n_assn)
% 2.52/3.49 (declare-fun tptp.bind_nat_int (tptp.list_nat (-> tptp.nat tptp.list_int)) tptp.list_int)
% 2.52/3.49 (declare-fun tptp.bind_nat_nat (tptp.list_nat (-> tptp.nat tptp.list_nat)) tptp.list_nat)
% 2.52/3.49 (declare-fun tptp.bind_n3181571989377952280n_assn (tptp.list_nat (-> tptp.nat tptp.list_P8527749157015355191n_assn)) tptp.list_P8527749157015355191n_assn)
% 2.52/3.49 (declare-fun tptp.bind_P8081679045764635286sn_int (tptp.list_P8527749157015355191n_assn (-> tptp.produc6575502325842934193n_assn tptp.list_int)) tptp.list_int)
% 2.52/3.49 (declare-fun tptp.bind_P8084169516273685562sn_nat (tptp.list_P8527749157015355191n_assn (-> tptp.produc6575502325842934193n_assn tptp.list_nat)) tptp.list_nat)
% 2.52/3.49 (declare-fun tptp.bind_P5664457578022171847n_assn (tptp.list_P8527749157015355191n_assn (-> tptp.produc6575502325842934193n_assn tptp.list_P8527749157015355191n_assn)) tptp.list_P8527749157015355191n_assn)
% 2.52/3.49 (declare-fun tptp.butlast_nat (tptp.list_nat) tptp.list_nat)
% 2.52/3.49 (declare-fun tptp.coset_int (tptp.list_int) tptp.set_int)
% 2.52/3.49 (declare-fun tptp.coset_nat (tptp.list_nat) tptp.set_nat)
% 2.52/3.49 (declare-fun tptp.coset_703488708621576356n_assn (tptp.list_P8527749157015355191n_assn) tptp.set_Pr5949110396991348497n_assn)
% 2.52/3.49 (declare-fun tptp.coset_Product_unit (tptp.list_Product_unit) tptp.set_Product_unit)
% 2.52/3.49 (declare-fun tptp.count_list_int (tptp.list_int tptp.int) tptp.nat)
% 2.52/3.49 (declare-fun tptp.count_list_nat (tptp.list_nat tptp.nat) tptp.nat)
% 2.52/3.49 (declare-fun tptp.count_2530312006313534765n_assn (tptp.list_P8527749157015355191n_assn tptp.produc6575502325842934193n_assn) tptp.nat)
% 2.52/3.49 (declare-fun tptp.distinct_int (tptp.list_int) Bool)
% 2.52/3.49 (declare-fun tptp.distinct_nat (tptp.list_nat) Bool)
% 2.52/3.49 (declare-fun tptp.drop_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 2.52/3.49 (declare-fun tptp.enumerate_int (tptp.nat tptp.list_int) tptp.list_P3521021558325789923at_int)
% 2.52/3.49 (declare-fun tptp.enumerate_nat (tptp.nat tptp.list_nat) tptp.list_P6011104703257516679at_nat)
% 2.52/3.49 (declare-fun tptp.enumer9200277086812776726n_assn (tptp.nat tptp.list_P8527749157015355191n_assn) tptp.list_P7711101519850957926n_assn)
% 2.52/3.49 (declare-fun tptp.fold_int_int ((-> tptp.int tptp.int tptp.int) tptp.list_int tptp.int) tptp.int)
% 2.52/3.49 (declare-fun tptp.fold_nat_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.list_nat tptp.nat) tptp.nat)
% 2.52/3.49 (declare-fun tptp.foldr_assn_assn ((-> tptp.assn tptp.assn tptp.assn) tptp.list_assn tptp.assn) tptp.assn)
% 2.52/3.49 (declare-fun tptp.gen_length_int (tptp.nat tptp.list_int) tptp.nat)
% 2.52/3.49 (declare-fun tptp.gen_length_nat (tptp.nat tptp.list_nat) tptp.nat)
% 2.52/3.49 (declare-fun tptp.gen_le1182329135810803268n_assn (tptp.nat tptp.list_P8527749157015355191n_assn) tptp.nat)
% 2.52/3.49 (declare-fun tptp.insert_int (tptp.int tptp.list_int) tptp.list_int)
% 2.52/3.49 (declare-fun tptp.insert_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 2.52/3.49 (declare-fun tptp.insert3246601298802261197n_assn (tptp.produc6575502325842934193n_assn tptp.list_P8527749157015355191n_assn) tptp.list_P8527749157015355191n_assn)
% 2.52/3.49 (declare-fun tptp.last_nat (tptp.list_nat) tptp.nat)
% 2.52/3.49 (declare-fun tptp.linord1735203802627413978nt_int ((-> tptp.int tptp.int) tptp.list_int) tptp.list_int)
% 2.52/3.49 (declare-fun tptp.linord738340561235409698at_nat ((-> tptp.nat tptp.nat) tptp.list_nat) tptp.list_nat)
% 2.52/3.49 (declare-fun tptp.linord2612477271533052124et_int (tptp.set_int) tptp.list_int)
% 2.52/3.49 (declare-fun tptp.linord2614967742042102400et_nat (tptp.set_nat) tptp.list_nat)
% 2.52/3.49 (declare-fun tptp.cons_int_nat ((-> tptp.int tptp.nat) tptp.list_int_nat) tptp.list_int_nat)
% 2.52/3.49 (declare-fun tptp.cons_nat_nat ((-> tptp.nat tptp.nat) tptp.list_nat_nat) tptp.list_nat_nat)
% 2.52/3.49 (declare-fun tptp.cons_P6219271836124797827_nat_o ((-> tptp.produc3658429121746597890et_nat Bool) tptp.list_P7985473006766602707_nat_o) tptp.list_P7985473006766602707_nat_o)
% 2.52/3.49 (declare-fun tptp.cons_assn (tptp.assn tptp.list_assn) tptp.list_assn)
% 2.52/3.49 (declare-fun tptp.cons_h4161061858534515843t_unit (tptp.heap_e7401611519738050253t_unit tptp.list_h2745205591237434579t_unit) tptp.list_h2745205591237434579t_unit)
% 2.52/3.49 (declare-fun tptp.cons_int (tptp.int tptp.list_int) tptp.list_int)
% 2.52/3.49 (declare-fun tptp.cons_list_int (tptp.list_int tptp.list_list_int) tptp.list_list_int)
% 2.52/3.49 (declare-fun tptp.cons_list_nat (tptp.list_nat tptp.list_list_nat) tptp.list_list_nat)
% 2.52/3.49 (declare-fun tptp.cons_l2423627976422276333n_assn (tptp.list_P8527749157015355191n_assn tptp.list_l6351802567095793725n_assn) tptp.list_l6351802567095793725n_assn)
% 2.52/3.49 (declare-fun tptp.cons_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 2.52/3.49 (declare-fun tptp.cons_P6329468272379687876et_nat (tptp.produc2732055786443039994et_nat tptp.list_P362550909693114634et_nat) tptp.list_P362550909693114634et_nat)
% 2.52/3.49 (declare-fun tptp.cons_P3419706843779801160et_nat (tptp.produc3925858234332021118et_nat tptp.list_P2321686559999237006et_nat) tptp.list_P2321686559999237006et_nat)
% 2.52/3.49 (declare-fun tptp.cons_P2971678138204555879n_assn (tptp.produc6575502325842934193n_assn tptp.list_P8527749157015355191n_assn) tptp.list_P8527749157015355191n_assn)
% 2.52/3.49 (declare-fun tptp.cons_P2869003950965171916et_nat (tptp.produc3658429121746597890et_nat tptp.list_P9062070895058802706et_nat) tptp.list_P9062070895058802706et_nat)
% 2.52/3.49 (declare-fun tptp.cons_P3334398858971670639nt_int (tptp.product_prod_int_int tptp.list_P5707943133018811711nt_int) tptp.list_P5707943133018811711nt_int)
% 2.52/3.49 (declare-fun tptp.cons_P7512249878480867347nt_nat (tptp.product_prod_int_nat tptp.list_P8198026277950538467nt_nat) tptp.list_P8198026277950538467nt_nat)
% 2.52/3.49 (declare-fun tptp.cons_P2335045147070616083at_int (tptp.product_prod_nat_int tptp.list_P3521021558325789923at_int) tptp.list_P3521021558325789923at_int)
% 2.52/3.49 (declare-fun tptp.cons_P6512896166579812791at_nat (tptp.product_prod_nat_nat tptp.list_P6011104703257516679at_nat) tptp.list_P6011104703257516679at_nat)
% 2.52/3.49 (declare-fun tptp.cons_set_nat (tptp.set_nat tptp.list_set_nat) tptp.list_set_nat)
% 2.52/3.49 (declare-fun tptp.nil_int_nat () tptp.list_int_nat)
% 2.52/3.49 (declare-fun tptp.nil_nat_nat () tptp.list_nat_nat)
% 2.52/3.49 (declare-fun tptp.nil_assn () tptp.list_assn)
% 2.52/3.49 (declare-fun tptp.nil_int () tptp.list_int)
% 2.52/3.49 (declare-fun tptp.nil_list_int () tptp.list_list_int)
% 2.52/3.49 (declare-fun tptp.nil_list_nat () tptp.list_list_nat)
% 2.52/3.49 (declare-fun tptp.nil_li5476096274760905021n_assn () tptp.list_l6351802567095793725n_assn)
% 2.52/3.49 (declare-fun tptp.nil_nat () tptp.list_nat)
% 2.52/3.49 (declare-fun tptp.nil_Pr5671120429643327159n_assn () tptp.list_P8527749157015355191n_assn)
% 2.52/3.49 (declare-fun tptp.nil_Pr2300489316682597567nt_int () tptp.list_P5707943133018811711nt_int)
% 2.52/3.49 (declare-fun tptp.nil_Pr6478340336191794275nt_nat () tptp.list_P8198026277950538467nt_nat)
% 2.52/3.49 (declare-fun tptp.nil_Pr2440414457004260852n_assn () tptp.list_P1495281457390866698n_assn)
% 2.52/3.49 (declare-fun tptp.nil_Pr1301135604781543011at_int () tptp.list_P3521021558325789923at_int)
% 2.52/3.49 (declare-fun tptp.nil_Pr5478986624290739719at_nat () tptp.list_P6011104703257516679at_nat)
% 2.52/3.49 (declare-fun tptp.nil_Pr680377793251149648n_assn () tptp.list_P7711101519850957926n_assn)
% 2.52/3.49 (declare-fun tptp.nil_Pr7991254345159696774sn_int () tptp.list_P421884338359569308sn_int)
% 2.52/3.49 (declare-fun tptp.nil_Pr2945733327814117674sn_nat () tptp.list_P2911967483291296064sn_nat)
% 2.52/3.49 (declare-fun tptp.nil_Pr4327835960982145133n_assn () tptp.list_P28140577958321773n_assn)
% 2.52/3.49 (declare-fun tptp.nil_Product_unit () tptp.list_Product_unit)
% 2.52/3.49 (declare-fun tptp.hd_nat (tptp.list_nat) tptp.nat)
% 2.52/3.49 (declare-fun tptp.list_all_int ((-> tptp.int Bool) tptp.list_int) Bool)
% 2.52/3.49 (declare-fun tptp.list_all_nat ((-> tptp.nat Bool) tptp.list_nat) Bool)
% 2.52/3.49 (declare-fun tptp.map_int_assn ((-> tptp.int tptp.assn) tptp.list_int) tptp.list_assn)
% 2.52/3.49 (declare-fun tptp.map_int_int ((-> tptp.int tptp.int) tptp.list_int) tptp.list_int)
% 2.52/3.49 (declare-fun tptp.map_int_nat ((-> tptp.int tptp.nat) tptp.list_int) tptp.list_nat)
% 2.52/3.49 (declare-fun tptp.map_in4427992030928829247n_assn ((-> tptp.int tptp.produc6575502325842934193n_assn) tptp.list_int) tptp.list_P8527749157015355191n_assn)
% 2.52/3.49 (declare-fun tptp.map_nat_assn ((-> tptp.nat tptp.assn) tptp.list_nat) tptp.list_assn)
% 2.52/3.49 (declare-fun tptp.map_nat_int ((-> tptp.nat tptp.int) tptp.list_nat) tptp.list_int)
% 2.52/3.49 (declare-fun tptp.map_nat_nat ((-> tptp.nat tptp.nat) tptp.list_nat) tptp.list_nat)
% 2.52/3.49 (declare-fun tptp.map_na2667955367175718043n_assn ((-> tptp.nat tptp.produc6575502325842934193n_assn) tptp.list_nat) tptp.list_P8527749157015355191n_assn)
% 2.52/3.49 (declare-fun tptp.map_Pr8991440229025900053n_assn ((-> tptp.produc6575502325842934193n_assn tptp.assn) tptp.list_P8527749157015355191n_assn) tptp.list_assn)
% 2.52/3.49 (declare-fun tptp.map_Pr7568062423562401049sn_int ((-> tptp.produc6575502325842934193n_assn tptp.int) tptp.list_P8527749157015355191n_assn) tptp.list_int)
% 2.52/3.49 (declare-fun tptp.map_Pr7570552894071451325sn_nat ((-> tptp.produc6575502325842934193n_assn tptp.nat) tptp.list_P8527749157015355191n_assn) tptp.list_nat)
% 2.52/3.49 (declare-fun tptp.map_Pr7925354932063753860n_assn ((-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn) tptp.list_P8527749157015355191n_assn) tptp.list_P8527749157015355191n_assn)
% 2.52/3.49 (declare-fun tptp.map_Pr7042224834074979589t_unit ((-> tptp.produc3658429121746597890et_nat tptp.heap_e7401611519738050253t_unit) tptp.list_P9062070895058802706et_nat) tptp.list_h2745205591237434579t_unit)
% 2.52/3.49 (declare-fun tptp.map_Pr4871828589360411470et_nat ((-> tptp.produc3658429121746597890et_nat tptp.set_nat) tptp.list_P9062070895058802706et_nat) tptp.list_set_nat)
% 2.52/3.49 (declare-fun tptp.map_Pr6494458893431244577nt_int ((-> tptp.product_prod_int_int tptp.int) tptp.list_P5707943133018811711nt_int) tptp.list_int)
% 2.52/3.49 (declare-fun tptp.map_Pr4307537318738222789at_int ((-> tptp.product_prod_int_nat tptp.int) tptp.list_P8198026277950538467nt_nat) tptp.list_int)
% 2.52/3.49 (declare-fun tptp.map_Pr4310027789247273065at_nat ((-> tptp.product_prod_int_nat tptp.nat) tptp.list_P8198026277950538467nt_nat) tptp.list_nat)
% 2.52/3.49 (declare-fun tptp.map_Pr6122805333194399941nt_int ((-> tptp.product_prod_nat_int tptp.int) tptp.list_P3521021558325789923at_int) tptp.list_int)
% 2.52/3.49 (declare-fun tptp.map_Pr6125295803703450217nt_nat ((-> tptp.product_prod_nat_int tptp.nat) tptp.list_P3521021558325789923at_int) tptp.list_nat)
% 2.52/3.49 (declare-fun tptp.map_Pr3938374229010428429at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.list_P6011104703257516679at_nat) tptp.list_nat)
% 2.52/3.49 (declare-fun tptp.set_int2 (tptp.list_int) tptp.set_int)
% 2.52/3.49 (declare-fun tptp.set_nat2 (tptp.list_nat) tptp.set_nat)
% 2.52/3.49 (declare-fun tptp.set_Pr1139785259514867910n_assn (tptp.list_P8527749157015355191n_assn) tptp.set_Pr5949110396991348497n_assn)
% 2.52/3.49 (declare-fun tptp.tl_nat (tptp.list_nat) tptp.list_nat)
% 2.52/3.49 (declare-fun tptp.list_ex1_int ((-> tptp.int Bool) tptp.list_int) Bool)
% 2.52/3.49 (declare-fun tptp.list_ex1_nat ((-> tptp.nat Bool) tptp.list_nat) Bool)
% 2.52/3.49 (declare-fun tptp.list_e7761433933450087034n_assn ((-> tptp.produc6575502325842934193n_assn Bool) tptp.list_P8527749157015355191n_assn) Bool)
% 2.52/3.49 (declare-fun tptp.list_ex_int ((-> tptp.int Bool) tptp.list_int) Bool)
% 2.52/3.49 (declare-fun tptp.list_ex_nat ((-> tptp.nat Bool) tptp.list_nat) Bool)
% 2.52/3.49 (declare-fun tptp.list_e1087220904399170805n_assn ((-> tptp.produc6575502325842934193n_assn Bool) tptp.list_P8527749157015355191n_assn) Bool)
% 2.52/3.49 (declare-fun tptp.map_filter_int_int ((-> tptp.int tptp.option_int) tptp.list_int) tptp.list_int)
% 2.52/3.49 (declare-fun tptp.map_filter_int_nat ((-> tptp.int tptp.option_nat) tptp.list_int) tptp.list_nat)
% 2.52/3.49 (declare-fun tptp.map_fi5526074278189050041n_assn ((-> tptp.int tptp.option7057359848497031415n_assn) tptp.list_int) tptp.list_P8527749157015355191n_assn)
% 2.52/3.49 (declare-fun tptp.map_filter_nat_int ((-> tptp.nat tptp.option_int) tptp.list_nat) tptp.list_int)
% 2.52/3.49 (declare-fun tptp.map_filter_nat_nat ((-> tptp.nat tptp.option_nat) tptp.list_nat) tptp.list_nat)
% 2.52/3.49 (declare-fun tptp.map_fi3766037614435938837n_assn ((-> tptp.nat tptp.option7057359848497031415n_assn) tptp.list_nat) tptp.list_P8527749157015355191n_assn)
% 2.52/3.49 (declare-fun tptp.map_fi8666144670822621843sn_int ((-> tptp.produc6575502325842934193n_assn tptp.option_int) tptp.list_P8527749157015355191n_assn) tptp.list_int)
% 2.52/3.49 (declare-fun tptp.map_fi8668635141331672119sn_nat ((-> tptp.produc6575502325842934193n_assn tptp.option_nat) tptp.list_P8527749157015355191n_assn) tptp.list_nat)
% 2.52/3.49 (declare-fun tptp.map_fi2680429960852639882n_assn ((-> tptp.produc6575502325842934193n_assn tptp.option7057359848497031415n_assn) tptp.list_P8527749157015355191n_assn) tptp.list_P8527749157015355191n_assn)
% 2.52/3.49 (declare-fun tptp.map_tailrec_nat_nat ((-> tptp.nat tptp.nat) tptp.list_nat) tptp.list_nat)
% 2.52/3.49 (declare-fun tptp.map_ta2194206859901583947n_assn ((-> tptp.produc6575502325842934193n_assn tptp.assn) tptp.list_P8527749157015355191n_assn) tptp.list_assn)
% 2.52/3.49 (declare-fun tptp.maps_int_int ((-> tptp.int tptp.list_int) tptp.list_int) tptp.list_int)
% 2.52/3.49 (declare-fun tptp.maps_int_nat ((-> tptp.int tptp.list_nat) tptp.list_int) tptp.list_nat)
% 2.52/3.49 (declare-fun tptp.maps_i2843482286296025986n_assn ((-> tptp.int tptp.list_P8527749157015355191n_assn) tptp.list_int) tptp.list_P8527749157015355191n_assn)
% 2.52/3.49 (declare-fun tptp.maps_nat_int ((-> tptp.nat tptp.list_int) tptp.list_nat) tptp.list_int)
% 2.52/3.49 (declare-fun tptp.maps_nat_nat ((-> tptp.nat tptp.list_nat) tptp.list_nat) tptp.list_nat)
% 2.52/3.49 (declare-fun tptp.maps_n1083445622542914782n_assn ((-> tptp.nat tptp.list_P8527749157015355191n_assn) tptp.list_nat) tptp.list_P8527749157015355191n_assn)
% 2.52/3.49 (declare-fun tptp.maps_P5983552678929597788sn_int ((-> tptp.produc6575502325842934193n_assn tptp.list_int) tptp.list_P8527749157015355191n_assn) tptp.list_int)
% 2.52/3.49 (declare-fun tptp.maps_P5986043149438648064sn_nat ((-> tptp.produc6575502325842934193n_assn tptp.list_nat) tptp.list_P8527749157015355191n_assn) tptp.list_nat)
% 2.52/3.49 (declare-fun tptp.maps_P4274076103917212289n_assn ((-> tptp.produc6575502325842934193n_assn tptp.list_P8527749157015355191n_assn) tptp.list_P8527749157015355191n_assn) tptp.list_P8527749157015355191n_assn)
% 2.52/3.49 (declare-fun tptp.measures_int (tptp.list_int_nat) tptp.set_Pr958786334691620121nt_int)
% 2.52/3.49 (declare-fun tptp.measures_nat (tptp.list_nat_nat) tptp.set_Pr1261947904930325089at_nat)
% 2.52/3.49 (declare-fun tptp.member_int (tptp.list_int tptp.int) Bool)
% 2.52/3.49 (declare-fun tptp.member_nat (tptp.list_nat tptp.nat) Bool)
% 2.52/3.49 (declare-fun tptp.member743271071679453132n_assn (tptp.list_P8527749157015355191n_assn tptp.produc6575502325842934193n_assn) Bool)
% 2.52/3.49 (declare-fun tptp.n_lists_int (tptp.nat tptp.list_int) tptp.list_list_int)
% 2.52/3.49 (declare-fun tptp.n_lists_nat (tptp.nat tptp.list_nat) tptp.list_list_nat)
% 2.52/3.49 (declare-fun tptp.n_list679713369942834879n_assn (tptp.nat tptp.list_P8527749157015355191n_assn) tptp.list_l6351802567095793725n_assn)
% 2.52/3.49 (declare-fun tptp.nth_Pr6840583978799713108_nat_o (tptp.list_P7985473006766602707_nat_o tptp.nat tptp.produc3658429121746597890et_nat) Bool)
% 2.52/3.49 (declare-fun tptp.nth_assn (tptp.list_assn tptp.nat) tptp.assn)
% 2.52/3.49 (declare-fun tptp.nth_he7452997726511547988t_unit (tptp.list_h2745205591237434579t_unit tptp.nat) tptp.heap_e7401611519738050253t_unit)
% 2.52/3.49 (declare-fun tptp.nth_int (tptp.list_int tptp.nat) tptp.int)
% 2.52/3.49 (declare-fun tptp.nth_nat (tptp.list_nat tptp.nat) tptp.nat)
% 2.52/3.49 (declare-fun tptp.nth_Pr7590663101126261939et_nat (tptp.list_P362550909693114634et_nat tptp.nat) tptp.produc2732055786443039994et_nat)
% 2.52/3.49 (declare-fun tptp.nth_Pr3610913089060847927et_nat (tptp.list_P2321686559999237006et_nat tptp.nat) tptp.produc3925858234332021118et_nat)
% 2.52/3.49 (declare-fun tptp.nth_Pr1769885009046257848n_assn (tptp.list_P8527749157015355191n_assn tptp.nat) tptp.produc6575502325842934193n_assn)
% 2.52/3.49 (declare-fun tptp.nth_Pr7683458668995092411et_nat (tptp.list_P9062070895058802706et_nat tptp.nat) tptp.produc3658429121746597890et_nat)
% 2.52/3.49 (declare-fun tptp.nth_Pr4439495888332055232nt_int (tptp.list_P5707943133018811711nt_int tptp.nat) tptp.product_prod_int_int)
% 2.52/3.49 (declare-fun tptp.nth_Pr8617346907841251940nt_nat (tptp.list_P8198026277950538467nt_nat tptp.nat) tptp.product_prod_int_nat)
% 2.52/3.49 (declare-fun tptp.nth_Pr3440142176431000676at_int (tptp.list_P3521021558325789923at_int tptp.nat) tptp.product_prod_nat_int)
% 2.52/3.49 (declare-fun tptp.nth_Pr7617993195940197384at_nat (tptp.list_P6011104703257516679at_nat tptp.nat) tptp.product_prod_nat_nat)
% 2.52/3.49 (declare-fun tptp.nth_set_nat (tptp.list_set_nat tptp.nat) tptp.set_nat)
% 2.52/3.49 (declare-fun tptp.nths_assn (tptp.list_assn tptp.set_nat) tptp.list_assn)
% 2.52/3.49 (declare-fun tptp.nths_int (tptp.list_int tptp.set_nat) tptp.list_int)
% 2.52/3.49 (declare-fun tptp.nths_nat (tptp.list_nat tptp.set_nat) tptp.list_nat)
% 2.52/3.49 (declare-fun tptp.nths_P5537322223065504949n_assn (tptp.list_P8527749157015355191n_assn tptp.set_nat) tptp.list_P8527749157015355191n_assn)
% 2.52/3.49 (declare-fun tptp.null_int (tptp.list_int) Bool)
% 2.52/3.49 (declare-fun tptp.null_nat (tptp.list_nat) Bool)
% 2.52/3.49 (declare-fun tptp.null_P7596217980778516671n_assn (tptp.list_P8527749157015355191n_assn) Bool)
% 2.52/3.49 (declare-fun tptp.produc7119410244218060998et_nat (tptp.list_P7985473006766602707_nat_o tptp.list_P2321686559999237006et_nat) tptp.list_P362550909693114634et_nat)
% 2.52/3.49 (declare-fun tptp.produc2866688925348378442et_nat (tptp.list_P7985473006766602707_nat_o tptp.list_P9062070895058802706et_nat) tptp.list_P2321686559999237006et_nat)
% 2.52/3.49 (declare-fun tptp.product_assn_assn (tptp.list_assn tptp.list_assn) tptp.list_P8527749157015355191n_assn)
% 2.52/3.49 (declare-fun tptp.produc7481864959766642638et_nat (tptp.list_h2745205591237434579t_unit tptp.list_set_nat) tptp.list_P9062070895058802706et_nat)
% 2.52/3.49 (declare-fun tptp.product_int_int (tptp.list_int tptp.list_int) tptp.list_P5707943133018811711nt_int)
% 2.52/3.49 (declare-fun tptp.product_int_nat (tptp.list_int tptp.list_nat) tptp.list_P8198026277950538467nt_nat)
% 2.52/3.49 (declare-fun tptp.product_nat_int (tptp.list_nat tptp.list_int) tptp.list_P3521021558325789923at_int)
% 2.52/3.49 (declare-fun tptp.product_nat_nat (tptp.list_nat tptp.list_nat) tptp.list_P6011104703257516679at_nat)
% 2.52/3.49 (declare-fun tptp.product_lists_int (tptp.list_list_int) tptp.list_list_int)
% 2.52/3.49 (declare-fun tptp.product_lists_nat (tptp.list_list_nat) tptp.list_list_nat)
% 2.52/3.49 (declare-fun tptp.produc1566369527784499744n_assn (tptp.list_l6351802567095793725n_assn) tptp.list_l6351802567095793725n_assn)
% 2.52/3.49 (declare-fun tptp.remdups_nat (tptp.list_nat) tptp.list_nat)
% 2.52/3.49 (declare-fun tptp.rotate1_assn (tptp.list_assn) tptp.list_assn)
% 2.52/3.49 (declare-fun tptp.rotate1_int (tptp.list_int) tptp.list_int)
% 2.52/3.49 (declare-fun tptp.rotate1_nat (tptp.list_nat) tptp.list_nat)
% 2.52/3.49 (declare-fun tptp.rotate328796349445179396n_assn (tptp.list_P8527749157015355191n_assn) tptp.list_P8527749157015355191n_assn)
% 2.52/3.49 (declare-fun tptp.sorted_wrt_int ((-> tptp.int tptp.int Bool) tptp.list_int) Bool)
% 2.52/3.49 (declare-fun tptp.sorted_wrt_nat ((-> tptp.nat tptp.nat Bool) tptp.list_nat) Bool)
% 2.52/3.49 (declare-fun tptp.splice_int (tptp.list_int tptp.list_int) tptp.list_int)
% 2.52/3.49 (declare-fun tptp.splice_nat (tptp.list_nat tptp.list_nat) tptp.list_nat)
% 2.52/3.49 (declare-fun tptp.splice4588524007259616650n_assn (tptp.list_P8527749157015355191n_assn tptp.list_P8527749157015355191n_assn) tptp.list_P8527749157015355191n_assn)
% 2.52/3.49 (declare-fun tptp.subseqs_int (tptp.list_int) tptp.list_list_int)
% 2.52/3.49 (declare-fun tptp.subseqs_nat (tptp.list_nat) tptp.list_list_nat)
% 2.52/3.49 (declare-fun tptp.subseq184808802919281286n_assn (tptp.list_P8527749157015355191n_assn) tptp.list_l6351802567095793725n_assn)
% 2.52/3.49 (declare-fun tptp.take_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 2.52/3.49 (declare-fun tptp.upt (tptp.nat tptp.nat) tptp.list_nat)
% 2.52/3.49 (declare-fun tptp.upto (tptp.int tptp.int) tptp.list_int)
% 2.52/3.49 (declare-fun tptp.upto_aux (tptp.int tptp.int tptp.list_int) tptp.list_int)
% 2.52/3.49 (declare-fun tptp.upto_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 2.52/3.49 (declare-fun tptp.zip_Pr8136144321567152340et_nat (tptp.list_P7985473006766602707_nat_o tptp.list_P2321686559999237006et_nat) tptp.list_P362550909693114634et_nat)
% 2.52/3.49 (declare-fun tptp.zip_Pr7134870689397686104et_nat (tptp.list_P7985473006766602707_nat_o tptp.list_P9062070895058802706et_nat) tptp.list_P2321686559999237006et_nat)
% 2.52/3.49 (declare-fun tptp.zip_assn_assn (tptp.list_assn tptp.list_assn) tptp.list_P8527749157015355191n_assn)
% 2.52/3.49 (declare-fun tptp.zip_he6711929980790699996et_nat (tptp.list_h2745205591237434579t_unit tptp.list_set_nat) tptp.list_P9062070895058802706et_nat)
% 2.52/3.49 (declare-fun tptp.zip_int_int (tptp.list_int tptp.list_int) tptp.list_P5707943133018811711nt_int)
% 2.52/3.49 (declare-fun tptp.zip_int_nat (tptp.list_int tptp.list_nat) tptp.list_P8198026277950538467nt_nat)
% 2.52/3.49 (declare-fun tptp.zip_in7098856637274830732n_assn (tptp.list_int tptp.list_P8527749157015355191n_assn) tptp.list_P1495281457390866698n_assn)
% 2.52/3.49 (declare-fun tptp.zip_nat_int (tptp.list_nat tptp.list_int) tptp.list_P3521021558325789923at_int)
% 2.52/3.49 (declare-fun tptp.zip_nat_nat (tptp.list_nat tptp.list_nat) tptp.list_P6011104703257516679at_nat)
% 2.52/3.49 (declare-fun tptp.zip_na5338819973521719528n_assn (tptp.list_nat tptp.list_P8527749157015355191n_assn) tptp.list_P7711101519850957926n_assn)
% 2.52/3.49 (declare-fun tptp.zip_Pr1015554993053626726sn_int (tptp.list_P8527749157015355191n_assn tptp.list_int) tptp.list_P421884338359569308sn_int)
% 2.52/3.49 (declare-fun tptp.zip_Pr1018045463562677002sn_nat (tptp.list_P8527749157015355191n_assn tptp.list_nat) tptp.list_P2911967483291296064sn_nat)
% 2.52/3.49 (declare-fun tptp.zip_Pr8806919808394484215n_assn (tptp.list_P8527749157015355191n_assn tptp.list_P8527749157015355191n_assn) tptp.list_P28140577958321773n_assn)
% 2.52/3.49 (declare-fun tptp.list_c1842222907148955684sn_int ((-> tptp.assn tptp.set_int) tptp.list_assn) tptp.set_int)
% 2.52/3.49 (declare-fun tptp.list_c1844713377658005960sn_nat ((-> tptp.assn tptp.set_nat) tptp.list_assn) tptp.set_nat)
% 2.52/3.49 (declare-fun tptp.list_c3449203510989861672nt_int ((-> tptp.int tptp.set_int) tptp.list_int) tptp.set_int)
% 2.52/3.49 (declare-fun tptp.list_c3451693981498911948nt_nat ((-> tptp.int tptp.set_nat) tptp.list_int) tptp.set_nat)
% 2.52/3.49 (declare-fun tptp.list_c2449849799088807116at_int ((-> tptp.nat tptp.set_int) tptp.list_nat) tptp.set_int)
% 2.52/3.49 (declare-fun tptp.list_c2452340269597857392at_nat ((-> tptp.nat tptp.set_nat) tptp.list_nat) tptp.set_nat)
% 2.52/3.49 (declare-fun tptp.list_c6059232572861898639sn_int ((-> tptp.produc6575502325842934193n_assn tptp.set_int) tptp.list_P8527749157015355191n_assn) tptp.set_int)
% 2.52/3.49 (declare-fun tptp.list_c6061723043370948915sn_nat ((-> tptp.produc6575502325842934193n_assn tptp.set_nat) tptp.list_P8527749157015355191n_assn) tptp.set_nat)
% 2.52/3.49 (declare-fun tptp.slice_int (tptp.nat tptp.nat tptp.list_int) tptp.list_int)
% 2.52/3.49 (declare-fun tptp.slice_nat (tptp.nat tptp.nat tptp.list_nat) tptp.list_nat)
% 2.52/3.49 (declare-fun tptp.slice_7964966981652229398n_assn (tptp.nat tptp.nat tptp.list_P8527749157015355191n_assn) tptp.list_P8527749157015355191n_assn)
% 2.52/3.49 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 2.52/3.49 (declare-fun tptp.semiri1314217659103216013at_int (tptp.nat) tptp.int)
% 2.52/3.49 (declare-fun tptp.semiri681578069525770553at_rat (tptp.nat) tptp.rat)
% 2.52/3.49 (declare-fun tptp.size_s8908918004648414271_nat_o (tptp.list_P7985473006766602707_nat_o) tptp.nat)
% 2.52/3.49 (declare-fun tptp.size_size_list_assn (tptp.list_assn) tptp.nat)
% 2.52/3.49 (declare-fun tptp.size_s7011499401410611007t_unit (tptp.list_h2745205591237434579t_unit) tptp.nat)
% 2.52/3.49 (declare-fun tptp.size_size_list_int (tptp.list_int) tptp.nat)
% 2.52/3.49 (declare-fun tptp.size_size_list_nat (tptp.list_nat) tptp.nat)
% 2.52/3.49 (declare-fun tptp.size_s6841928198497307170et_nat (tptp.list_P2321686559999237006et_nat) tptp.nat)
% 2.52/3.49 (declare-fun tptp.size_s6829681357464350627n_assn (tptp.list_P8527749157015355191n_assn) tptp.nat)
% 2.52/3.49 (declare-fun tptp.size_s2864271983995610790et_nat (tptp.list_P9062070895058802706et_nat) tptp.nat)
% 2.52/3.49 (declare-fun tptp.size_s5157815400016825771nt_int (tptp.list_P5707943133018811711nt_int) tptp.nat)
% 2.52/3.49 (declare-fun tptp.size_s7647898544948552527nt_nat (tptp.list_P8198026277950538467nt_nat) tptp.nat)
% 2.52/3.49 (declare-fun tptp.size_s2970893825323803983at_int (tptp.list_P3521021558325789923at_int) tptp.nat)
% 2.52/3.49 (declare-fun tptp.size_s5460976970255530739at_nat (tptp.list_P6011104703257516679at_nat) tptp.nat)
% 2.52/3.49 (declare-fun tptp.size_s3254054031482475050et_nat (tptp.list_set_nat) tptp.nat)
% 2.52/3.49 (declare-fun tptp.bitM (tptp.num) tptp.num)
% 2.52/3.49 (declare-fun tptp.inc (tptp.num) tptp.num)
% 2.52/3.49 (declare-fun tptp.nat_of_num (tptp.num) tptp.nat)
% 2.52/3.49 (declare-fun tptp.neg_nu8804712462038260780nteger (tptp.code_integer) tptp.code_integer)
% 2.52/3.49 (declare-fun tptp.neg_numeral_dbl_int (tptp.int) tptp.int)
% 2.52/3.49 (declare-fun tptp.neg_numeral_dbl_rat (tptp.rat) tptp.rat)
% 2.52/3.49 (declare-fun tptp.neg_nu7757733837767384882nteger (tptp.code_integer) tptp.code_integer)
% 2.52/3.49 (declare-fun tptp.neg_nu3811975205180677377ec_int (tptp.int) tptp.int)
% 2.52/3.49 (declare-fun tptp.neg_nu3179335615603231917ec_rat (tptp.rat) tptp.rat)
% 2.52/3.49 (declare-fun tptp.neg_nu5831290666863070958nteger (tptp.code_integer) tptp.code_integer)
% 2.52/3.49 (declare-fun tptp.neg_nu5851722552734809277nc_int (tptp.int) tptp.int)
% 2.52/3.49 (declare-fun tptp.neg_nu5219082963157363817nc_rat (tptp.rat) tptp.rat)
% 2.52/3.49 (declare-fun tptp.neg_nu5755505904847501662nteger (tptp.num tptp.num) tptp.code_integer)
% 2.52/3.49 (declare-fun tptp.neg_numeral_sub_int (tptp.num tptp.num) tptp.int)
% 2.52/3.49 (declare-fun tptp.neg_numeral_sub_rat (tptp.num tptp.num) tptp.rat)
% 2.52/3.49 (declare-fun tptp.bit0 (tptp.num) tptp.num)
% 2.52/3.49 (declare-fun tptp.bit1 (tptp.num) tptp.num)
% 2.52/3.49 (declare-fun tptp.one () tptp.num)
% 2.52/3.49 (declare-fun tptp.num_of_nat (tptp.nat) tptp.num)
% 2.52/3.49 (declare-fun tptp.numera6620942414471956472nteger (tptp.num) tptp.code_integer)
% 2.52/3.49 (declare-fun tptp.numera5444537566228673987atural (tptp.num) tptp.code_natural)
% 2.52/3.49 (declare-fun tptp.numeral_numeral_int (tptp.num) tptp.int)
% 2.52/3.49 (declare-fun tptp.numeral_numeral_nat (tptp.num) tptp.nat)
% 2.52/3.49 (declare-fun tptp.numeral_numeral_rat (tptp.num) tptp.rat)
% 2.52/3.49 (declare-fun tptp.pred_numeral (tptp.num) tptp.nat)
% 2.52/3.49 (declare-fun tptp.order_underS_nat (tptp.set_Pr1261947904930325089at_nat tptp.nat) tptp.set_nat)
% 2.52/3.49 (declare-fun tptp.bot_bo8147686125503663512_int_o (tptp.product_prod_int_int) Bool)
% 2.52/3.49 (declare-fun tptp.bot_bot_assn () tptp.assn)
% 2.52/3.49 (declare-fun tptp.bot_bo7824918357723582233_nat_o () tptp.set_Pr4532377907799695533_nat_o)
% 2.52/3.49 (declare-fun tptp.bot_bot_set_int () tptp.set_int)
% 2.52/3.49 (declare-fun tptp.bot_bot_set_nat () tptp.set_nat)
% 2.52/3.49 (declare-fun tptp.bot_bo2099793752762293965at_nat () tptp.set_Pr1261947904930325089at_nat)
% 2.52/3.49 (declare-fun tptp.bot_bo3957492148770167129t_unit () tptp.set_Product_unit)
% 2.52/3.49 (declare-fun tptp.ord_le8213806771718485336_int_o ((-> tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool)) Bool)
% 2.52/3.49 (declare-fun tptp.ord_less_assn (tptp.assn tptp.assn) Bool)
% 2.52/3.49 (declare-fun tptp.ord_le6747313008572928689nteger (tptp.code_integer tptp.code_integer) Bool)
% 2.52/3.49 (declare-fun tptp.ord_le5570908160329646204atural (tptp.code_natural tptp.code_natural) Bool)
% 2.52/3.49 (declare-fun tptp.ord_less_int (tptp.int tptp.int) Bool)
% 2.52/3.49 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 2.52/3.49 (declare-fun tptp.ord_less_num (tptp.num tptp.num) Bool)
% 2.52/3.49 (declare-fun tptp.ord_less_rat (tptp.rat tptp.rat) Bool)
% 2.52/3.49 (declare-fun tptp.ord_less_set_int (tptp.set_int tptp.set_int) Bool)
% 2.52/3.49 (declare-fun tptp.ord_less_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 2.52/3.49 (declare-fun tptp.ord_le7866589430770878221at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 2.52/3.49 (declare-fun tptp.ord_le8056459307392131481t_unit (tptp.set_Product_unit tptp.set_Product_unit) Bool)
% 2.52/3.49 (declare-fun tptp.ord_le8369615600986905444_int_o ((-> tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool)) Bool)
% 2.52/3.49 (declare-fun tptp.ord_less_eq_assn (tptp.assn tptp.assn) Bool)
% 2.52/3.49 (declare-fun tptp.ord_le3102999989581377725nteger (tptp.code_integer tptp.code_integer) Bool)
% 2.52/3.49 (declare-fun tptp.ord_le1926595141338095240atural (tptp.code_natural tptp.code_natural) Bool)
% 2.52/3.49 (declare-fun tptp.ord_less_eq_int (tptp.int tptp.int) Bool)
% 2.52/3.49 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 2.52/3.49 (declare-fun tptp.ord_less_eq_num (tptp.num tptp.num) Bool)
% 2.52/3.49 (declare-fun tptp.ord_less_eq_rat (tptp.rat tptp.rat) Bool)
% 2.52/3.49 (declare-fun tptp.ord_le2965882846123202637_nat_o (tptp.set_Pr4532377907799695533_nat_o tptp.set_Pr4532377907799695533_nat_o) Bool)
% 2.52/3.49 (declare-fun tptp.ord_less_eq_set_int (tptp.set_int tptp.set_int) Bool)
% 2.52/3.49 (declare-fun tptp.ord_le6045566169113846134st_nat (tptp.set_list_nat tptp.set_list_nat) Bool)
% 2.52/3.49 (declare-fun tptp.ord_less_eq_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 2.52/3.49 (declare-fun tptp.ord_le3146513528884898305at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 2.52/3.49 (declare-fun tptp.ord_le3507040750410214029t_unit (tptp.set_Product_unit tptp.set_Product_unit) Bool)
% 2.52/3.49 (declare-fun tptp.ord_max_Code_integer (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 2.52/3.49 (declare-fun tptp.ord_max_Code_natural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 2.52/3.49 (declare-fun tptp.ord_max_int (tptp.int tptp.int) tptp.int)
% 2.52/3.49 (declare-fun tptp.ord_max_nat (tptp.nat tptp.nat) tptp.nat)
% 2.52/3.49 (declare-fun tptp.ord_max_rat (tptp.rat tptp.rat) tptp.rat)
% 2.52/3.49 (declare-fun tptp.ord_min_nat (tptp.nat tptp.nat) tptp.nat)
% 2.52/3.49 (declare-fun tptp.top_to1578927101902068148_int_o (tptp.product_prod_int_int) Bool)
% 2.52/3.49 (declare-fun tptp.top_top_assn () tptp.assn)
% 2.52/3.49 (declare-fun tptp.top_top_set_int () tptp.set_int)
% 2.52/3.49 (declare-fun tptp.top_top_set_nat () tptp.set_nat)
% 2.52/3.49 (declare-fun tptp.top_to5722533637347664993n_assn () tptp.set_Pr5949110396991348497n_assn)
% 2.52/3.49 (declare-fun tptp.top_to4669805908274784177at_nat () tptp.set_Pr1261947904930325089at_nat)
% 2.52/3.49 (declare-fun tptp.top_to1996260823553986621t_unit () tptp.set_Product_unit)
% 2.52/3.49 (declare-fun tptp.power_power_assn (tptp.assn tptp.nat) tptp.assn)
% 2.52/3.49 (declare-fun tptp.power_8256067586552552935nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 2.52/3.49 (declare-fun tptp.power_7079662738309270450atural (tptp.code_natural tptp.nat) tptp.code_natural)
% 2.52/3.49 (declare-fun tptp.power_power_int (tptp.int tptp.nat) tptp.int)
% 2.52/3.49 (declare-fun tptp.power_power_nat (tptp.nat tptp.nat) tptp.nat)
% 2.52/3.49 (declare-fun tptp.power_power_rat (tptp.rat tptp.nat) tptp.rat)
% 2.52/3.49 (declare-fun tptp.produc8618682346314911123st_int ((-> tptp.int tptp.int Bool) tptp.list_int) tptp.produc5834231552977413017st_int)
% 2.52/3.49 (declare-fun tptp.produc6519019827157805250st_int ((-> tptp.int tptp.int Bool) tptp.produc1186641810826059865st_int) tptp.produc6134427711877206866st_int)
% 2.52/3.49 (declare-fun tptp.produc3135705617881911306st_nat ((-> tptp.int tptp.nat Bool) tptp.produc3676724955757786621st_nat) tptp.produc5074578776457504922st_nat)
% 2.52/3.49 (declare-fun tptp.produc3092413063583913184n_assn ((-> tptp.int tptp.produc6575502325842934193n_assn Bool) tptp.produc8582807064127716720n_assn) tptp.produc4944321512348556200n_assn)
% 2.52/3.49 (declare-fun tptp.produc3116401902672145424st_int ((-> tptp.int Bool) tptp.produc5625914783551145028st_int) tptp.produc141556263843406102st_int)
% 2.52/3.49 (declare-fun tptp.produc6511047662141078538st_int ((-> tptp.nat tptp.int Bool) tptp.produc8561936516282095101st_int) tptp.produc5847166148257158298st_int)
% 2.52/3.49 (declare-fun tptp.produc4727192421694094319st_nat ((-> tptp.nat tptp.nat Bool) tptp.list_nat) tptp.produc254973753779126261st_nat)
% 2.52/3.49 (declare-fun tptp.produc3127733452865184594st_nat ((-> tptp.nat tptp.nat Bool) tptp.produc1828647624359046049st_nat) tptp.produc4787317212837456354st_nat)
% 2.52/3.49 (declare-fun tptp.produc1692222275734866400n_assn ((-> tptp.nat tptp.produc6575502325842934193n_assn Bool) tptp.produc2555908794901494476n_assn) tptp.produc3272579373640082088n_assn)
% 2.52/3.49 (declare-fun tptp.produc2404789219858123352st_nat ((-> tptp.nat Bool) tptp.produc8368264342088597808st_nat) tptp.produc6155704871766690142st_nat)
% 2.52/3.49 (declare-fun tptp.produc7143791561355829714st_int ((-> tptp.produc6575502325842934193n_assn tptp.int Bool) tptp.produc4164172529858598818st_int) tptp.produc4920635200459206554st_int)
% 2.52/3.49 (declare-fun tptp.produc6179912464936081618st_nat ((-> tptp.produc6575502325842934193n_assn tptp.nat Bool) tptp.produc6654255674790325574st_nat) tptp.produc6280221377895650458st_nat)
% 2.52/3.49 (declare-fun tptp.produc6115016301897879072n_assn ((-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn Bool) tptp.list_P8527749157015355191n_assn) tptp.produc4530688714081574576n_assn)
% 2.52/3.49 (declare-fun tptp.produc218933061472242640n_assn ((-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn Bool) tptp.produc337509097454979815n_assn) tptp.produc6691681559177096800n_assn)
% 2.52/3.49 (declare-fun tptp.produc7995034776595945426n_assn ((-> tptp.produc6575502325842934193n_assn Bool) tptp.produc858023921370090807n_assn) tptp.produc3251403909973641504n_assn)
% 2.52/3.49 (declare-fun tptp.produc2245416461498447860et_nat ((-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat) tptp.produc2732055786443039994et_nat)
% 2.52/3.49 (declare-fun tptp.produc5001842942810119800et_nat ((-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat) tptp.produc3925858234332021118et_nat)
% 2.52/3.49 (declare-fun tptp.produc3762353314782720579et_nat (Bool tptp.produc3658429121746597890et_nat) tptp.produc6197004810343482825et_nat)
% 2.52/3.49 (declare-fun tptp.produc6677183202524767010eger_o (tptp.code_integer Bool) tptp.produc6271795597528267376eger_o)
% 2.52/3.49 (declare-fun tptp.produc1086072967326762835nteger (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 2.52/3.49 (declare-fun tptp.produc3574140220909816553atural (tptp.code_natural tptp.code_natural) tptp.produc7822875418678951345atural)
% 2.52/3.49 (declare-fun tptp.produc6639722614265839536atural (tptp.code_natural tptp.produc7822875418678951345atural) tptp.produc5835291356934675326atural)
% 2.52/3.49 (declare-fun tptp.produc7507926704131184380et_nat (tptp.heap_e7401611519738050253t_unit tptp.set_nat) tptp.produc3658429121746597890et_nat)
% 2.52/3.49 (declare-fun tptp.product_Pair_int_int (tptp.int tptp.int) tptp.product_prod_int_int)
% 2.52/3.49 (declare-fun tptp.product_Pair_int_nat (tptp.int tptp.nat) tptp.product_prod_int_nat)
% 2.52/3.49 (declare-fun tptp.produc364263696895485585st_int (tptp.list_int tptp.list_int) tptp.produc1186641810826059865st_int)
% 2.52/3.49 (declare-fun tptp.produc4542114716404682293st_nat (tptp.list_int tptp.list_nat) tptp.produc3676724955757786621st_nat)
% 2.52/3.49 (declare-fun tptp.produc4510294837168919970n_assn (tptp.list_int tptp.list_P8527749157015355191n_assn) tptp.produc8582807064127716720n_assn)
% 2.52/3.49 (declare-fun tptp.produc7739558402351520821st_int (tptp.list_nat tptp.list_int) tptp.produc8561936516282095101st_int)
% 2.52/3.49 (declare-fun tptp.produc2694037385005941721st_nat (tptp.list_nat tptp.list_nat) tptp.produc1828647624359046049st_nat)
% 2.52/3.49 (declare-fun tptp.produc7706768604797473534n_assn (tptp.list_nat tptp.list_P8527749157015355191n_assn) tptp.produc2555908794901494476n_assn)
% 2.52/3.49 (declare-fun tptp.produc1996262876970182428st_int (tptp.list_P8527749157015355191n_assn tptp.list_int) tptp.produc4164172529858598818st_int)
% 2.52/3.49 (declare-fun tptp.produc6174113896479379136st_nat (tptp.list_P8527749157015355191n_assn tptp.list_nat) tptp.produc6654255674790325574st_nat)
% 2.52/3.49 (declare-fun tptp.produc3014731801419794263n_assn (tptp.list_P8527749157015355191n_assn tptp.list_P8527749157015355191n_assn) tptp.produc337509097454979815n_assn)
% 2.52/3.49 (declare-fun tptp.product_Pair_nat_int (tptp.nat tptp.int) tptp.product_prod_nat_int)
% 2.52/3.49 (declare-fun tptp.product_Pair_nat_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 2.52/3.49 (declare-fun tptp.produc6571967182415643454st_int (tptp.produc1186641810826059865st_int tptp.list_int) tptp.produc5625914783551145028st_int)
% 2.52/3.49 (declare-fun tptp.produc1778712578675790378st_nat (tptp.produc1828647624359046049st_nat tptp.list_nat) tptp.produc8368264342088597808st_nat)
% 2.52/3.49 (declare-fun tptp.produc7497315745449715623n_assn (tptp.produc337509097454979815n_assn tptp.list_P8527749157015355191n_assn) tptp.produc858023921370090807n_assn)
% 2.52/3.49 (declare-fun tptp.produc457027306803732586at_nat (tptp.set_nat (-> tptp.nat tptp.set_nat)) tptp.set_Pr1261947904930325089at_nat)
% 2.52/3.49 (declare-fun tptp.product_Unity () tptp.product_unit)
% 2.52/3.49 (declare-fun tptp.produc6499014454317279255nteger ((-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 2.52/3.49 (declare-fun tptp.produc7274209992780475162assn_o ((-> tptp.assn tptp.assn Bool) tptp.produc6575502325842934193n_assn) Bool)
% 2.52/3.49 (declare-fun tptp.produc1553301316500091796er_int ((-> tptp.code_integer tptp.code_integer tptp.int) tptp.produc8923325533196201883nteger) tptp.int)
% 2.52/3.49 (declare-fun tptp.produc1555791787009142072er_nat ((-> tptp.code_integer tptp.code_integer tptp.nat) tptp.produc8923325533196201883nteger) tptp.nat)
% 2.52/3.49 (declare-fun tptp.produc7336495610019696514er_num ((-> tptp.code_integer tptp.code_integer tptp.num) tptp.produc8923325533196201883nteger) tptp.num)
% 2.52/3.49 (declare-fun tptp.produc9125791028180074456eger_o ((-> tptp.code_integer tptp.code_integer tptp.produc6271795597528267376eger_o) tptp.produc8923325533196201883nteger) tptp.produc6271795597528267376eger_o)
% 2.52/3.49 (declare-fun tptp.produc6916734918728496179nteger ((-> tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 2.52/3.49 (declare-fun tptp.produc4245557441103728435nt_int ((-> tptp.int tptp.int tptp.product_prod_int_int) tptp.product_prod_int_int) tptp.product_prod_int_int)
% 2.52/3.49 (declare-fun tptp.produc6081775807080527818_nat_o ((-> tptp.nat tptp.nat Bool) tptp.product_prod_nat_nat) Bool)
% 2.52/3.49 (declare-fun tptp.produc2626176000494625587at_nat ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 2.52/3.49 (declare-fun tptp.produc9167289414957590229n_assn (tptp.produc6575502325842934193n_assn) tptp.assn)
% 2.52/3.49 (declare-fun tptp.produc8508995932063986495nteger (tptp.produc8923325533196201883nteger) tptp.code_integer)
% 2.52/3.49 (declare-fun tptp.produc1824681642469235216et_nat (tptp.produc3658429121746597890et_nat) tptp.heap_e7401611519738050253t_unit)
% 2.52/3.49 (declare-fun tptp.product_fst_int_int (tptp.product_prod_int_int) tptp.int)
% 2.52/3.49 (declare-fun tptp.product_fst_int_nat (tptp.product_prod_int_nat) tptp.int)
% 2.52/3.49 (declare-fun tptp.product_fst_nat_int (tptp.product_prod_nat_int) tptp.nat)
% 2.52/3.49 (declare-fun tptp.product_fst_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 2.52/3.49 (declare-fun tptp.produc2051961928117032727n_assn (tptp.produc6575502325842934193n_assn) tptp.assn)
% 2.52/3.49 (declare-fun tptp.produc6174133586879617921nteger (tptp.produc8923325533196201883nteger) tptp.code_integer)
% 2.52/3.49 (declare-fun tptp.produc8586169260539613262et_nat (tptp.produc3658429121746597890et_nat) tptp.set_nat)
% 2.52/3.49 (declare-fun tptp.product_snd_int_int (tptp.product_prod_int_int) tptp.int)
% 2.52/3.49 (declare-fun tptp.product_snd_int_nat (tptp.product_prod_int_nat) tptp.nat)
% 2.52/3.49 (declare-fun tptp.product_snd_nat_int (tptp.product_prod_nat_int) tptp.int)
% 2.52/3.49 (declare-fun tptp.product_snd_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 2.52/3.49 (declare-fun tptp.produc5538323210962509403atural ((-> tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural) (-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural) tptp.produc7822875418678951345atural) tptp.produc5835291356934675326atural)
% 2.52/3.49 (declare-fun tptp.inc_shift (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 2.52/3.49 (declare-fun tptp.iterat8892046348760725948atural (tptp.code_natural (-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural) tptp.code_natural tptp.produc7822875418678951345atural) tptp.produc5835291356934675326atural)
% 2.52/3.49 (declare-fun tptp.log (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 2.52/3.49 (declare-fun tptp.log_rel (tptp.produc7822875418678951345atural tptp.produc7822875418678951345atural) Bool)
% 2.52/3.49 (declare-fun tptp.minus_shift (tptp.code_natural tptp.code_natural tptp.code_natural) tptp.code_natural)
% 2.52/3.49 (declare-fun tptp.next (tptp.produc7822875418678951345atural) tptp.produc5835291356934675326atural)
% 2.52/3.49 (declare-fun tptp.range (tptp.code_natural tptp.produc7822875418678951345atural) tptp.produc5835291356934675326atural)
% 2.52/3.49 (declare-fun tptp.abs_Rat (tptp.product_prod_int_int) tptp.rat)
% 2.52/3.49 (declare-fun tptp.fract (tptp.int tptp.int) tptp.rat)
% 2.52/3.49 (declare-fun tptp.frct (tptp.product_prod_int_int) tptp.rat)
% 2.52/3.49 (declare-fun tptp.rep_Rat (tptp.rat) tptp.product_prod_int_int)
% 2.52/3.49 (declare-fun tptp.normalize (tptp.product_prod_int_int) tptp.product_prod_int_int)
% 2.52/3.49 (declare-fun tptp.of_int (tptp.int) tptp.rat)
% 2.52/3.49 (declare-fun tptp.pcr_rat (tptp.product_prod_int_int tptp.rat) Bool)
% 2.52/3.49 (declare-fun tptp.quotient_of (tptp.rat) tptp.product_prod_int_int)
% 2.52/3.49 (declare-fun tptp.ratrel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 2.52/3.49 (declare-fun tptp.refine_Imp_assert (Bool) tptp.heap_T5738788834812785303t_unit)
% 2.52/3.49 (declare-fun tptp.domainp_int_int ((-> tptp.int tptp.int Bool) tptp.int) Bool)
% 2.52/3.49 (declare-fun tptp.domain9213661015745956397nt_rat ((-> tptp.product_prod_int_int tptp.rat Bool) tptp.product_prod_int_int) Bool)
% 2.52/3.49 (declare-fun tptp.algebr932160517623751201me_int (tptp.int tptp.int) Bool)
% 2.52/3.49 (declare-fun tptp.algebr934650988132801477me_nat (tptp.nat tptp.nat) Bool)
% 2.52/3.49 (declare-fun tptp.divide6298287555418463151nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 2.52/3.49 (declare-fun tptp.divide5121882707175180666atural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 2.52/3.49 (declare-fun tptp.divide_divide_int (tptp.int tptp.int) tptp.int)
% 2.52/3.49 (declare-fun tptp.divide_divide_nat (tptp.nat tptp.nat) tptp.nat)
% 2.52/3.49 (declare-fun tptp.divide_divide_rat (tptp.rat tptp.rat) tptp.rat)
% 2.52/3.49 (declare-fun tptp.dvd_dvd_assn (tptp.assn tptp.assn) Bool)
% 2.52/3.49 (declare-fun tptp.dvd_dvd_Code_integer (tptp.code_integer tptp.code_integer) Bool)
% 2.52/3.49 (declare-fun tptp.dvd_dvd_Code_natural (tptp.code_natural tptp.code_natural) Bool)
% 2.52/3.49 (declare-fun tptp.dvd_dvd_int (tptp.int tptp.int) Bool)
% 2.52/3.49 (declare-fun tptp.dvd_dvd_nat (tptp.nat tptp.nat) Bool)
% 2.52/3.49 (declare-fun tptp.dvd_dvd_rat (tptp.rat tptp.rat) Bool)
% 2.52/3.49 (declare-fun tptp.modulo364778990260209775nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 2.52/3.49 (declare-fun tptp.modulo8411746178871703098atural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 2.52/3.49 (declare-fun tptp.modulo_modulo_int (tptp.int tptp.int) tptp.int)
% 2.52/3.49 (declare-fun tptp.modulo_modulo_nat (tptp.nat tptp.nat) tptp.nat)
% 2.52/3.49 (declare-fun tptp.unit_f2748546683901255202or_nat (tptp.nat) tptp.nat)
% 2.52/3.49 (declare-fun tptp.zero_n356916108424825756nteger (Bool) tptp.code_integer)
% 2.52/3.49 (declare-fun tptp.zero_n8403883297036319079atural (Bool) tptp.code_natural)
% 2.52/3.49 (declare-fun tptp.zero_n2684676970156552555ol_int (Bool) tptp.int)
% 2.52/3.49 (declare-fun tptp.zero_n2687167440665602831ol_nat (Bool) tptp.nat)
% 2.52/3.49 (declare-fun tptp.zero_n2052037380579107095ol_rat (Bool) tptp.rat)
% 2.52/3.49 (declare-fun tptp.collec939566748876313656_nat_o ((-> (-> tptp.produc3658429121746597890et_nat Bool) Bool)) tptp.set_Pr4532377907799695533_nat_o)
% 2.52/3.49 (declare-fun tptp.collect_int ((-> tptp.int Bool)) tptp.set_int)
% 2.52/3.49 (declare-fun tptp.collect_list_nat ((-> tptp.list_nat Bool)) tptp.set_list_nat)
% 2.52/3.49 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 2.52/3.49 (declare-fun tptp.collec3392354462482085612at_nat ((-> tptp.product_prod_nat_nat Bool)) tptp.set_Pr1261947904930325089at_nat)
% 2.52/3.49 (declare-fun tptp.image_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 2.52/3.49 (declare-fun tptp.insert5175938949040314269_nat_o ((-> tptp.produc3658429121746597890et_nat Bool) tptp.set_Pr4532377907799695533_nat_o) tptp.set_Pr4532377907799695533_nat_o)
% 2.52/3.49 (declare-fun tptp.insert_int2 (tptp.int tptp.set_int) tptp.set_int)
% 2.52/3.49 (declare-fun tptp.insert_nat2 (tptp.nat tptp.set_nat) tptp.set_nat)
% 2.52/3.49 (declare-fun tptp.insert8211810215607154385at_nat (tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 2.52/3.49 (declare-fun tptp.set_fo2584398358068434914at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat tptp.nat tptp.nat) tptp.nat)
% 2.52/3.49 (declare-fun tptp.set_or189985376899183464nteger (tptp.code_integer tptp.code_integer) tptp.set_Code_integer)
% 2.52/3.49 (declare-fun tptp.set_or1266510415728281911st_int (tptp.int tptp.int) tptp.set_int)
% 2.52/3.49 (declare-fun tptp.set_or1269000886237332187st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 2.52/3.49 (declare-fun tptp.set_or8404916559141939852nteger (tptp.code_integer tptp.code_integer) tptp.set_Code_integer)
% 2.52/3.49 (declare-fun tptp.set_or4662586982721622107an_int (tptp.int tptp.int) tptp.set_int)
% 2.52/3.49 (declare-fun tptp.set_or4665077453230672383an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 2.52/3.49 (declare-fun tptp.set_ord_atMost_nat (tptp.nat) tptp.set_nat)
% 2.52/3.49 (declare-fun tptp.set_or2715278749043346189nteger (tptp.code_integer tptp.code_integer) tptp.set_Code_integer)
% 2.52/3.49 (declare-fun tptp.set_or6656581121297822940st_int (tptp.int tptp.int) tptp.set_int)
% 2.52/3.49 (declare-fun tptp.set_or6659071591806873216st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 2.52/3.49 (declare-fun tptp.set_or4266950643985792945nteger (tptp.code_integer tptp.code_integer) tptp.set_Code_integer)
% 2.52/3.49 (declare-fun tptp.set_or5832277885323065728an_int (tptp.int tptp.int) tptp.set_int)
% 2.52/3.49 (declare-fun tptp.set_or5834768355832116004an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 2.52/3.49 (declare-fun tptp.set_ord_lessThan_nat (tptp.nat) tptp.set_nat)
% 2.52/3.49 (declare-fun tptp.syntax3673046151410588037r_assn ((-> tptp.assn tptp.assn tptp.assn)) Bool)
% 2.52/3.49 (declare-fun tptp.syntax414191934074104506nteger ((-> tptp.code_integer tptp.code_integer tptp.code_integer)) Bool)
% 2.52/3.49 (declare-fun tptp.syntax8461159122685597829atural ((-> tptp.code_natural tptp.code_natural tptp.code_natural)) Bool)
% 2.52/3.49 (declare-fun tptp.syntax8798048597141670025or_int ((-> tptp.int tptp.int tptp.int)) Bool)
% 2.52/3.49 (declare-fun tptp.syntax8800539067650720301or_nat ((-> tptp.nat tptp.nat tptp.nat)) Bool)
% 2.52/3.49 (declare-fun tptp.syntax8165409007564224565or_rat ((-> tptp.rat tptp.rat tptp.rat)) Bool)
% 2.52/3.49 (declare-fun tptp.syntax7398250324933576852n_assn (tptp.assn tptp.assn) Bool)
% 2.52/3.49 (declare-fun tptp.syntax380677951125133566nteger (tptp.code_integer tptp.code_integer) Bool)
% 2.52/3.49 (declare-fun tptp.syntax2868745204708187284atural (tptp.code_natural tptp.code_natural) Bool)
% 2.52/3.49 (declare-fun tptp.syntax5678989248478167196nt_int (tptp.int tptp.int) Bool)
% 2.52/3.49 (declare-fun tptp.syntax4682126007086162916at_nat (tptp.nat tptp.nat) Bool)
% 2.52/3.49 (declare-fun tptp.syntax3730441303064801268at_rat (tptp.rat tptp.rat) Bool)
% 2.52/3.49 (declare-fun tptp.type_d3909072315231072503_nat_o ((-> tptp.assn tptp.produc3658429121746597890et_nat Bool) (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.assn) tptp.set_Pr4532377907799695533_nat_o) Bool)
% 2.52/3.49 (declare-fun tptp.accp_P1862375125659990705et_nat ((-> tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat Bool) tptp.produc2732055786443039994et_nat) Bool)
% 2.52/3.49 (declare-fun tptp.accp_P8126237942716283194atural ((-> tptp.produc7822875418678951345atural tptp.produc7822875418678951345atural Bool) tptp.produc7822875418678951345atural) Bool)
% 2.52/3.49 (declare-fun tptp.accp_P5801069581201407417et_nat ((-> tptp.produc3658429121746597890et_nat tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat) Bool)
% 2.52/3.49 (declare-fun tptp.accp_P1096762738010456898nt_int ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 2.52/3.49 (declare-fun tptp.accp_P4275260045618599050at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat) Bool)
% 2.52/3.49 (declare-fun tptp.member6576561426505652726_nat_o ((-> tptp.produc3658429121746597890et_nat Bool) tptp.set_Pr4532377907799695533_nat_o) Bool)
% 2.52/3.49 (declare-fun tptp.member_int2 (tptp.int tptp.set_int) Bool)
% 2.52/3.49 (declare-fun tptp.member_list_int (tptp.list_int tptp.set_list_int) Bool)
% 2.52/3.49 (declare-fun tptp.member_list_nat (tptp.list_nat tptp.set_list_nat) Bool)
% 2.52/3.49 (declare-fun tptp.member_nat2 (tptp.nat tptp.set_nat) Bool)
% 2.52/3.49 (declare-fun tptp.member7957490590177025114n_assn (tptp.produc6575502325842934193n_assn tptp.set_Pr5949110396991348497n_assn) Bool)
% 2.52/3.49 (declare-fun tptp.member5262025264175285858nt_int (tptp.product_prod_int_int tptp.set_Pr958786334691620121nt_int) Bool)
% 2.52/3.49 (declare-fun tptp.member8440522571783428010at_nat (tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 2.52/3.49 (declare-fun tptp.f () tptp.assn)
% 2.52/3.49 (declare-fun tptp.p () tptp.assn)
% 2.52/3.49 (declare-fun tptp.q () tptp.assn)
% 2.52/3.49 (assert (let ((_let_1 (@ tptp.times_times_assn tptp.sln))) (@ (@ (@ (@ (@ (@ tptp.fi tptp.nil_Pr5671120429643327159n_assn) (@ _let_1 tptp.p)) (@ _let_1 tptp.q)) tptp.sln) tptp.sln) tptp.f)))
% 2.52/3.49 (assert (= tptp.fI_QUERY (lambda ((P tptp.assn) (Q tptp.assn) (F tptp.assn)) (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn Q) F)))))
% 2.52/3.49 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn A))) (= (@ (@ tptp.times_times_assn (@ _let_1 B)) C) (@ (@ tptp.times_times_assn (@ _let_1 C)) B)))))
% 2.52/3.49 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn A))) (let ((_let_2 (@ tptp.times_times_assn B))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 2.52/3.49 (assert (= tptp.times_times_assn (lambda ((A2 tptp.assn) (B2 tptp.assn)) (@ (@ tptp.times_times_assn B2) A2))))
% 2.52/3.49 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn A))) (= (@ (@ tptp.times_times_assn (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_assn B) C))))))
% 2.52/3.49 (assert (forall ((P2 tptp.assn)) (= (@ (@ tptp.times_times_assn tptp.sln) P2) P2)))
% 2.52/3.49 (assert (forall ((P2 tptp.assn)) (= (@ (@ tptp.times_times_assn P2) tptp.sln) P2)))
% 2.52/3.49 (assert (forall ((P2 tptp.assn) (Q2 tptp.assn)) (let ((_let_1 (@ (@ tptp.entails P2) Q2))) (=> _let_1 _let_1))))
% 2.52/3.49 (assert (forall ((P2 tptp.assn) (P3 tptp.assn) (Q2 tptp.assn) (Q3 tptp.assn)) (=> (@ (@ tptp.entails P2) P3) (=> (@ (@ tptp.entails Q2) Q3) (@ (@ tptp.entails (@ (@ tptp.times_times_assn P2) Q2)) (@ (@ tptp.times_times_assn P3) Q3))))))
% 2.52/3.49 (assert (forall ((A3 tptp.assn) (B3 tptp.assn)) (=> (@ (@ tptp.entails A3) B3) (=> (@ (@ tptp.entails B3) A3) (= A3 B3)))))
% 2.52/3.49 (assert (forall ((P2 tptp.assn)) (@ (@ tptp.entails P2) P2)))
% 2.52/3.49 (assert (forall ((P2 tptp.assn) (Q2 tptp.assn) (R tptp.assn)) (let ((_let_1 (@ tptp.entails P2))) (=> (@ _let_1 Q2) (=> (@ (@ tptp.entails Q2) R) (@ _let_1 R))))))
% 2.52/3.49 (assert (= tptp.times_times_assn (lambda ((P tptp.assn) (Q tptp.assn)) (@ (@ tptp.times_times_assn Q) P))))
% 2.52/3.49 (assert (forall ((P2 tptp.assn) (Q2 tptp.assn) (R tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn P2))) (= (@ (@ tptp.times_times_assn (@ _let_1 Q2)) R) (@ _let_1 (@ (@ tptp.times_times_assn Q2) R))))))
% 2.52/3.49 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn A))) (= (@ (@ tptp.times_times_assn (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_assn B) C))))))
% 2.52/3.49 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_int B) C))))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 2.52/3.49 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural A))) (= (@ (@ tptp.times_2397367101498566445atural (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_2397367101498566445atural B) C))))))
% 2.52/3.49 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn A))) (= (@ (@ tptp.times_times_assn (@ _let_1 B)) C) (@ (@ tptp.times_times_assn (@ _let_1 C)) B)))))
% 2.52/3.49 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 B)) C) (@ (@ tptp.times_times_nat (@ _let_1 C)) B)))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 B)) C) (@ (@ tptp.times_times_int (@ _let_1 C)) B)))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 B)) C) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 C)) B)))))
% 2.52/3.49 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural A))) (= (@ (@ tptp.times_2397367101498566445atural (@ _let_1 B)) C) (@ (@ tptp.times_2397367101498566445atural (@ _let_1 C)) B)))))
% 2.52/3.49 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn A))) (= (@ (@ tptp.times_times_assn (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_assn B) C))))))
% 2.52/3.49 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_int B) C))))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 2.52/3.49 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural A))) (= (@ (@ tptp.times_2397367101498566445atural (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_2397367101498566445atural B) C))))))
% 2.52/3.49 (assert (= tptp.times_times_assn (lambda ((A2 tptp.assn) (B2 tptp.assn)) (@ (@ tptp.times_times_assn B2) A2))))
% 2.52/3.49 (assert (= tptp.times_times_nat (lambda ((A2 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.times_times_nat B2) A2))))
% 2.52/3.49 (assert (= tptp.times_times_int (lambda ((A2 tptp.int) (B2 tptp.int)) (@ (@ tptp.times_times_int B2) A2))))
% 2.52/3.49 (assert (= tptp.times_3573771949741848930nteger (lambda ((A2 tptp.code_integer) (B2 tptp.code_integer)) (@ (@ tptp.times_3573771949741848930nteger B2) A2))))
% 2.52/3.49 (assert (= tptp.times_2397367101498566445atural (lambda ((A2 tptp.code_natural) (B2 tptp.code_natural)) (@ (@ tptp.times_2397367101498566445atural B2) A2))))
% 2.52/3.49 (assert (forall ((B tptp.assn) (A tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn B))) (let ((_let_2 (@ tptp.times_times_assn A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 2.52/3.49 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B))) (let ((_let_2 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 2.52/3.49 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (let ((_let_2 (@ tptp.times_times_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 2.52/3.49 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger B))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 2.52/3.49 (assert (forall ((B tptp.code_natural) (A tptp.code_natural) (C tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural B))) (let ((_let_2 (@ tptp.times_2397367101498566445atural A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 2.52/3.49 (assert (forall ((Q2 tptp.assn) (P2 tptp.assn) (R tptp.assn)) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn Q2) P2)) R) (@ (@ tptp.entails P2) (@ (@ tptp.wand_assn Q2) R)))))
% 2.52/3.49 (assert (forall ((P2 tptp.assn) (Q2 tptp.assn)) (@ (@ tptp.entails (@ (@ tptp.times_times_assn P2) (@ (@ tptp.wand_assn P2) Q2))) Q2)))
% 2.52/3.49 (assert (forall ((P2 (-> tptp.produc6575502325842934193n_assn Bool))) (not (@ (@ tptp.list_e7761433933450087034n_assn P2) tptp.nil_Pr5671120429643327159n_assn))))
% 2.52/3.49 (assert (forall ((P2 (-> tptp.int Bool))) (not (@ (@ tptp.list_ex1_int P2) tptp.nil_int))))
% 2.52/3.49 (assert (forall ((P2 (-> tptp.nat Bool))) (not (@ (@ tptp.list_ex1_nat P2) tptp.nil_nat))))
% 2.52/3.49 (assert (forall ((Uu tptp.list_assn)) (= (@ (@ tptp.product_assn_assn tptp.nil_assn) Uu) tptp.nil_Pr5671120429643327159n_assn)))
% 2.52/3.49 (assert (forall ((A tptp.assn) (B tptp.assn)) (=> (@ tptp.is_pure_assn A) (=> (@ tptp.is_pure_assn B) (@ tptp.is_pure_assn (@ (@ tptp.times_times_assn A) B))))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.produc6575502325842934193n_assn tptp.list_P8527749157015355191n_assn))) (= (@ (@ tptp.bind_P5664457578022171847n_assn tptp.nil_Pr5671120429643327159n_assn) F2) tptp.nil_Pr5671120429643327159n_assn)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.produc6575502325842934193n_assn tptp.list_int))) (= (@ (@ tptp.bind_P8081679045764635286sn_int tptp.nil_Pr5671120429643327159n_assn) F2) tptp.nil_int)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.produc6575502325842934193n_assn tptp.list_nat))) (= (@ (@ tptp.bind_P8084169516273685562sn_nat tptp.nil_Pr5671120429643327159n_assn) F2) tptp.nil_nat)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.int tptp.list_P8527749157015355191n_assn))) (= (@ (@ tptp.bind_i4941608653131063484n_assn tptp.nil_int) F2) tptp.nil_Pr5671120429643327159n_assn)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.int tptp.list_int))) (= (@ (@ tptp.bind_int_int tptp.nil_int) F2) tptp.nil_int)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.int tptp.list_nat))) (= (@ (@ tptp.bind_int_nat tptp.nil_int) F2) tptp.nil_nat)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.nat tptp.list_P8527749157015355191n_assn))) (= (@ (@ tptp.bind_n3181571989377952280n_assn tptp.nil_nat) F2) tptp.nil_Pr5671120429643327159n_assn)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.nat tptp.list_int))) (= (@ (@ tptp.bind_nat_int tptp.nil_nat) F2) tptp.nil_int)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.nat tptp.list_nat))) (= (@ (@ tptp.bind_nat_nat tptp.nil_nat) F2) tptp.nil_nat)))
% 2.52/3.49 (assert (forall ((Y tptp.produc6575502325842934193n_assn)) (not (@ (@ tptp.member743271071679453132n_assn tptp.nil_Pr5671120429643327159n_assn) Y))))
% 2.52/3.49 (assert (forall ((Y tptp.int)) (not (@ (@ tptp.member_int tptp.nil_int) Y))))
% 2.52/3.49 (assert (forall ((Y tptp.nat)) (not (@ (@ tptp.member_nat tptp.nil_nat) Y))))
% 2.52/3.49 (assert (forall ((X tptp.nat) (Y tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.syntax4682126007086162916at_nat (@ (@ tptp.times_times_nat X) Y)) A) (= (@ (@ tptp.times_times_nat A) B) (@ (@ tptp.times_times_nat B) A)))))
% 2.52/3.49 (assert (forall ((X tptp.int) (Y tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.syntax5678989248478167196nt_int (@ (@ tptp.times_times_int X) Y)) A) (= (@ (@ tptp.times_times_int A) B) (@ (@ tptp.times_times_int B) A)))))
% 2.52/3.49 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.syntax380677951125133566nteger (@ (@ tptp.times_3573771949741848930nteger X) Y)) A) (= (@ (@ tptp.times_3573771949741848930nteger A) B) (@ (@ tptp.times_3573771949741848930nteger B) A)))))
% 2.52/3.49 (assert (forall ((X tptp.code_natural) (Y tptp.code_natural) (A tptp.code_natural) (B tptp.code_natural)) (=> (@ (@ tptp.syntax2868745204708187284atural (@ (@ tptp.times_2397367101498566445atural X) Y)) A) (= (@ (@ tptp.times_2397367101498566445atural A) B) (@ (@ tptp.times_2397367101498566445atural B) A)))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn) (A tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.syntax7398250324933576852n_assn (@ (@ tptp.times_times_assn X) Y)) A) (= (@ (@ tptp.times_times_assn A) B) (@ (@ tptp.times_times_assn B) A)))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn) (A tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.syntax7398250324933576852n_assn (@ (@ tptp.times_times_assn X) Y)) A) (= (@ (@ tptp.times_times_assn A) B) (@ (@ tptp.times_times_assn B) A)))))
% 2.52/3.49 (assert (forall ((P2 tptp.assn) (B Bool) (Q2 tptp.assn)) (= (@ (@ tptp.entails (@ (@ tptp.times_times_assn P2) (@ tptp.pure_assn B))) Q2) (=> B (@ (@ tptp.entails P2) Q2)))))
% 2.52/3.49 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.gen_le1182329135810803268n_assn N) tptp.nil_Pr5671120429643327159n_assn) N)))
% 2.52/3.49 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.gen_length_int N) tptp.nil_int) N)))
% 2.52/3.49 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.gen_length_nat N) tptp.nil_nat) N)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.produc6575502325842934193n_assn tptp.list_P8527749157015355191n_assn))) (= (@ (@ tptp.maps_P4274076103917212289n_assn F2) tptp.nil_Pr5671120429643327159n_assn) tptp.nil_Pr5671120429643327159n_assn)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.produc6575502325842934193n_assn tptp.list_int))) (= (@ (@ tptp.maps_P5983552678929597788sn_int F2) tptp.nil_Pr5671120429643327159n_assn) tptp.nil_int)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.produc6575502325842934193n_assn tptp.list_nat))) (= (@ (@ tptp.maps_P5986043149438648064sn_nat F2) tptp.nil_Pr5671120429643327159n_assn) tptp.nil_nat)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.int tptp.list_P8527749157015355191n_assn))) (= (@ (@ tptp.maps_i2843482286296025986n_assn F2) tptp.nil_int) tptp.nil_Pr5671120429643327159n_assn)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.int tptp.list_int))) (= (@ (@ tptp.maps_int_int F2) tptp.nil_int) tptp.nil_int)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.int tptp.list_nat))) (= (@ (@ tptp.maps_int_nat F2) tptp.nil_int) tptp.nil_nat)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.nat tptp.list_P8527749157015355191n_assn))) (= (@ (@ tptp.maps_n1083445622542914782n_assn F2) tptp.nil_nat) tptp.nil_Pr5671120429643327159n_assn)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.nat tptp.list_int))) (= (@ (@ tptp.maps_nat_int F2) tptp.nil_nat) tptp.nil_int)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.nat tptp.list_nat))) (= (@ (@ tptp.maps_nat_nat F2) tptp.nil_nat) tptp.nil_nat)))
% 2.52/3.49 (assert (forall ((P2 Bool) (Q2 Bool)) (= (= (@ tptp.pure_assn P2) (@ tptp.pure_assn Q2)) (= P2 Q2))))
% 2.52/3.49 (assert (forall ((A Bool) (B Bool)) (= (@ (@ tptp.times_times_assn (@ tptp.pure_assn A)) (@ tptp.pure_assn B)) (@ tptp.pure_assn (and A B)))))
% 2.52/3.49 (assert (forall ((P2 Bool)) (@ tptp.is_pure_assn (@ tptp.pure_assn P2))))
% 2.52/3.49 (assert (= tptp.is_pure_assn (lambda ((A2 tptp.assn)) (exists ((P Bool)) (= A2 (@ tptp.pure_assn P))))))
% 2.52/3.49 (assert (forall ((A tptp.assn)) (=> (@ tptp.is_pure_assn A) (not (forall ((P4 Bool)) (not (= A (@ tptp.pure_assn P4))))))))
% 2.52/3.49 (assert (= tptp.syntax7398250324933576852n_assn (lambda ((Pat tptp.assn) (Obj tptp.assn)) true)))
% 2.52/3.49 (assert (forall ((P2 tptp.assn) (Q2 tptp.assn) (B Bool)) (let ((_let_1 (@ tptp.entails P2))) (= (@ _let_1 (@ (@ tptp.times_times_assn Q2) (@ tptp.pure_assn B))) (and (forall ((H tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P2) H) B)) (@ _let_1 Q2))))))
% 2.52/3.49 (assert (forall ((B Bool) (Q2 tptp.assn)) (= (@ (@ tptp.entails (@ tptp.pure_assn B)) Q2) (=> B (@ (@ tptp.entails tptp.one_one_assn) Q2)))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.assn tptp.assn tptp.assn)) (X tptp.assn) (Y tptp.assn) (A tptp.assn) (B tptp.assn)) (=> (@ tptp.syntax3673046151410588037r_assn F2) (=> (@ (@ tptp.syntax7398250324933576852n_assn (@ (@ F2 X) Y)) A) (= (@ (@ F2 A) B) (@ (@ F2 B) A))))))
% 2.52/3.49 (assert (forall ((P2 tptp.assn) (B Bool) (Q2 tptp.assn)) (let ((_let_1 (@ tptp.pure_assn B))) (= (@ (@ tptp.inf_inf_assn (@ (@ tptp.times_times_assn P2) _let_1)) Q2) (@ (@ tptp.times_times_assn (@ (@ tptp.inf_inf_assn P2) Q2)) _let_1)))))
% 2.52/3.49 (assert (forall ((P2 tptp.assn) (Q2 tptp.assn) (B Bool)) (let ((_let_1 (@ tptp.pure_assn B))) (let ((_let_2 (@ tptp.inf_inf_assn P2))) (= (@ _let_2 (@ (@ tptp.times_times_assn Q2) _let_1)) (@ (@ tptp.times_times_assn (@ _let_2 Q2)) _let_1))))))
% 2.52/3.49 (assert (@ tptp.null_P7596217980778516671n_assn tptp.nil_Pr5671120429643327159n_assn))
% 2.52/3.49 (assert (@ tptp.null_int tptp.nil_int))
% 2.52/3.49 (assert (@ tptp.null_nat tptp.nil_nat))
% 2.52/3.49 (assert (forall ((A tptp.int) (P2 (-> tptp.int Bool))) (= (@ (@ tptp.member_int2 A) (@ tptp.collect_int P2)) (@ P2 A))))
% 2.52/3.49 (assert (forall ((A (-> tptp.produc3658429121746597890et_nat Bool)) (P2 (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (= (@ (@ tptp.member6576561426505652726_nat_o A) (@ tptp.collec939566748876313656_nat_o P2)) (@ P2 A))))
% 2.52/3.49 (assert (forall ((A tptp.list_nat) (P2 (-> tptp.list_nat Bool))) (= (@ (@ tptp.member_list_nat A) (@ tptp.collect_list_nat P2)) (@ P2 A))))
% 2.52/3.49 (assert (forall ((A tptp.nat) (P2 (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat2 A) (@ tptp.collect_nat P2)) (@ P2 A))))
% 2.52/3.49 (assert (forall ((A tptp.product_prod_nat_nat) (P2 (-> tptp.product_prod_nat_nat Bool))) (= (@ (@ tptp.member8440522571783428010at_nat A) (@ tptp.collec3392354462482085612at_nat P2)) (@ P2 A))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_int)) (= (@ tptp.collect_int (lambda ((X2 tptp.int)) (@ (@ tptp.member_int2 X2) A3))) A3)))
% 2.52/3.49 (assert (forall ((A3 tptp.set_Pr4532377907799695533_nat_o)) (= (@ tptp.collec939566748876313656_nat_o (lambda ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (@ (@ tptp.member6576561426505652726_nat_o X2) A3))) A3)))
% 2.52/3.49 (assert (forall ((A3 tptp.set_list_nat)) (= (@ tptp.collect_list_nat (lambda ((X2 tptp.list_nat)) (@ (@ tptp.member_list_nat X2) A3))) A3)))
% 2.52/3.49 (assert (forall ((A3 tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat2 X2) A3))) A3)))
% 2.52/3.49 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.collec3392354462482085612at_nat (lambda ((X2 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X2) A3))) A3)))
% 2.52/3.49 (assert (forall ((P2 (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool)) (Q2 (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (= (@ P2 X3) (@ Q2 X3))) (= (@ tptp.collec939566748876313656_nat_o P2) (@ tptp.collec939566748876313656_nat_o Q2)))))
% 2.52/3.49 (assert (forall ((P2 (-> tptp.list_nat Bool)) (Q2 (-> tptp.list_nat Bool))) (=> (forall ((X3 tptp.list_nat)) (= (@ P2 X3) (@ Q2 X3))) (= (@ tptp.collect_list_nat P2) (@ tptp.collect_list_nat Q2)))))
% 2.52/3.49 (assert (forall ((P2 (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (forall ((X3 tptp.nat)) (= (@ P2 X3) (@ Q2 X3))) (= (@ tptp.collect_nat P2) (@ tptp.collect_nat Q2)))))
% 2.52/3.49 (assert (forall ((P2 (-> tptp.product_prod_nat_nat Bool)) (Q2 (-> tptp.product_prod_nat_nat Bool))) (=> (forall ((X3 tptp.product_prod_nat_nat)) (= (@ P2 X3) (@ Q2 X3))) (= (@ tptp.collec3392354462482085612at_nat P2) (@ tptp.collec3392354462482085612at_nat Q2)))))
% 2.52/3.49 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn)) (= (= Xs tptp.nil_Pr5671120429643327159n_assn) (@ tptp.null_P7596217980778516671n_assn Xs))))
% 2.52/3.49 (assert (forall ((Xs tptp.list_int)) (= (= Xs tptp.nil_int) (@ tptp.null_int Xs))))
% 2.52/3.49 (assert (forall ((Xs tptp.list_nat)) (= (= Xs tptp.nil_nat) (@ tptp.null_nat Xs))))
% 2.52/3.49 (assert (forall ((Ys tptp.list_assn)) (= (@ (@ tptp.zip_assn_assn tptp.nil_assn) Ys) tptp.nil_Pr5671120429643327159n_assn)))
% 2.52/3.49 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_P8527749157015355191n_assn)) (= (= tptp.nil_Pr4327835960982145133n_assn (@ (@ tptp.zip_Pr8806919808394484215n_assn Xs) Ys)) (or (= Xs tptp.nil_Pr5671120429643327159n_assn) (= Ys tptp.nil_Pr5671120429643327159n_assn)))))
% 2.52/3.49 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_int)) (= (= tptp.nil_Pr7991254345159696774sn_int (@ (@ tptp.zip_Pr1015554993053626726sn_int Xs) Ys)) (or (= Xs tptp.nil_Pr5671120429643327159n_assn) (= Ys tptp.nil_int)))))
% 2.52/3.49 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_nat)) (= (= tptp.nil_Pr2945733327814117674sn_nat (@ (@ tptp.zip_Pr1018045463562677002sn_nat Xs) Ys)) (or (= Xs tptp.nil_Pr5671120429643327159n_assn) (= Ys tptp.nil_nat)))))
% 2.52/3.49 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_P8527749157015355191n_assn)) (= (= tptp.nil_Pr2440414457004260852n_assn (@ (@ tptp.zip_in7098856637274830732n_assn Xs) Ys)) (or (= Xs tptp.nil_int) (= Ys tptp.nil_Pr5671120429643327159n_assn)))))
% 2.52/3.49 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (= (= tptp.nil_Pr2300489316682597567nt_int (@ (@ tptp.zip_int_int Xs) Ys)) (or (= Xs tptp.nil_int) (= Ys tptp.nil_int)))))
% 2.52/3.49 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_nat)) (= (= tptp.nil_Pr6478340336191794275nt_nat (@ (@ tptp.zip_int_nat Xs) Ys)) (or (= Xs tptp.nil_int) (= Ys tptp.nil_nat)))))
% 2.52/3.49 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_P8527749157015355191n_assn)) (= (= tptp.nil_Pr680377793251149648n_assn (@ (@ tptp.zip_na5338819973521719528n_assn Xs) Ys)) (or (= Xs tptp.nil_nat) (= Ys tptp.nil_Pr5671120429643327159n_assn)))))
% 2.52/3.49 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_int)) (= (= tptp.nil_Pr1301135604781543011at_int (@ (@ tptp.zip_nat_int Xs) Ys)) (or (= Xs tptp.nil_nat) (= Ys tptp.nil_int)))))
% 2.52/3.49 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (= (= tptp.nil_Pr5478986624290739719at_nat (@ (@ tptp.zip_nat_nat Xs) Ys)) (or (= Xs tptp.nil_nat) (= Ys tptp.nil_nat)))))
% 2.52/3.49 (assert (forall ((Xs tptp.list_assn) (Ys tptp.list_assn)) (= (= tptp.nil_Pr5671120429643327159n_assn (@ (@ tptp.zip_assn_assn Xs) Ys)) (or (= Xs tptp.nil_assn) (= Ys tptp.nil_assn)))))
% 2.52/3.49 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_P8527749157015355191n_assn)) (= (= (@ (@ tptp.zip_Pr8806919808394484215n_assn Xs) Ys) tptp.nil_Pr4327835960982145133n_assn) (or (= Xs tptp.nil_Pr5671120429643327159n_assn) (= Ys tptp.nil_Pr5671120429643327159n_assn)))))
% 2.52/3.49 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_int)) (= (= (@ (@ tptp.zip_Pr1015554993053626726sn_int Xs) Ys) tptp.nil_Pr7991254345159696774sn_int) (or (= Xs tptp.nil_Pr5671120429643327159n_assn) (= Ys tptp.nil_int)))))
% 2.52/3.49 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_nat)) (= (= (@ (@ tptp.zip_Pr1018045463562677002sn_nat Xs) Ys) tptp.nil_Pr2945733327814117674sn_nat) (or (= Xs tptp.nil_Pr5671120429643327159n_assn) (= Ys tptp.nil_nat)))))
% 2.52/3.49 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_P8527749157015355191n_assn)) (= (= (@ (@ tptp.zip_in7098856637274830732n_assn Xs) Ys) tptp.nil_Pr2440414457004260852n_assn) (or (= Xs tptp.nil_int) (= Ys tptp.nil_Pr5671120429643327159n_assn)))))
% 2.52/3.49 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (= (= (@ (@ tptp.zip_int_int Xs) Ys) tptp.nil_Pr2300489316682597567nt_int) (or (= Xs tptp.nil_int) (= Ys tptp.nil_int)))))
% 2.52/3.49 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_nat)) (= (= (@ (@ tptp.zip_int_nat Xs) Ys) tptp.nil_Pr6478340336191794275nt_nat) (or (= Xs tptp.nil_int) (= Ys tptp.nil_nat)))))
% 2.52/3.49 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_P8527749157015355191n_assn)) (= (= (@ (@ tptp.zip_na5338819973521719528n_assn Xs) Ys) tptp.nil_Pr680377793251149648n_assn) (or (= Xs tptp.nil_nat) (= Ys tptp.nil_Pr5671120429643327159n_assn)))))
% 2.52/3.49 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_int)) (= (= (@ (@ tptp.zip_nat_int Xs) Ys) tptp.nil_Pr1301135604781543011at_int) (or (= Xs tptp.nil_nat) (= Ys tptp.nil_int)))))
% 2.52/3.49 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (= (= (@ (@ tptp.zip_nat_nat Xs) Ys) tptp.nil_Pr5478986624290739719at_nat) (or (= Xs tptp.nil_nat) (= Ys tptp.nil_nat)))))
% 2.52/3.49 (assert (forall ((Xs tptp.list_assn) (Ys tptp.list_assn)) (= (= (@ (@ tptp.zip_assn_assn Xs) Ys) tptp.nil_Pr5671120429643327159n_assn) (or (= Xs tptp.nil_assn) (= Ys tptp.nil_assn)))))
% 2.52/3.49 (assert (forall ((P2 tptp.assn) (B Bool) (H2 tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn P2) (@ tptp.pure_assn B))) H2) (and (@ (@ tptp.rep_assn P2) H2) B))))
% 2.52/3.49 (assert (forall ((P2 (-> tptp.produc6575502325842934193n_assn Bool))) (not (@ (@ tptp.list_e1087220904399170805n_assn P2) tptp.nil_Pr5671120429643327159n_assn))))
% 2.52/3.49 (assert (forall ((P2 (-> tptp.int Bool))) (not (@ (@ tptp.list_ex_int P2) tptp.nil_int))))
% 2.52/3.49 (assert (forall ((P2 (-> tptp.nat Bool))) (not (@ (@ tptp.list_ex_nat P2) tptp.nil_nat))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (= (@ tptp.rep_assn X) (@ tptp.rep_assn Y)) (= X Y))))
% 2.52/3.49 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)))
% 2.52/3.49 (assert (forall ((A tptp.assn)) (= (@ (@ tptp.times_times_assn tptp.one_one_assn) A) A)))
% 2.52/3.49 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 2.52/3.49 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 2.52/3.49 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger tptp.one_one_Code_integer) A) A)))
% 2.52/3.49 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.times_2397367101498566445atural tptp.one_one_Code_natural) A) A)))
% 2.52/3.49 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)))
% 2.52/3.49 (assert (forall ((A tptp.assn)) (= (@ (@ tptp.times_times_assn A) tptp.one_one_assn) A)))
% 2.52/3.49 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 2.52/3.49 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 2.52/3.49 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger A) tptp.one_one_Code_integer) A)))
% 2.52/3.49 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.times_2397367101498566445atural A) tptp.one_one_Code_natural) A)))
% 2.52/3.49 (assert (forall ((A Bool) (B Bool)) (= (@ (@ tptp.inf_inf_assn (@ tptp.pure_assn A)) (@ tptp.pure_assn B)) (@ tptp.pure_assn (and A B)))))
% 2.52/3.49 (assert (= (@ tptp.pure_assn true) tptp.one_one_assn))
% 2.52/3.49 (assert (forall ((P2 Bool)) (= (= (@ tptp.pure_assn P2) tptp.one_one_assn) P2)))
% 2.52/3.49 (assert (forall ((P2 tptp.assn) (B Bool)) (let ((_let_1 (@ tptp.entails P2))) (= (@ _let_1 (@ tptp.pure_assn B)) (and (forall ((H tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P2) H) B)) (@ _let_1 tptp.one_one_assn))))))
% 2.52/3.49 (assert (forall ((P2 tptp.assn) (B Bool)) (let ((_let_1 (@ tptp.pure_assn B))) (= (@ (@ tptp.inf_inf_assn P2) _let_1) (@ (@ tptp.times_times_assn (@ (@ tptp.inf_inf_assn tptp.one_one_assn) P2)) _let_1)))))
% 2.52/3.49 (assert (forall ((B Bool) (Q2 tptp.assn)) (let ((_let_1 (@ tptp.pure_assn B))) (= (@ (@ tptp.inf_inf_assn _let_1) Q2) (@ (@ tptp.times_times_assn (@ (@ tptp.inf_inf_assn tptp.one_one_assn) Q2)) _let_1)))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (= (@ (@ tptp.inf_inf_assn (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_inf_assn Y) Z))))))
% 2.52/3.49 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn X) X) X)))
% 2.52/3.49 (assert (= tptp.inf_inf_assn (lambda ((X2 tptp.assn) (Y2 tptp.assn)) (@ (@ tptp.inf_inf_assn Y2) X2))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (let ((_let_2 (@ tptp.inf_inf_assn Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 2.52/3.49 (assert (forall ((X tptp.code_integer)) (= (= tptp.one_one_Code_integer X) (= X tptp.one_one_Code_integer))))
% 2.52/3.49 (assert (forall ((X tptp.assn)) (= (= tptp.one_one_assn X) (= X tptp.one_one_assn))))
% 2.52/3.49 (assert (forall ((X tptp.rat)) (= (= tptp.one_one_rat X) (= X tptp.one_one_rat))))
% 2.52/3.49 (assert (forall ((X tptp.nat)) (= (= tptp.one_one_nat X) (= X tptp.one_one_nat))))
% 2.52/3.49 (assert (forall ((X tptp.int)) (= (= tptp.one_one_int X) (= X tptp.one_one_int))))
% 2.52/3.49 (assert (forall ((P2 tptp.assn) (Q2 tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn (@ (@ tptp.inf_inf_assn P2) Q2)) H2) (and (@ (@ tptp.rep_assn P2) H2) (@ (@ tptp.rep_assn Q2) H2)))))
% 2.52/3.49 (assert (forall ((A tptp.assn) (B tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn A) B)) H2) (not (=> (exists ((X_1 tptp.produc3658429121746597890et_nat)) (@ (@ tptp.rep_assn A) X_1)) (forall ((H_2 tptp.produc3658429121746597890et_nat)) (not (@ (@ tptp.rep_assn B) H_2))))))))
% 2.52/3.49 (assert (forall ((A3 tptp.assn) (B3 tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn A3) B3)) H2) (exists ((H1 tptp.produc3658429121746597890et_nat) (H22 tptp.produc3658429121746597890et_nat)) (and (@ (@ tptp.rep_assn A3) H1) (@ (@ tptp.rep_assn B3) H22))))))
% 2.52/3.49 (assert (= tptp.entails (lambda ((P tptp.assn) (Q tptp.assn)) (forall ((H tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P) H) (@ (@ tptp.rep_assn Q) H))))))
% 2.52/3.49 (assert (forall ((P2 tptp.assn) (Q2 tptp.assn)) (=> (forall ((H3 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P2) H3) (@ (@ tptp.rep_assn Q2) H3))) (@ (@ tptp.entails P2) Q2))))
% 2.52/3.49 (assert (forall ((P2 tptp.assn) (Q2 tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.entails P2) Q2) (=> (@ (@ tptp.rep_assn P2) H2) (@ (@ tptp.rep_assn Q2) H2)))))
% 2.52/3.49 (assert (forall ((P2 tptp.assn) (H2 tptp.produc3658429121746597890et_nat) (Q2 tptp.assn)) (=> (@ (@ tptp.rep_assn P2) H2) (=> (@ (@ tptp.entails P2) Q2) (@ (@ tptp.rep_assn Q2) H2)))))
% 2.52/3.49 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)))
% 2.52/3.49 (assert (forall ((A tptp.assn)) (= (@ (@ tptp.times_times_assn A) tptp.one_one_assn) A)))
% 2.52/3.49 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 2.52/3.49 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 2.52/3.49 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger A) tptp.one_one_Code_integer) A)))
% 2.52/3.49 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.times_2397367101498566445atural A) tptp.one_one_Code_natural) A)))
% 2.52/3.49 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)))
% 2.52/3.49 (assert (forall ((A tptp.assn)) (= (@ (@ tptp.times_times_assn tptp.one_one_assn) A) A)))
% 2.52/3.49 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 2.52/3.49 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 2.52/3.49 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger tptp.one_one_Code_integer) A) A)))
% 2.52/3.49 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.times_2397367101498566445atural tptp.one_one_Code_natural) A) A)))
% 2.52/3.49 (assert (forall ((B3 tptp.assn) (C2 tptp.assn) (A3 tptp.assn)) (=> (@ (@ tptp.entails B3) C2) (@ (@ tptp.entails (@ (@ tptp.inf_inf_assn A3) B3)) C2))))
% 2.52/3.49 (assert (forall ((A3 tptp.assn) (C2 tptp.assn) (B3 tptp.assn)) (=> (@ (@ tptp.entails A3) C2) (@ (@ tptp.entails (@ (@ tptp.inf_inf_assn A3) B3)) C2))))
% 2.52/3.49 (assert (forall ((A3 tptp.assn) (B3 tptp.assn) (C2 tptp.assn)) (let ((_let_1 (@ tptp.entails A3))) (=> (@ _let_1 B3) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.inf_inf_assn B3) C2)))))))
% 2.52/3.49 (assert (forall ((P2 tptp.assn)) (= (@ (@ tptp.times_times_assn tptp.one_one_assn) P2) P2)))
% 2.52/3.49 (assert (forall ((A tptp.assn)) (= (@ (@ tptp.times_times_assn tptp.one_one_assn) A) A)))
% 2.52/3.49 (assert (forall ((A tptp.assn)) (= (@ (@ tptp.times_times_assn A) tptp.one_one_assn) A)))
% 2.52/3.49 (assert (@ tptp.is_pure_assn tptp.one_one_assn))
% 2.52/3.49 (assert (= tptp.sln tptp.one_one_assn))
% 2.52/3.49 (assert (@ tptp.syntax3673046151410588037r_assn tptp.times_times_assn))
% 2.52/3.49 (assert (@ tptp.syntax8800539067650720301or_nat tptp.times_times_nat))
% 2.52/3.49 (assert (@ tptp.syntax8798048597141670025or_int tptp.times_times_int))
% 2.52/3.49 (assert (@ tptp.syntax414191934074104506nteger tptp.times_3573771949741848930nteger))
% 2.52/3.49 (assert (@ tptp.syntax8461159122685597829atural tptp.times_2397367101498566445atural))
% 2.52/3.49 (assert (forall ((Xs tptp.list_assn)) (= (@ (@ tptp.zip_assn_assn Xs) tptp.nil_assn) tptp.nil_Pr5671120429643327159n_assn)))
% 2.52/3.49 (assert (= tptp.inf_in3604695632404883862_int_o (lambda ((F3 (-> tptp.product_prod_int_int Bool)) (G (-> tptp.product_prod_int_int Bool)) (X2 tptp.product_prod_int_int)) (@ (@ tptp.inf_inf_o (@ F3 X2)) (@ G X2)))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn)) (let ((_let_1 (@ (@ tptp.inf_inf_assn X) Y))) (= (@ (@ tptp.inf_inf_assn _let_1) Y) _let_1))))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ tptp.inf_in2572325071724192079at_nat X) Y))) (= (@ (@ tptp.inf_in2572325071724192079at_nat _let_1) Y) _let_1))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (let ((_let_1 (@ (@ tptp.inf_inf_set_nat X) Y))) (= (@ (@ tptp.inf_inf_set_nat _let_1) Y) _let_1))))
% 2.52/3.49 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.inf_inf_nat X) Y))) (= (@ (@ tptp.inf_inf_nat _let_1) Y) _let_1))))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ (@ tptp.inf_in3604695632404883862_int_o X) Y))) (= (@ (@ tptp.inf_in3604695632404883862_int_o _let_1) Y) _let_1))))
% 2.52/3.49 (assert (forall ((A tptp.assn) (B tptp.assn)) (let ((_let_1 (@ (@ tptp.inf_inf_assn A) B))) (= (@ (@ tptp.inf_inf_assn _let_1) B) _let_1))))
% 2.52/3.49 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A) B))) (= (@ (@ tptp.inf_in2572325071724192079at_nat _let_1) B) _let_1))))
% 2.52/3.49 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ (@ tptp.inf_inf_set_nat A) B))) (= (@ (@ tptp.inf_inf_set_nat _let_1) B) _let_1))))
% 2.52/3.49 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.inf_inf_nat A) B))) (= (@ (@ tptp.inf_inf_nat _let_1) B) _let_1))))
% 2.52/3.49 (assert (forall ((A (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ (@ tptp.inf_in3604695632404883862_int_o A) B))) (= (@ (@ tptp.inf_in3604695632404883862_int_o _let_1) B) _let_1))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 2.52/3.49 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.inf_in3604695632404883862_int_o X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 2.52/3.49 (assert (forall ((A tptp.assn) (B tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 2.52/3.49 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 2.52/3.49 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 2.52/3.49 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 2.52/3.49 (assert (forall ((A (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.inf_in3604695632404883862_int_o A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 2.52/3.49 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn X) X) X)))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat X) X) X)))
% 2.52/3.49 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X) X) X)))
% 2.52/3.49 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.inf_inf_nat X) X) X)))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.inf_in3604695632404883862_int_o X) X) X)))
% 2.52/3.49 (assert (forall ((A tptp.assn)) (= (@ (@ tptp.inf_inf_assn A) A) A)))
% 2.52/3.49 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A) A) A)))
% 2.52/3.49 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A) A) A)))
% 2.52/3.49 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.inf_inf_nat A) A) A)))
% 2.52/3.49 (assert (forall ((A (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.inf_in3604695632404883862_int_o A) A) A)))
% 2.52/3.49 (assert (= tptp.inf_in3604695632404883862_int_o (lambda ((F3 (-> tptp.product_prod_int_int Bool)) (G (-> tptp.product_prod_int_int Bool)) (X2 tptp.product_prod_int_int)) (@ (@ tptp.inf_inf_o (@ F3 X2)) (@ G X2)))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 2.52/3.49 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.inf_in3604695632404883862_int_o X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (let ((_let_2 (@ tptp.inf_inf_assn Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (let ((_let_2 (@ tptp.inf_in2572325071724192079at_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (let ((_let_2 (@ tptp.inf_inf_set_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 2.52/3.49 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (let ((_let_2 (@ tptp.inf_inf_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool)) (Z (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.inf_in3604695632404883862_int_o X))) (let ((_let_2 (@ tptp.inf_in3604695632404883862_int_o Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (= (@ (@ tptp.inf_inf_assn (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_inf_assn Y) Z))))))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z))))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (= (@ (@ tptp.inf_inf_set_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y) Z))))))
% 2.52/3.49 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (= (@ (@ tptp.inf_inf_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z))))))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool)) (Z (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.inf_in3604695632404883862_int_o X))) (= (@ (@ tptp.inf_in3604695632404883862_int_o (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_in3604695632404883862_int_o Y) Z))))))
% 2.52/3.49 (assert (= tptp.inf_inf_assn (lambda ((X2 tptp.assn) (Y2 tptp.assn)) (@ (@ tptp.inf_inf_assn Y2) X2))))
% 2.52/3.49 (assert (= tptp.inf_in2572325071724192079at_nat (lambda ((X2 tptp.set_Pr1261947904930325089at_nat) (Y2 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.inf_in2572325071724192079at_nat Y2) X2))))
% 2.52/3.49 (assert (= tptp.inf_inf_set_nat (lambda ((X2 tptp.set_nat) (Y2 tptp.set_nat)) (@ (@ tptp.inf_inf_set_nat Y2) X2))))
% 2.52/3.49 (assert (= tptp.inf_inf_nat (lambda ((X2 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.inf_inf_nat Y2) X2))))
% 2.52/3.49 (assert (= tptp.inf_in3604695632404883862_int_o (lambda ((X2 (-> tptp.product_prod_int_int Bool)) (Y2 (-> tptp.product_prod_int_int Bool)) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ (@ tptp.inf_in3604695632404883862_int_o Y2) X2) __flatten_var_0))))
% 2.52/3.49 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn A))) (= (@ (@ tptp.inf_inf_assn (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.inf_inf_assn B) C))))))
% 2.52/3.49 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A))) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B) C))))))
% 2.52/3.49 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (= (@ (@ tptp.inf_inf_set_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.inf_inf_set_nat B) C))))))
% 2.52/3.49 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat A))) (= (@ (@ tptp.inf_inf_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.inf_inf_nat B) C))))))
% 2.52/3.49 (assert (forall ((A (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool)) (C (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.inf_in3604695632404883862_int_o A))) (= (@ (@ tptp.inf_in3604695632404883862_int_o (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.inf_in3604695632404883862_int_o B) C))))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (= (@ (@ tptp.inf_inf_assn (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_inf_assn Y) Z))))))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z))))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (= (@ (@ tptp.inf_inf_set_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y) Z))))))
% 2.52/3.49 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (= (@ (@ tptp.inf_inf_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z))))))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool)) (Z (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.inf_in3604695632404883862_int_o X))) (= (@ (@ tptp.inf_in3604695632404883862_int_o (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_in3604695632404883862_int_o Y) Z))))))
% 2.52/3.49 (assert (= tptp.inf_inf_assn (lambda ((A2 tptp.assn) (B2 tptp.assn)) (@ (@ tptp.inf_inf_assn B2) A2))))
% 2.52/3.49 (assert (= tptp.inf_in2572325071724192079at_nat (lambda ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.inf_in2572325071724192079at_nat B2) A2))))
% 2.52/3.49 (assert (= tptp.inf_inf_set_nat (lambda ((A2 tptp.set_nat) (B2 tptp.set_nat)) (@ (@ tptp.inf_inf_set_nat B2) A2))))
% 2.52/3.49 (assert (= tptp.inf_inf_nat (lambda ((A2 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.inf_inf_nat B2) A2))))
% 2.52/3.49 (assert (= tptp.inf_in3604695632404883862_int_o (lambda ((A2 (-> tptp.product_prod_int_int Bool)) (B2 (-> tptp.product_prod_int_int Bool)) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ (@ tptp.inf_in3604695632404883862_int_o B2) A2) __flatten_var_0))))
% 2.52/3.49 (assert (= tptp.inf_inf_assn (lambda ((X2 tptp.assn) (Y2 tptp.assn)) (@ (@ tptp.inf_inf_assn Y2) X2))))
% 2.52/3.49 (assert (= tptp.inf_in2572325071724192079at_nat (lambda ((X2 tptp.set_Pr1261947904930325089at_nat) (Y2 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.inf_in2572325071724192079at_nat Y2) X2))))
% 2.52/3.49 (assert (= tptp.inf_inf_set_nat (lambda ((X2 tptp.set_nat) (Y2 tptp.set_nat)) (@ (@ tptp.inf_inf_set_nat Y2) X2))))
% 2.52/3.49 (assert (= tptp.inf_inf_nat (lambda ((X2 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.inf_inf_nat Y2) X2))))
% 2.52/3.49 (assert (= tptp.inf_in3604695632404883862_int_o (lambda ((X2 (-> tptp.product_prod_int_int Bool)) (Y2 (-> tptp.product_prod_int_int Bool)) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ (@ tptp.inf_in3604695632404883862_int_o Y2) X2) __flatten_var_0))))
% 2.52/3.49 (assert (forall ((B tptp.assn) (A tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn B))) (let ((_let_2 (@ tptp.inf_inf_assn A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 2.52/3.49 (assert (forall ((B tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat B))) (let ((_let_2 (@ tptp.inf_in2572325071724192079at_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 2.52/3.49 (assert (forall ((B tptp.set_nat) (A tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat B))) (let ((_let_2 (@ tptp.inf_inf_set_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 2.52/3.49 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat B))) (let ((_let_2 (@ tptp.inf_inf_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 2.52/3.49 (assert (forall ((B (-> tptp.product_prod_int_int Bool)) (A (-> tptp.product_prod_int_int Bool)) (C (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.inf_in3604695632404883862_int_o B))) (let ((_let_2 (@ tptp.inf_in3604695632404883862_int_o A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (let ((_let_2 (@ tptp.inf_inf_assn Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (let ((_let_2 (@ tptp.inf_in2572325071724192079at_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (let ((_let_2 (@ tptp.inf_inf_set_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 2.52/3.49 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (let ((_let_2 (@ tptp.inf_inf_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool)) (Z (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.inf_in3604695632404883862_int_o X))) (let ((_let_2 (@ tptp.inf_in3604695632404883862_int_o Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 2.52/3.49 (assert (forall ((A3 tptp.assn) (K tptp.assn) (A tptp.assn) (B tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.inf_inf_assn A3) B) (@ _let_1 (@ (@ tptp.inf_inf_assn A) B)))))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (K tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) B) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A) B)))))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_nat) (K tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.inf_inf_set_nat A3) B) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B)))))))
% 2.52/3.49 (assert (forall ((A3 tptp.nat) (K tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.inf_inf_nat A3) B) (@ _let_1 (@ (@ tptp.inf_inf_nat A) B)))))))
% 2.52/3.49 (assert (forall ((A3 (-> tptp.product_prod_int_int Bool)) (K (-> tptp.product_prod_int_int Bool)) (A (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.inf_in3604695632404883862_int_o K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.inf_in3604695632404883862_int_o A3) B) (@ _let_1 (@ (@ tptp.inf_in3604695632404883862_int_o A) B)))))))
% 2.52/3.49 (assert (forall ((B3 tptp.assn) (K tptp.assn) (B tptp.assn) (A tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn A))) (let ((_let_2 (@ tptp.inf_inf_assn K))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B))))))))
% 2.52/3.49 (assert (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (K tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A))) (let ((_let_2 (@ tptp.inf_in2572325071724192079at_nat K))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B))))))))
% 2.52/3.49 (assert (forall ((B3 tptp.set_nat) (K tptp.set_nat) (B tptp.set_nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (let ((_let_2 (@ tptp.inf_inf_set_nat K))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B))))))))
% 2.52/3.49 (assert (forall ((B3 tptp.nat) (K tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat A))) (let ((_let_2 (@ tptp.inf_inf_nat K))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B))))))))
% 2.52/3.49 (assert (forall ((B3 (-> tptp.product_prod_int_int Bool)) (K (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool)) (A (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.inf_in3604695632404883862_int_o A))) (let ((_let_2 (@ tptp.inf_in3604695632404883862_int_o K))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B))))))))
% 2.52/3.49 (assert (@ (@ tptp.monoid_rat tptp.times_times_rat) tptp.one_one_rat))
% 2.52/3.49 (assert (@ (@ tptp.monoid_assn tptp.times_times_assn) tptp.one_one_assn))
% 2.52/3.49 (assert (@ (@ tptp.monoid_nat tptp.times_times_nat) tptp.one_one_nat))
% 2.52/3.49 (assert (@ (@ tptp.monoid_int tptp.times_times_int) tptp.one_one_int))
% 2.52/3.49 (assert (@ (@ tptp.monoid_Code_integer tptp.times_3573771949741848930nteger) tptp.one_one_Code_integer))
% 2.52/3.49 (assert (@ (@ tptp.monoid_Code_natural tptp.times_2397367101498566445atural) tptp.one_one_Code_natural))
% 2.52/3.49 (assert (forall ((P2 tptp.assn)) (= (@ (@ tptp.entails P2) tptp.bot_bot_assn) (forall ((H tptp.produc3658429121746597890et_nat)) (not (@ (@ tptp.rep_assn P2) H))))))
% 2.52/3.49 (assert (@ (@ tptp.comm_monoid_rat tptp.times_times_rat) tptp.one_one_rat))
% 2.52/3.49 (assert (@ (@ tptp.comm_monoid_assn tptp.times_times_assn) tptp.one_one_assn))
% 2.52/3.49 (assert (@ (@ tptp.comm_monoid_nat tptp.times_times_nat) tptp.one_one_nat))
% 2.52/3.49 (assert (@ (@ tptp.comm_monoid_int tptp.times_times_int) tptp.one_one_int))
% 2.52/3.49 (assert (@ (@ tptp.comm_m1654649897431166824nteger tptp.times_3573771949741848930nteger) tptp.one_one_Code_integer))
% 2.52/3.49 (assert (@ (@ tptp.comm_m478245049187884339atural tptp.times_2397367101498566445atural) tptp.one_one_Code_natural))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.produc6575502325842934193n_assn tptp.option7057359848497031415n_assn))) (= (@ (@ tptp.map_fi2680429960852639882n_assn F2) tptp.nil_Pr5671120429643327159n_assn) tptp.nil_Pr5671120429643327159n_assn)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.produc6575502325842934193n_assn tptp.option_int))) (= (@ (@ tptp.map_fi8666144670822621843sn_int F2) tptp.nil_Pr5671120429643327159n_assn) tptp.nil_int)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.produc6575502325842934193n_assn tptp.option_nat))) (= (@ (@ tptp.map_fi8668635141331672119sn_nat F2) tptp.nil_Pr5671120429643327159n_assn) tptp.nil_nat)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.int tptp.option7057359848497031415n_assn))) (= (@ (@ tptp.map_fi5526074278189050041n_assn F2) tptp.nil_int) tptp.nil_Pr5671120429643327159n_assn)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.int tptp.option_int))) (= (@ (@ tptp.map_filter_int_int F2) tptp.nil_int) tptp.nil_int)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.int tptp.option_nat))) (= (@ (@ tptp.map_filter_int_nat F2) tptp.nil_int) tptp.nil_nat)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.nat tptp.option7057359848497031415n_assn))) (= (@ (@ tptp.map_fi3766037614435938837n_assn F2) tptp.nil_nat) tptp.nil_Pr5671120429643327159n_assn)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.nat tptp.option_int))) (= (@ (@ tptp.map_filter_nat_int F2) tptp.nil_nat) tptp.nil_int)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.nat tptp.option_nat))) (= (@ (@ tptp.map_filter_nat_nat F2) tptp.nil_nat) tptp.nil_nat)))
% 2.52/3.49 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn)) (= (@ (@ tptp.splice4588524007259616650n_assn Xs) tptp.nil_Pr5671120429643327159n_assn) Xs)))
% 2.52/3.49 (assert (forall ((Xs tptp.list_int)) (= (@ (@ tptp.splice_int Xs) tptp.nil_int) Xs)))
% 2.52/3.49 (assert (forall ((Xs tptp.list_nat)) (= (@ (@ tptp.splice_nat Xs) tptp.nil_nat) Xs)))
% 2.52/3.49 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_P8527749157015355191n_assn)) (= (= (@ (@ tptp.splice4588524007259616650n_assn Xs) Ys) tptp.nil_Pr5671120429643327159n_assn) (and (= Xs tptp.nil_Pr5671120429643327159n_assn) (= Ys tptp.nil_Pr5671120429643327159n_assn)))))
% 2.52/3.49 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (= (= (@ (@ tptp.splice_int Xs) Ys) tptp.nil_int) (and (= Xs tptp.nil_int) (= Ys tptp.nil_int)))))
% 2.52/3.49 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (= (= (@ (@ tptp.splice_nat Xs) Ys) tptp.nil_nat) (and (= Xs tptp.nil_nat) (= Ys tptp.nil_nat)))))
% 2.52/3.49 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn)) (= (= (@ tptp.rotate328796349445179396n_assn Xs) tptp.nil_Pr5671120429643327159n_assn) (= Xs tptp.nil_Pr5671120429643327159n_assn))))
% 2.52/3.49 (assert (forall ((Xs tptp.list_int)) (= (= (@ tptp.rotate1_int Xs) tptp.nil_int) (= Xs tptp.nil_int))))
% 2.52/3.49 (assert (forall ((Xs tptp.list_nat)) (= (= (@ tptp.rotate1_nat Xs) tptp.nil_nat) (= Xs tptp.nil_nat))))
% 2.52/3.49 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.enumer9200277086812776726n_assn N) tptp.nil_Pr5671120429643327159n_assn) tptp.nil_Pr680377793251149648n_assn)))
% 2.52/3.49 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.enumerate_int N) tptp.nil_int) tptp.nil_Pr1301135604781543011at_int)))
% 2.52/3.49 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.enumerate_nat N) tptp.nil_nat) tptp.nil_Pr5478986624290739719at_nat)))
% 2.52/3.49 (assert (forall ((P2 tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P2) H2) (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn P2) tptp.top_top_assn)) H2))))
% 2.52/3.49 (assert (forall ((P2 tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn P2) tptp.top_top_assn)) H2) (not (forall ((H4 tptp.produc3658429121746597890et_nat)) (not (@ (@ tptp.rep_assn P2) H4)))))))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat X) tptp.bot_bo2099793752762293965at_nat) tptp.bot_bo2099793752762293965at_nat)))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.inf_in3604695632404883862_int_o X) tptp.bot_bo8147686125503663512_int_o) tptp.bot_bo8147686125503663512_int_o)))
% 2.52/3.49 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn X) tptp.bot_bot_assn) tptp.bot_bot_assn)))
% 2.52/3.49 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X) tptp.bot_bot_set_nat) tptp.bot_bot_set_nat)))
% 2.52/3.49 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int X) tptp.bot_bot_set_int) tptp.bot_bot_set_int)))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bot_bo2099793752762293965at_nat) X) tptp.bot_bo2099793752762293965at_nat)))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.inf_in3604695632404883862_int_o tptp.bot_bo8147686125503663512_int_o) X) tptp.bot_bo8147686125503663512_int_o)))
% 2.52/3.49 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn tptp.bot_bot_assn) X) tptp.bot_bot_assn)))
% 2.52/3.49 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat tptp.bot_bot_set_nat) X) tptp.bot_bot_set_nat)))
% 2.52/3.49 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int tptp.bot_bot_set_int) X) tptp.bot_bot_set_int)))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat X) tptp.bot_bo2099793752762293965at_nat) tptp.bot_bo2099793752762293965at_nat)))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.inf_in3604695632404883862_int_o X) tptp.bot_bo8147686125503663512_int_o) tptp.bot_bo8147686125503663512_int_o)))
% 2.52/3.49 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn X) tptp.bot_bot_assn) tptp.bot_bot_assn)))
% 2.52/3.49 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X) tptp.bot_bot_set_nat) tptp.bot_bot_set_nat)))
% 2.52/3.49 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int X) tptp.bot_bot_set_int) tptp.bot_bot_set_int)))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bot_bo2099793752762293965at_nat) X) tptp.bot_bo2099793752762293965at_nat)))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.inf_in3604695632404883862_int_o tptp.bot_bo8147686125503663512_int_o) X) tptp.bot_bo8147686125503663512_int_o)))
% 2.52/3.49 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn tptp.bot_bot_assn) X) tptp.bot_bot_assn)))
% 2.52/3.49 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat tptp.bot_bot_set_nat) X) tptp.bot_bot_set_nat)))
% 2.52/3.49 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int tptp.bot_bot_set_int) X) tptp.bot_bot_set_int)))
% 2.52/3.49 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A) tptp.top_to4669805908274784177at_nat) A)))
% 2.52/3.49 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A) tptp.top_top_set_nat) A)))
% 2.52/3.49 (assert (forall ((A (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.inf_in3604695632404883862_int_o A) tptp.top_to1578927101902068148_int_o) A)))
% 2.52/3.49 (assert (forall ((A tptp.assn)) (= (@ (@ tptp.inf_inf_assn A) tptp.top_top_assn) A)))
% 2.52/3.49 (assert (forall ((A tptp.set_Product_unit)) (= (@ (@ tptp.inf_in4660618365625256667t_unit A) tptp.top_to1996260823553986621t_unit) A)))
% 2.52/3.49 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (= tptp.top_to4669805908274784177at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) (and (= A tptp.top_to4669805908274784177at_nat) (= B tptp.top_to4669805908274784177at_nat)))))
% 2.52/3.49 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (= tptp.top_top_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) (and (= A tptp.top_top_set_nat) (= B tptp.top_top_set_nat)))))
% 2.52/3.49 (assert (forall ((A (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool))) (= (= tptp.top_to1578927101902068148_int_o (@ (@ tptp.inf_in3604695632404883862_int_o A) B)) (and (= A tptp.top_to1578927101902068148_int_o) (= B tptp.top_to1578927101902068148_int_o)))))
% 2.52/3.49 (assert (forall ((A tptp.assn) (B tptp.assn)) (= (= tptp.top_top_assn (@ (@ tptp.inf_inf_assn A) B)) (and (= A tptp.top_top_assn) (= B tptp.top_top_assn)))))
% 2.52/3.49 (assert (forall ((A tptp.set_Product_unit) (B tptp.set_Product_unit)) (= (= tptp.top_to1996260823553986621t_unit (@ (@ tptp.inf_in4660618365625256667t_unit A) B)) (and (= A tptp.top_to1996260823553986621t_unit) (= B tptp.top_to1996260823553986621t_unit)))))
% 2.52/3.49 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.top_to4669805908274784177at_nat) A) A)))
% 2.52/3.49 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat tptp.top_top_set_nat) A) A)))
% 2.52/3.49 (assert (forall ((A (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.inf_in3604695632404883862_int_o tptp.top_to1578927101902068148_int_o) A) A)))
% 2.52/3.49 (assert (forall ((A tptp.assn)) (= (@ (@ tptp.inf_inf_assn tptp.top_top_assn) A) A)))
% 2.52/3.49 (assert (forall ((A tptp.set_Product_unit)) (= (@ (@ tptp.inf_in4660618365625256667t_unit tptp.top_to1996260823553986621t_unit) A) A)))
% 2.52/3.49 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.inf_in2572325071724192079at_nat A) B) tptp.top_to4669805908274784177at_nat) (and (= A tptp.top_to4669805908274784177at_nat) (= B tptp.top_to4669805908274784177at_nat)))))
% 2.52/3.49 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat A) B) tptp.top_top_set_nat) (and (= A tptp.top_top_set_nat) (= B tptp.top_top_set_nat)))))
% 2.52/3.49 (assert (forall ((A (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool))) (= (= (@ (@ tptp.inf_in3604695632404883862_int_o A) B) tptp.top_to1578927101902068148_int_o) (and (= A tptp.top_to1578927101902068148_int_o) (= B tptp.top_to1578927101902068148_int_o)))))
% 2.52/3.49 (assert (forall ((A tptp.assn) (B tptp.assn)) (= (= (@ (@ tptp.inf_inf_assn A) B) tptp.top_top_assn) (and (= A tptp.top_top_assn) (= B tptp.top_top_assn)))))
% 2.52/3.49 (assert (forall ((A tptp.set_Product_unit) (B tptp.set_Product_unit)) (= (= (@ (@ tptp.inf_in4660618365625256667t_unit A) B) tptp.top_to1996260823553986621t_unit) (and (= A tptp.top_to1996260823553986621t_unit) (= B tptp.top_to1996260823553986621t_unit)))))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (= tptp.top_to4669805908274784177at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)) (and (= X tptp.top_to4669805908274784177at_nat) (= Y tptp.top_to4669805908274784177at_nat)))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (= tptp.top_top_set_nat (@ (@ tptp.inf_inf_set_nat X) Y)) (and (= X tptp.top_top_set_nat) (= Y tptp.top_top_set_nat)))))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool))) (= (= tptp.top_to1578927101902068148_int_o (@ (@ tptp.inf_in3604695632404883862_int_o X) Y)) (and (= X tptp.top_to1578927101902068148_int_o) (= Y tptp.top_to1578927101902068148_int_o)))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (= tptp.top_top_assn (@ (@ tptp.inf_inf_assn X) Y)) (and (= X tptp.top_top_assn) (= Y tptp.top_top_assn)))))
% 2.52/3.49 (assert (forall ((X tptp.set_Product_unit) (Y tptp.set_Product_unit)) (= (= tptp.top_to1996260823553986621t_unit (@ (@ tptp.inf_in4660618365625256667t_unit X) Y)) (and (= X tptp.top_to1996260823553986621t_unit) (= Y tptp.top_to1996260823553986621t_unit)))))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.inf_in2572325071724192079at_nat X) Y) tptp.top_to4669805908274784177at_nat) (and (= X tptp.top_to4669805908274784177at_nat) (= Y tptp.top_to4669805908274784177at_nat)))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat X) Y) tptp.top_top_set_nat) (and (= X tptp.top_top_set_nat) (= Y tptp.top_top_set_nat)))))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool))) (= (= (@ (@ tptp.inf_in3604695632404883862_int_o X) Y) tptp.top_to1578927101902068148_int_o) (and (= X tptp.top_to1578927101902068148_int_o) (= Y tptp.top_to1578927101902068148_int_o)))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (= (@ (@ tptp.inf_inf_assn X) Y) tptp.top_top_assn) (and (= X tptp.top_top_assn) (= Y tptp.top_top_assn)))))
% 2.52/3.49 (assert (forall ((X tptp.set_Product_unit) (Y tptp.set_Product_unit)) (= (= (@ (@ tptp.inf_in4660618365625256667t_unit X) Y) tptp.top_to1996260823553986621t_unit) (and (= X tptp.top_to1996260823553986621t_unit) (= Y tptp.top_to1996260823553986621t_unit)))))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat X) tptp.top_to4669805908274784177at_nat) X)))
% 2.52/3.49 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X) tptp.top_top_set_nat) X)))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.inf_in3604695632404883862_int_o X) tptp.top_to1578927101902068148_int_o) X)))
% 2.52/3.49 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn X) tptp.top_top_assn) X)))
% 2.52/3.49 (assert (forall ((X tptp.set_Product_unit)) (= (@ (@ tptp.inf_in4660618365625256667t_unit X) tptp.top_to1996260823553986621t_unit) X)))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.top_to4669805908274784177at_nat) X) X)))
% 2.52/3.49 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat tptp.top_top_set_nat) X) X)))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.inf_in3604695632404883862_int_o tptp.top_to1578927101902068148_int_o) X) X)))
% 2.52/3.49 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn tptp.top_top_assn) X) X)))
% 2.52/3.49 (assert (forall ((X tptp.set_Product_unit)) (= (@ (@ tptp.inf_in4660618365625256667t_unit tptp.top_to1996260823553986621t_unit) X) X)))
% 2.52/3.49 (assert (= (@ (@ tptp.times_times_assn tptp.top_top_assn) tptp.top_top_assn) tptp.top_top_assn))
% 2.52/3.49 (assert (forall ((P2 tptp.assn)) (= (@ (@ tptp.times_times_assn P2) tptp.bot_bot_assn) tptp.bot_bot_assn)))
% 2.52/3.49 (assert (forall ((P2 tptp.assn)) (= (@ (@ tptp.times_times_assn tptp.bot_bot_assn) P2) tptp.bot_bot_assn)))
% 2.52/3.49 (assert (= (@ tptp.pure_assn false) tptp.bot_bot_assn))
% 2.52/3.49 (assert (forall ((P2 Bool)) (= (= (@ tptp.pure_assn P2) tptp.bot_bot_assn) (not P2))))
% 2.52/3.49 (assert (not (= tptp.top_top_assn tptp.one_one_assn)))
% 2.52/3.49 (assert (not (= tptp.top_top_assn tptp.bot_bot_assn)))
% 2.52/3.49 (assert (not (= tptp.bot_bot_assn tptp.one_one_assn)))
% 2.52/3.49 (assert (@ (@ tptp.comm_m5709050211238513046at_nat tptp.inf_in2572325071724192079at_nat) tptp.top_to4669805908274784177at_nat))
% 2.52/3.49 (assert (@ (@ tptp.comm_monoid_set_nat tptp.inf_inf_set_nat) tptp.top_top_set_nat))
% 2.52/3.49 (assert (@ (@ tptp.comm_m5839176995973721103_int_o tptp.inf_in3604695632404883862_int_o) tptp.top_to1578927101902068148_int_o))
% 2.52/3.49 (assert (@ (@ tptp.comm_monoid_assn tptp.inf_inf_assn) tptp.top_top_assn))
% 2.52/3.49 (assert (@ (@ tptp.comm_m7591727228438362018t_unit tptp.inf_in4660618365625256667t_unit) tptp.top_to1996260823553986621t_unit))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat X) tptp.top_to4669805908274784177at_nat) X)))
% 2.52/3.49 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X) tptp.top_top_set_nat) X)))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.inf_in3604695632404883862_int_o X) tptp.top_to1578927101902068148_int_o) X)))
% 2.52/3.49 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn X) tptp.top_top_assn) X)))
% 2.52/3.49 (assert (forall ((X tptp.set_Product_unit)) (= (@ (@ tptp.inf_in4660618365625256667t_unit X) tptp.top_to1996260823553986621t_unit) X)))
% 2.52/3.49 (assert (@ (@ tptp.monoid1519094961268053602at_nat tptp.inf_in2572325071724192079at_nat) tptp.top_to4669805908274784177at_nat))
% 2.52/3.49 (assert (@ (@ tptp.monoid_set_nat tptp.inf_inf_set_nat) tptp.top_top_set_nat))
% 2.52/3.49 (assert (@ (@ tptp.monoid6910981727789844035_int_o tptp.inf_in3604695632404883862_int_o) tptp.top_to1578927101902068148_int_o))
% 2.52/3.49 (assert (@ (@ tptp.monoid_assn tptp.inf_inf_assn) tptp.top_top_assn))
% 2.52/3.49 (assert (@ (@ tptp.monoid202360481972076142t_unit tptp.inf_in4660618365625256667t_unit) tptp.top_to1996260823553986621t_unit))
% 2.52/3.49 (assert (forall ((P2 tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn tptp.top_top_assn))) (let ((_let_2 (@ _let_1 P2))) (= (@ _let_1 _let_2) _let_2)))))
% 2.52/3.49 (assert (forall ((H2 tptp.produc3658429121746597890et_nat)) (not (@ (@ tptp.rep_assn tptp.bot_bot_assn) H2))))
% 2.52/3.49 (assert (forall ((P2 tptp.assn)) (@ (@ tptp.entails tptp.bot_bot_assn) P2)))
% 2.52/3.49 (assert (forall ((P2 tptp.assn)) (@ (@ tptp.entails P2) tptp.top_top_assn)))
% 2.52/3.49 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn tptp.bot_bot_assn) X) tptp.bot_bot_assn)))
% 2.52/3.49 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn X) tptp.bot_bot_assn) tptp.bot_bot_assn)))
% 2.52/3.49 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn tptp.top_top_assn) X) X)))
% 2.52/3.49 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn X) tptp.top_top_assn) X)))
% 2.52/3.49 (assert (@ tptp.is_pure_assn tptp.bot_bot_assn))
% 2.52/3.49 (assert (= (@ tptp.rotate328796349445179396n_assn tptp.nil_Pr5671120429643327159n_assn) tptp.nil_Pr5671120429643327159n_assn))
% 2.52/3.49 (assert (= (@ tptp.rotate1_int tptp.nil_int) tptp.nil_int))
% 2.52/3.49 (assert (= (@ tptp.rotate1_nat tptp.nil_nat) tptp.nil_nat))
% 2.52/3.49 (assert (forall ((Ys tptp.list_P8527749157015355191n_assn)) (= (@ (@ tptp.splice4588524007259616650n_assn tptp.nil_Pr5671120429643327159n_assn) Ys) Ys)))
% 2.52/3.49 (assert (forall ((Ys tptp.list_int)) (= (@ (@ tptp.splice_int tptp.nil_int) Ys) Ys)))
% 2.52/3.49 (assert (forall ((Ys tptp.list_nat)) (= (@ (@ tptp.splice_nat tptp.nil_nat) Ys) Ys)))
% 2.52/3.49 (assert (= tptp.entailst (lambda ((P tptp.assn) (Q tptp.assn)) (@ (@ tptp.entails (@ (@ tptp.times_times_assn P) tptp.top_top_assn)) (@ (@ tptp.times_times_assn Q) tptp.top_top_assn)))))
% 2.52/3.49 (assert (= tptp.entailst (lambda ((A4 tptp.assn) (B4 tptp.assn)) (@ (@ tptp.entails A4) (@ (@ tptp.times_times_assn B4) tptp.top_top_assn)))))
% 2.52/3.49 (assert (forall ((P2 tptp.assn) (Q2 tptp.assn)) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn P2) tptp.top_top_assn)) (@ (@ tptp.times_times_assn Q2) tptp.top_top_assn)) (@ (@ tptp.entailst P2) Q2))))
% 2.52/3.49 (assert (forall ((A3 tptp.assn) (B3 tptp.assn)) (=> (@ (@ tptp.entails A3) (@ (@ tptp.times_times_assn B3) tptp.top_top_assn)) (@ (@ tptp.entailst A3) B3))))
% 2.52/3.49 (assert (forall ((A3 tptp.assn) (B3 tptp.assn)) (=> (@ (@ tptp.entailst A3) B3) (@ (@ tptp.entails A3) (@ (@ tptp.times_times_assn B3) tptp.top_top_assn)))))
% 2.52/3.49 (assert (forall ((A3 tptp.assn) (B3 tptp.assn)) (= (@ (@ tptp.entailst (@ (@ tptp.times_times_assn A3) tptp.top_top_assn)) B3) (@ (@ tptp.entailst A3) B3))))
% 2.52/3.49 (assert (forall ((A3 tptp.assn) (B3 tptp.assn)) (let ((_let_1 (@ tptp.entailst A3))) (= (@ _let_1 (@ (@ tptp.times_times_assn B3) tptp.top_top_assn)) (@ _let_1 B3)))))
% 2.52/3.49 (assert (@ (@ tptp.semila858173770281612099at_nat tptp.inf_in2572325071724192079at_nat) tptp.top_to4669805908274784177at_nat))
% 2.52/3.49 (assert (@ (@ tptp.semila1241773964035338532et_nat tptp.inf_inf_set_nat) tptp.top_top_set_nat))
% 2.52/3.49 (assert (@ (@ tptp.semila6538661356715008162_int_o tptp.inf_in3604695632404883862_int_o) tptp.top_to1578927101902068148_int_o))
% 2.52/3.49 (assert (@ (@ tptp.semila5388846958306562758r_assn tptp.inf_inf_assn) tptp.top_top_assn))
% 2.52/3.49 (assert (@ (@ tptp.semila7638931295954862799t_unit tptp.inf_in4660618365625256667t_unit) tptp.top_to1996260823553986621t_unit))
% 2.52/3.49 (assert (forall ((A3 tptp.assn)) (@ (@ tptp.entailst A3) A3)))
% 2.52/3.49 (assert (forall ((A3 tptp.assn)) (@ (@ tptp.entailst A3) tptp.top_top_assn)))
% 2.52/3.49 (assert (forall ((A3 tptp.assn)) (@ (@ tptp.entailst A3) tptp.one_one_assn)))
% 2.52/3.49 (assert (forall ((A3 tptp.assn) (B3 tptp.assn) (C2 tptp.assn)) (let ((_let_1 (@ tptp.entailst A3))) (=> (@ _let_1 B3) (=> (@ (@ tptp.entailst B3) C2) (@ _let_1 C2))))))
% 2.52/3.49 (assert (forall ((P2 tptp.assn) (Q2 tptp.assn) (A3 tptp.assn) (F4 tptp.assn) (B3 tptp.assn)) (let ((_let_1 (@ tptp.entailst A3))) (=> (@ (@ tptp.entailst P2) Q2) (=> (@ _let_1 (@ (@ tptp.times_times_assn P2) F4)) (=> (@ (@ tptp.entailst (@ (@ tptp.times_times_assn Q2) F4)) B3) (@ _let_1 B3)))))))
% 2.52/3.49 (assert (forall ((A3 tptp.assn) (B3 tptp.assn) (C2 tptp.assn) (D tptp.assn)) (=> (@ (@ tptp.entailst A3) B3) (=> (@ (@ tptp.entailst C2) D) (@ (@ tptp.entailst (@ (@ tptp.times_times_assn A3) C2)) (@ (@ tptp.times_times_assn B3) D))))))
% 2.52/3.49 (assert (forall ((P2 tptp.assn) (Q2 tptp.assn)) (=> (@ (@ tptp.entails P2) Q2) (@ (@ tptp.entailst P2) Q2))))
% 2.52/3.49 (assert (forall ((H2 tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn tptp.top_top_assn) H2) (@ tptp.in_range H2))))
% 2.52/3.49 (assert (forall ((P2 tptp.assn) (Q2 tptp.assn) (H2 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) tptp.bot_bot_set_nat))) (= (@ (@ tptp.rep_assn (@ (@ tptp.inf_inf_assn P2) Q2)) _let_1) (and (@ (@ tptp.rep_assn P2) _let_1) (@ (@ tptp.rep_assn Q2) _let_1))))))
% 2.52/3.49 (assert (forall ((B Bool) (H2 tptp.heap_e7401611519738050253t_unit)) (= (@ (@ tptp.rep_assn (@ tptp.pure_assn B)) (@ (@ tptp.produc7507926704131184380et_nat H2) tptp.bot_bot_set_nat)) B)))
% 2.52/3.49 (assert (forall ((H2 tptp.heap_e7401611519738050253t_unit)) (@ tptp.in_range (@ (@ tptp.produc7507926704131184380et_nat H2) tptp.bot_bot_set_nat))))
% 2.52/3.49 (assert (forall ((P2 tptp.assn) (Q2 tptp.assn) (H2 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) tptp.bot_bot_set_nat))) (= (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn P2) Q2)) _let_1) (and (@ (@ tptp.rep_assn P2) _let_1) (@ (@ tptp.rep_assn Q2) _let_1))))))
% 2.52/3.49 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (not (forall ((H3 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (not (= X (@ (@ tptp.produc7507926704131184380et_nat H3) As)))))))
% 2.52/3.49 (assert (forall ((P2 tptp.assn) (H2 tptp.heap_e7401611519738050253t_unit) (H5 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ tptp.rep_assn P2))) (= (@ _let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) tptp.bot_bot_set_nat)) (@ _let_1 (@ (@ tptp.produc7507926704131184380et_nat H5) tptp.bot_bot_set_nat))))))
% 2.52/3.49 (assert (@ tptp.abel_semigroup_assn tptp.times_times_assn))
% 2.52/3.49 (assert (@ tptp.abel_semigroup_nat tptp.times_times_nat))
% 2.52/3.49 (assert (@ tptp.abel_semigroup_int tptp.times_times_int))
% 2.52/3.49 (assert (@ tptp.abel_s8772020223019846471nteger tptp.times_3573771949741848930nteger))
% 2.52/3.49 (assert (@ tptp.abel_s7595615374776563986atural tptp.times_2397367101498566445atural))
% 2.52/3.49 (assert (forall ((P2 tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P2) H2) (@ tptp.in_range H2))))
% 2.52/3.49 (assert (@ tptp.abel_semigroup_assn tptp.inf_inf_assn))
% 2.52/3.49 (assert (@ tptp.abel_s1357164767337380599at_nat tptp.inf_in2572325071724192079at_nat))
% 2.52/3.49 (assert (@ tptp.abel_s3907380067910933104et_nat tptp.inf_inf_set_nat))
% 2.52/3.49 (assert (@ tptp.abel_semigroup_nat tptp.inf_inf_nat))
% 2.52/3.49 (assert (@ tptp.abel_s3861158783995384302_int_o tptp.inf_in3604695632404883862_int_o))
% 2.52/3.49 (assert (@ tptp.semigroup_assn tptp.times_times_assn))
% 2.52/3.49 (assert (@ tptp.semigroup_nat tptp.times_times_nat))
% 2.52/3.49 (assert (@ tptp.semigroup_int tptp.times_times_int))
% 2.52/3.49 (assert (@ tptp.semigr7036097719740861967nteger tptp.times_3573771949741848930nteger))
% 2.52/3.49 (assert (@ tptp.semigr5859692871497579482atural tptp.times_2397367101498566445atural))
% 2.52/3.49 (assert (@ tptp.semilattice_assn tptp.inf_inf_assn))
% 2.52/3.49 (assert (@ tptp.semila6306352305301525377at_nat tptp.inf_in2572325071724192079at_nat))
% 2.52/3.49 (assert (@ tptp.semilattice_set_nat tptp.inf_inf_set_nat))
% 2.52/3.49 (assert (@ tptp.semilattice_nat tptp.inf_inf_nat))
% 2.52/3.49 (assert (@ tptp.semila1175464891343163876_int_o tptp.inf_in3604695632404883862_int_o))
% 2.52/3.49 (assert (@ tptp.semigroup_assn tptp.inf_inf_assn))
% 2.52/3.49 (assert (@ tptp.semigr3814207799437385263at_nat tptp.inf_in2572325071724192079at_nat))
% 2.52/3.49 (assert (@ tptp.semigroup_set_nat tptp.inf_inf_set_nat))
% 2.52/3.49 (assert (@ tptp.semigroup_nat tptp.inf_inf_nat))
% 2.52/3.49 (assert (@ tptp.semigr8095932293087610038_int_o tptp.inf_in3604695632404883862_int_o))
% 2.52/3.49 (assert (forall ((H2 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.rep_assn tptp.top_top_assn) (@ (@ tptp.produc7507926704131184380et_nat H2) tptp.bot_bot_set_nat))))
% 2.52/3.49 (assert (forall ((H2 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.rep_assn tptp.one_one_assn) (@ (@ tptp.produc7507926704131184380et_nat H2) tptp.bot_bot_set_nat))))
% 2.52/3.49 (assert (forall ((X Bool) (Xa tptp.produc3658429121746597890et_nat)) (=> (not (@ (@ tptp.pure_a825153325127701367it_nat X) Xa)) (not (forall ((H3 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (= Xa (@ (@ tptp.produc7507926704131184380et_nat H3) As)) (and (= As tptp.bot_bot_set_nat) X)))))))
% 2.52/3.49 (assert (forall ((X Bool) (Xa tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.pure_a825153325127701367it_nat X) Xa) (not (forall ((H3 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (= Xa (@ (@ tptp.produc7507926704131184380et_nat H3) As)) (not (and (= As tptp.bot_bot_set_nat) X))))))))
% 2.52/3.49 (assert (forall ((X Bool) (Xa tptp.produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ (@ tptp.pure_a825153325127701367it_nat X) Xa) Y) (not (forall ((H3 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (= Xa (@ (@ tptp.produc7507926704131184380et_nat H3) As)) (= Y (not (and (= As tptp.bot_bot_set_nat) X)))))))))
% 2.52/3.49 (assert (forall ((B Bool) (H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (= (@ (@ tptp.pure_a825153325127701367it_nat B) (@ (@ tptp.produc7507926704131184380et_nat H2) As2)) (and (= As2 tptp.bot_bot_set_nat) B))))
% 2.52/3.49 (assert (forall ((A3 tptp.assn) (B3 tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn A3) B3)) H2) (exists ((Hr tptp.heap_e7401611519738050253t_unit) (As1 tptp.set_nat) (As22 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat Hr))) (and (= H2 (@ _let_1 (@ (@ tptp.sup_sup_set_nat As1) As22))) (= (@ (@ tptp.inf_inf_set_nat As1) As22) tptp.bot_bot_set_nat) (@ (@ tptp.rep_assn A3) (@ _let_1 As1)) (@ (@ tptp.rep_assn B3) (@ _let_1 As22))))))))
% 2.52/3.49 (assert (forall ((P2 tptp.assn) (H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat) (Q2 tptp.assn) (As3 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H2))) (=> (@ (@ tptp.rep_assn P2) (@ _let_1 As2)) (=> (@ (@ tptp.rep_assn Q2) (@ _let_1 As3)) (=> (= (@ (@ tptp.inf_inf_set_nat As2) As3) tptp.bot_bot_set_nat) (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn P2) Q2)) (@ _let_1 (@ (@ tptp.sup_sup_set_nat As2) As3)))))))))
% 2.52/3.49 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (=> (not (@ tptp.one_assn_raw X)) (not (forall ((H3 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (= X (@ (@ tptp.produc7507926704131184380et_nat H3) As)) (= As tptp.bot_bot_set_nat)))))))
% 2.52/3.49 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ (@ tptp.sup_sup_set_nat A) B))) (= (@ (@ tptp.sup_sup_set_nat _let_1) B) _let_1))))
% 2.52/3.49 (assert (forall ((A tptp.assn) (B tptp.assn)) (let ((_let_1 (@ (@ tptp.sup_sup_assn A) B))) (= (@ (@ tptp.sup_sup_assn _let_1) B) _let_1))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 2.52/3.49 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 2.52/3.49 (assert (forall ((A tptp.assn) (B tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat X) X) X)))
% 2.52/3.49 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.sup_sup_assn X) X) X)))
% 2.52/3.49 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A) A) A)))
% 2.52/3.49 (assert (forall ((A tptp.assn)) (= (@ (@ tptp.sup_sup_assn A) A) A)))
% 2.52/3.49 (assert (forall ((A tptp.assn)) (= (@ (@ tptp.sup_sup_assn A) tptp.bot_bot_assn) A)))
% 2.52/3.49 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A) tptp.bot_bot_set_nat) A)))
% 2.52/3.49 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int A) tptp.bot_bot_set_int) A)))
% 2.52/3.49 (assert (forall ((A tptp.assn) (B tptp.assn)) (= (= tptp.bot_bot_assn (@ (@ tptp.sup_sup_assn A) B)) (and (= A tptp.bot_bot_assn) (= B tptp.bot_bot_assn)))))
% 2.52/3.49 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (= tptp.bot_bot_set_nat (@ (@ tptp.sup_sup_set_nat A) B)) (and (= A tptp.bot_bot_set_nat) (= B tptp.bot_bot_set_nat)))))
% 2.52/3.49 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (= (= tptp.bot_bot_set_int (@ (@ tptp.sup_sup_set_int A) B)) (and (= A tptp.bot_bot_set_int) (= B tptp.bot_bot_set_int)))))
% 2.52/3.49 (assert (forall ((A tptp.assn)) (= (@ (@ tptp.sup_sup_assn tptp.bot_bot_assn) A) A)))
% 2.52/3.49 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat tptp.bot_bot_set_nat) A) A)))
% 2.52/3.49 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int tptp.bot_bot_set_int) A) A)))
% 2.52/3.49 (assert (forall ((A tptp.assn) (B tptp.assn)) (= (= (@ (@ tptp.sup_sup_assn A) B) tptp.bot_bot_assn) (and (= A tptp.bot_bot_assn) (= B tptp.bot_bot_assn)))))
% 2.52/3.49 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (= (@ (@ tptp.sup_sup_set_nat A) B) tptp.bot_bot_set_nat) (and (= A tptp.bot_bot_set_nat) (= B tptp.bot_bot_set_nat)))))
% 2.52/3.49 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (= (= (@ (@ tptp.sup_sup_set_int A) B) tptp.bot_bot_set_int) (and (= A tptp.bot_bot_set_int) (= B tptp.bot_bot_set_int)))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (= (@ (@ tptp.sup_sup_assn X) Y) tptp.bot_bot_assn) (and (= X tptp.bot_bot_assn) (= Y tptp.bot_bot_assn)))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (= (@ (@ tptp.sup_sup_set_nat X) Y) tptp.bot_bot_set_nat) (and (= X tptp.bot_bot_set_nat) (= Y tptp.bot_bot_set_nat)))))
% 2.52/3.49 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (= (@ (@ tptp.sup_sup_set_int X) Y) tptp.bot_bot_set_int) (and (= X tptp.bot_bot_set_int) (= Y tptp.bot_bot_set_int)))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (= tptp.bot_bot_assn (@ (@ tptp.sup_sup_assn X) Y)) (and (= X tptp.bot_bot_assn) (= Y tptp.bot_bot_assn)))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (= tptp.bot_bot_set_nat (@ (@ tptp.sup_sup_set_nat X) Y)) (and (= X tptp.bot_bot_set_nat) (= Y tptp.bot_bot_set_nat)))))
% 2.52/3.49 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (= tptp.bot_bot_set_int (@ (@ tptp.sup_sup_set_int X) Y)) (and (= X tptp.bot_bot_set_int) (= Y tptp.bot_bot_set_int)))))
% 2.52/3.49 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.sup_sup_assn X) tptp.bot_bot_assn) X)))
% 2.52/3.49 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat X) tptp.bot_bot_set_nat) X)))
% 2.52/3.49 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int X) tptp.bot_bot_set_int) X)))
% 2.52/3.49 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.sup_sup_assn tptp.bot_bot_assn) X) X)))
% 2.52/3.49 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat tptp.bot_bot_set_nat) X) X)))
% 2.52/3.49 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int tptp.bot_bot_set_int) X) X)))
% 2.52/3.49 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat X) tptp.top_top_set_nat) tptp.top_top_set_nat)))
% 2.52/3.49 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.sup_sup_assn X) tptp.top_top_assn) tptp.top_top_assn)))
% 2.52/3.49 (assert (forall ((X tptp.set_Product_unit)) (= (@ (@ tptp.sup_su793286257634532545t_unit X) tptp.top_to1996260823553986621t_unit) tptp.top_to1996260823553986621t_unit)))
% 2.52/3.49 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat tptp.top_top_set_nat) X) tptp.top_top_set_nat)))
% 2.52/3.49 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.sup_sup_assn tptp.top_top_assn) X) tptp.top_top_assn)))
% 2.52/3.49 (assert (forall ((X tptp.set_Product_unit)) (= (@ (@ tptp.sup_su793286257634532545t_unit tptp.top_to1996260823553986621t_unit) X) tptp.top_to1996260823553986621t_unit)))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat X) (@ (@ tptp.sup_su6327502436637775413at_nat X) Y)) X)))
% 2.52/3.49 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.inf_inf_nat X) (@ (@ tptp.sup_sup_nat X) Y)) X)))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.inf_in3604695632404883862_int_o X) (@ (@ tptp.sup_su8463660629351352368_int_o X) Y)) X)))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X) (@ (@ tptp.sup_sup_set_nat X) Y)) X)))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (@ (@ tptp.inf_inf_assn X) (@ (@ tptp.sup_sup_assn X) Y)) X)))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat X) (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)) X)))
% 2.52/3.49 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.sup_sup_nat X) (@ (@ tptp.inf_inf_nat X) Y)) X)))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.sup_su8463660629351352368_int_o X) (@ (@ tptp.inf_in3604695632404883862_int_o X) Y)) X)))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat X) (@ (@ tptp.inf_inf_set_nat X) Y)) X)))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (@ (@ tptp.sup_sup_assn X) (@ (@ tptp.inf_inf_assn X) Y)) X)))
% 2.52/3.49 (assert (forall ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat) (As3 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H2))) (= (@ tptp.in_range (@ _let_1 (@ (@ tptp.sup_sup_set_nat As2) As3))) (and (@ tptp.in_range (@ _let_1 As2)) (@ tptp.in_range (@ _let_1 As3)))))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (let ((_let_2 (@ tptp.sup_sup_set_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (let ((_let_2 (@ tptp.sup_sup_assn Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 2.52/3.49 (assert (forall ((B tptp.set_nat) (A tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat B))) (let ((_let_2 (@ tptp.sup_sup_set_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 2.52/3.49 (assert (forall ((B tptp.assn) (A tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn B))) (let ((_let_2 (@ tptp.sup_sup_assn A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 2.52/3.49 (assert (= tptp.sup_sup_set_nat (lambda ((X2 tptp.set_nat) (Y2 tptp.set_nat)) (@ (@ tptp.sup_sup_set_nat Y2) X2))))
% 2.52/3.49 (assert (= tptp.sup_sup_assn (lambda ((X2 tptp.assn) (Y2 tptp.assn)) (@ (@ tptp.sup_sup_assn Y2) X2))))
% 2.52/3.49 (assert (= tptp.sup_sup_set_nat (lambda ((A2 tptp.set_nat) (B2 tptp.set_nat)) (@ (@ tptp.sup_sup_set_nat B2) A2))))
% 2.52/3.49 (assert (= tptp.sup_sup_assn (lambda ((A2 tptp.assn) (B2 tptp.assn)) (@ (@ tptp.sup_sup_assn B2) A2))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup_sup_set_nat Y) Z))))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (= (@ (@ tptp.sup_sup_assn (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup_sup_assn Y) Z))))))
% 2.52/3.49 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A))) (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.sup_sup_set_nat B) C))))))
% 2.52/3.49 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn A))) (= (@ (@ tptp.sup_sup_assn (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.sup_sup_assn B) C))))))
% 2.52/3.49 (assert (= tptp.sup_sup_set_nat (lambda ((X2 tptp.set_nat) (Y2 tptp.set_nat)) (@ (@ tptp.sup_sup_set_nat Y2) X2))))
% 2.52/3.49 (assert (= tptp.sup_sup_assn (lambda ((X2 tptp.assn) (Y2 tptp.assn)) (@ (@ tptp.sup_sup_assn Y2) X2))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup_sup_set_nat Y) Z))))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (= (@ (@ tptp.sup_sup_assn (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup_sup_assn Y) Z))))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (let ((_let_2 (@ tptp.sup_sup_set_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (let ((_let_2 (@ tptp.sup_sup_assn Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.sup_su6327502436637775413at_nat X))) (=> (forall ((X3 tptp.set_Pr1261947904930325089at_nat) (Y3 tptp.set_Pr1261947904930325089at_nat) (Z2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X3))) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat Y3) Z2)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 Y3)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 Y)) (@ _let_1 Z)))))))
% 2.52/3.49 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X3))) (= (@ _let_1 (@ (@ tptp.sup_sup_nat Y3) Z2)) (@ (@ tptp.sup_sup_nat (@ _let_1 Y3)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z)) (@ (@ tptp.inf_inf_nat (@ _let_1 Y)) (@ _let_1 Z)))))))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool)) (Z (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.sup_su8463660629351352368_int_o X))) (=> (forall ((X3 (-> tptp.product_prod_int_int Bool)) (Y3 (-> tptp.product_prod_int_int Bool)) (Z2 (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.inf_in3604695632404883862_int_o X3))) (= (@ _let_1 (@ (@ tptp.sup_su8463660629351352368_int_o Y3) Z2)) (@ (@ tptp.sup_su8463660629351352368_int_o (@ _let_1 Y3)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.inf_in3604695632404883862_int_o Y) Z)) (@ (@ tptp.inf_in3604695632404883862_int_o (@ _let_1 Y)) (@ _let_1 Z)))))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (=> (forall ((X3 tptp.set_nat) (Y3 tptp.set_nat) (Z2 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X3))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat Y3) Z2)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 Y3)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y) Z)) (@ (@ tptp.inf_inf_set_nat (@ _let_1 Y)) (@ _let_1 Z)))))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn) (Z2 tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X3))) (= (@ _let_1 (@ (@ tptp.sup_sup_assn Y3) Z2)) (@ (@ tptp.sup_sup_assn (@ _let_1 Y3)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.inf_inf_assn Y) Z)) (@ (@ tptp.inf_inf_assn (@ _let_1 Y)) (@ _let_1 Z)))))))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (=> (forall ((X3 tptp.set_Pr1261947904930325089at_nat) (Y3 tptp.set_Pr1261947904930325089at_nat) (Z2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.sup_su6327502436637775413at_nat X3))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y3) Z2)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 Y3)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat Y) Z)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 Y)) (@ _let_1 Z)))))))
% 2.52/3.49 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X3))) (= (@ _let_1 (@ (@ tptp.inf_inf_nat Y3) Z2)) (@ (@ tptp.inf_inf_nat (@ _let_1 Y3)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.sup_sup_nat Y) Z)) (@ (@ tptp.sup_sup_nat (@ _let_1 Y)) (@ _let_1 Z)))))))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool)) (Z (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.inf_in3604695632404883862_int_o X))) (=> (forall ((X3 (-> tptp.product_prod_int_int Bool)) (Y3 (-> tptp.product_prod_int_int Bool)) (Z2 (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.sup_su8463660629351352368_int_o X3))) (= (@ _let_1 (@ (@ tptp.inf_in3604695632404883862_int_o Y3) Z2)) (@ (@ tptp.inf_in3604695632404883862_int_o (@ _let_1 Y3)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.sup_su8463660629351352368_int_o Y) Z)) (@ (@ tptp.sup_su8463660629351352368_int_o (@ _let_1 Y)) (@ _let_1 Z)))))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (=> (forall ((X3 tptp.set_nat) (Y3 tptp.set_nat) (Z2 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X3))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y3) Z2)) (@ (@ tptp.inf_inf_set_nat (@ _let_1 Y3)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat Y) Z)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 Y)) (@ _let_1 Z)))))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn) (Z2 tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X3))) (= (@ _let_1 (@ (@ tptp.inf_inf_assn Y3) Z2)) (@ (@ tptp.inf_inf_assn (@ _let_1 Y3)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.sup_sup_assn Y) Z)) (@ (@ tptp.sup_sup_assn (@ _let_1 Y)) (@ _let_1 Z)))))))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat Y) Z)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 2.52/3.49 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (= (@ _let_1 (@ (@ tptp.sup_sup_nat Y) Z)) (@ (@ tptp.sup_sup_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool)) (Z (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.inf_in3604695632404883862_int_o X))) (= (@ _let_1 (@ (@ tptp.sup_su8463660629351352368_int_o Y) Z)) (@ (@ tptp.sup_su8463660629351352368_int_o (@ _let_1 Y)) (@ _let_1 Z))))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat Y) Z)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (= (@ _let_1 (@ (@ tptp.sup_sup_assn Y) Z)) (@ (@ tptp.sup_sup_assn (@ _let_1 Y)) (@ _let_1 Z))))))
% 2.52/3.49 (assert (forall ((Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat Y) Z)) X) (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat Y) X)) (@ (@ tptp.inf_in2572325071724192079at_nat Z) X)))))
% 2.52/3.49 (assert (forall ((Y tptp.nat) (Z tptp.nat) (X tptp.nat)) (= (@ (@ tptp.inf_inf_nat (@ (@ tptp.sup_sup_nat Y) Z)) X) (@ (@ tptp.sup_sup_nat (@ (@ tptp.inf_inf_nat Y) X)) (@ (@ tptp.inf_inf_nat Z) X)))))
% 2.52/3.49 (assert (forall ((Y (-> tptp.product_prod_int_int Bool)) (Z (-> tptp.product_prod_int_int Bool)) (X (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.inf_in3604695632404883862_int_o (@ (@ tptp.sup_su8463660629351352368_int_o Y) Z)) X) (@ (@ tptp.sup_su8463660629351352368_int_o (@ (@ tptp.inf_in3604695632404883862_int_o Y) X)) (@ (@ tptp.inf_in3604695632404883862_int_o Z) X)))))
% 2.52/3.49 (assert (forall ((Y tptp.set_nat) (Z tptp.set_nat) (X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat Y) Z)) X) (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat Y) X)) (@ (@ tptp.inf_inf_set_nat Z) X)))))
% 2.52/3.49 (assert (forall ((Y tptp.assn) (Z tptp.assn) (X tptp.assn)) (= (@ (@ tptp.inf_inf_assn (@ (@ tptp.sup_sup_assn Y) Z)) X) (@ (@ tptp.sup_sup_assn (@ (@ tptp.inf_inf_assn Y) X)) (@ (@ tptp.inf_inf_assn Z) X)))))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.sup_su6327502436637775413at_nat X))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 2.52/3.49 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z)) (@ (@ tptp.inf_inf_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool)) (Z (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.sup_su8463660629351352368_int_o X))) (= (@ _let_1 (@ (@ tptp.inf_in3604695632404883862_int_o Y) Z)) (@ (@ tptp.inf_in3604695632404883862_int_o (@ _let_1 Y)) (@ _let_1 Z))))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y) Z)) (@ (@ tptp.inf_inf_set_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (= (@ _let_1 (@ (@ tptp.inf_inf_assn Y) Z)) (@ (@ tptp.inf_inf_assn (@ _let_1 Y)) (@ _let_1 Z))))))
% 2.52/3.49 (assert (forall ((Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z)) X) (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat Y) X)) (@ (@ tptp.sup_su6327502436637775413at_nat Z) X)))))
% 2.52/3.49 (assert (forall ((Y tptp.nat) (Z tptp.nat) (X tptp.nat)) (= (@ (@ tptp.sup_sup_nat (@ (@ tptp.inf_inf_nat Y) Z)) X) (@ (@ tptp.inf_inf_nat (@ (@ tptp.sup_sup_nat Y) X)) (@ (@ tptp.sup_sup_nat Z) X)))))
% 2.52/3.49 (assert (forall ((Y (-> tptp.product_prod_int_int Bool)) (Z (-> tptp.product_prod_int_int Bool)) (X (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.sup_su8463660629351352368_int_o (@ (@ tptp.inf_in3604695632404883862_int_o Y) Z)) X) (@ (@ tptp.inf_in3604695632404883862_int_o (@ (@ tptp.sup_su8463660629351352368_int_o Y) X)) (@ (@ tptp.sup_su8463660629351352368_int_o Z) X)))))
% 2.52/3.49 (assert (forall ((Y tptp.set_nat) (Z tptp.set_nat) (X tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat Y) Z)) X) (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat Y) X)) (@ (@ tptp.sup_sup_set_nat Z) X)))))
% 2.52/3.49 (assert (forall ((Y tptp.assn) (Z tptp.assn) (X tptp.assn)) (= (@ (@ tptp.sup_sup_assn (@ (@ tptp.inf_inf_assn Y) Z)) X) (@ (@ tptp.inf_inf_assn (@ (@ tptp.sup_sup_assn Y) X)) (@ (@ tptp.sup_sup_assn Z) X)))))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat Y) Z)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool)) (Z (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.inf_in3604695632404883862_int_o X))) (= (@ _let_1 (@ (@ tptp.sup_su8463660629351352368_int_o Y) Z)) (@ (@ tptp.sup_su8463660629351352368_int_o (@ _let_1 Y)) (@ _let_1 Z))))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat Y) Z)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (= (@ _let_1 (@ (@ tptp.sup_sup_assn Y) Z)) (@ (@ tptp.sup_sup_assn (@ _let_1 Y)) (@ _let_1 Z))))))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.sup_su6327502436637775413at_nat X))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool)) (Z (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.sup_su8463660629351352368_int_o X))) (= (@ _let_1 (@ (@ tptp.inf_in3604695632404883862_int_o Y) Z)) (@ (@ tptp.inf_in3604695632404883862_int_o (@ _let_1 Y)) (@ _let_1 Z))))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y) Z)) (@ (@ tptp.inf_inf_set_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (= (@ _let_1 (@ (@ tptp.inf_inf_assn Y) Z)) (@ (@ tptp.inf_inf_assn (@ _let_1 Y)) (@ _let_1 Z))))))
% 2.52/3.49 (assert (forall ((Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat Y) Z)) X) (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat Y) X)) (@ (@ tptp.inf_in2572325071724192079at_nat Z) X)))))
% 2.52/3.49 (assert (forall ((Y (-> tptp.product_prod_int_int Bool)) (Z (-> tptp.product_prod_int_int Bool)) (X (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.inf_in3604695632404883862_int_o (@ (@ tptp.sup_su8463660629351352368_int_o Y) Z)) X) (@ (@ tptp.sup_su8463660629351352368_int_o (@ (@ tptp.inf_in3604695632404883862_int_o Y) X)) (@ (@ tptp.inf_in3604695632404883862_int_o Z) X)))))
% 2.52/3.49 (assert (forall ((Y tptp.set_nat) (Z tptp.set_nat) (X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat Y) Z)) X) (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat Y) X)) (@ (@ tptp.inf_inf_set_nat Z) X)))))
% 2.52/3.49 (assert (forall ((Y tptp.assn) (Z tptp.assn) (X tptp.assn)) (= (@ (@ tptp.inf_inf_assn (@ (@ tptp.sup_sup_assn Y) Z)) X) (@ (@ tptp.sup_sup_assn (@ (@ tptp.inf_inf_assn Y) X)) (@ (@ tptp.inf_inf_assn Z) X)))))
% 2.52/3.49 (assert (forall ((Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z)) X) (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat Y) X)) (@ (@ tptp.sup_su6327502436637775413at_nat Z) X)))))
% 2.52/3.49 (assert (forall ((Y (-> tptp.product_prod_int_int Bool)) (Z (-> tptp.product_prod_int_int Bool)) (X (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.sup_su8463660629351352368_int_o (@ (@ tptp.inf_in3604695632404883862_int_o Y) Z)) X) (@ (@ tptp.inf_in3604695632404883862_int_o (@ (@ tptp.sup_su8463660629351352368_int_o Y) X)) (@ (@ tptp.sup_su8463660629351352368_int_o Z) X)))))
% 2.52/3.49 (assert (forall ((Y tptp.set_nat) (Z tptp.set_nat) (X tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat Y) Z)) X) (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat Y) X)) (@ (@ tptp.sup_sup_set_nat Z) X)))))
% 2.52/3.49 (assert (forall ((Y tptp.assn) (Z tptp.assn) (X tptp.assn)) (= (@ (@ tptp.sup_sup_assn (@ (@ tptp.inf_inf_assn Y) Z)) X) (@ (@ tptp.inf_inf_assn (@ (@ tptp.sup_sup_assn Y) X)) (@ (@ tptp.sup_sup_assn Z) X)))))
% 2.52/3.49 (assert (@ tptp.abel_s3907380067910933104et_nat tptp.sup_sup_set_nat))
% 2.52/3.49 (assert (@ tptp.abel_semigroup_assn tptp.sup_sup_assn))
% 2.52/3.49 (assert (@ tptp.semilattice_set_nat tptp.sup_sup_set_nat))
% 2.52/3.49 (assert (@ tptp.semilattice_assn tptp.sup_sup_assn))
% 2.52/3.49 (assert (@ tptp.semigroup_set_nat tptp.sup_sup_set_nat))
% 2.52/3.49 (assert (@ tptp.semigroup_assn tptp.sup_sup_assn))
% 2.52/3.49 (assert (@ (@ tptp.comm_monoid_assn tptp.sup_sup_assn) tptp.bot_bot_assn))
% 2.52/3.49 (assert (@ (@ tptp.comm_monoid_set_nat tptp.sup_sup_set_nat) tptp.bot_bot_set_nat))
% 2.52/3.49 (assert (@ (@ tptp.comm_monoid_set_int tptp.sup_sup_set_int) tptp.bot_bot_set_int))
% 2.52/3.49 (assert (@ (@ tptp.monoid_assn tptp.sup_sup_assn) tptp.bot_bot_assn))
% 2.52/3.49 (assert (@ (@ tptp.monoid_set_nat tptp.sup_sup_set_nat) tptp.bot_bot_set_nat))
% 2.52/3.49 (assert (@ (@ tptp.monoid_set_int tptp.sup_sup_set_int) tptp.bot_bot_set_int))
% 2.52/3.49 (assert (@ (@ tptp.semila5388846958306562758r_assn tptp.sup_sup_assn) tptp.bot_bot_assn))
% 2.52/3.49 (assert (@ (@ tptp.semila1241773964035338532et_nat tptp.sup_sup_set_nat) tptp.bot_bot_set_nat))
% 2.52/3.49 (assert (@ (@ tptp.semila6287294981380917632et_int tptp.sup_sup_set_int) tptp.bot_bot_set_int))
% 2.52/3.49 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.sup_su6327502436637775413at_nat A))) (let ((_let_2 (@ tptp.inf_in2572325071724192079at_nat A))) (=> (= (@ _let_2 X) tptp.bot_bo2099793752762293965at_nat) (=> (= (@ _let_1 X) tptp.top_to4669805908274784177at_nat) (=> (= (@ _let_2 Y) tptp.bot_bo2099793752762293965at_nat) (=> (= (@ _let_1 Y) tptp.top_to4669805908274784177at_nat) (= X Y)))))))))
% 2.52/3.49 (assert (forall ((A (-> tptp.product_prod_int_int Bool)) (X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.sup_su8463660629351352368_int_o A))) (let ((_let_2 (@ tptp.inf_in3604695632404883862_int_o A))) (=> (= (@ _let_2 X) tptp.bot_bo8147686125503663512_int_o) (=> (= (@ _let_1 X) tptp.top_to1578927101902068148_int_o) (=> (= (@ _let_2 Y) tptp.bot_bo8147686125503663512_int_o) (=> (= (@ _let_1 Y) tptp.top_to1578927101902068148_int_o) (= X Y)))))))))
% 2.52/3.49 (assert (forall ((A tptp.set_nat) (X tptp.set_nat) (Y tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A))) (let ((_let_2 (@ tptp.inf_inf_set_nat A))) (=> (= (@ _let_2 X) tptp.bot_bot_set_nat) (=> (= (@ _let_1 X) tptp.top_top_set_nat) (=> (= (@ _let_2 Y) tptp.bot_bot_set_nat) (=> (= (@ _let_1 Y) tptp.top_top_set_nat) (= X Y)))))))))
% 2.52/3.49 (assert (forall ((A tptp.set_int) (X tptp.set_int) (Y tptp.set_int)) (let ((_let_1 (@ tptp.sup_sup_set_int A))) (let ((_let_2 (@ tptp.inf_inf_set_int A))) (=> (= (@ _let_2 X) tptp.bot_bot_set_int) (=> (= (@ _let_1 X) tptp.top_top_set_int) (=> (= (@ _let_2 Y) tptp.bot_bot_set_int) (=> (= (@ _let_1 Y) tptp.top_top_set_int) (= X Y)))))))))
% 2.52/3.49 (assert (forall ((A tptp.assn) (X tptp.assn) (Y tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn A))) (let ((_let_2 (@ tptp.inf_inf_assn A))) (=> (= (@ _let_2 X) tptp.bot_bot_assn) (=> (= (@ _let_1 X) tptp.top_top_assn) (=> (= (@ _let_2 Y) tptp.bot_bot_assn) (=> (= (@ _let_1 Y) tptp.top_top_assn) (= X Y)))))))))
% 2.52/3.49 (assert (forall ((A tptp.set_Product_unit) (X tptp.set_Product_unit) (Y tptp.set_Product_unit)) (let ((_let_1 (@ tptp.sup_su793286257634532545t_unit A))) (let ((_let_2 (@ tptp.inf_in4660618365625256667t_unit A))) (=> (= (@ _let_2 X) tptp.bot_bo3957492148770167129t_unit) (=> (= (@ _let_1 X) tptp.top_to1996260823553986621t_unit) (=> (= (@ _let_2 Y) tptp.bot_bo3957492148770167129t_unit) (=> (= (@ _let_1 Y) tptp.top_to1996260823553986621t_unit) (= X Y)))))))))
% 2.52/3.49 (assert (forall ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (= (@ tptp.one_assn_raw (@ (@ tptp.produc7507926704131184380et_nat H2) As2)) (= As2 tptp.bot_bot_set_nat))))
% 2.52/3.49 (assert (forall ((X tptp.produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ tptp.one_assn_raw X) Y) (not (forall ((H3 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (= X (@ (@ tptp.produc7507926704131184380et_nat H3) As)) (= Y (not (= As tptp.bot_bot_set_nat)))))))))
% 2.52/3.49 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (=> (@ tptp.one_assn_raw X) (not (forall ((H3 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (= X (@ (@ tptp.produc7507926704131184380et_nat H3) As)) (not (= As tptp.bot_bot_set_nat))))))))
% 2.52/3.49 (assert (forall ((T tptp.set_Pr1261947904930325089at_nat) (S tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat T) (@ (@ tptp.inf_in2572325071724192079at_nat S) T)) T)))
% 2.52/3.49 (assert (forall ((T tptp.set_nat) (S tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat T) (@ (@ tptp.inf_inf_set_nat S) T)) T)))
% 2.52/3.49 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat S) (@ (@ tptp.inf_in2572325071724192079at_nat S) T)) S)))
% 2.52/3.49 (assert (forall ((S tptp.set_nat) (T tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat S) (@ (@ tptp.inf_inf_set_nat S) T)) S)))
% 2.52/3.49 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat S) T)) T) T)))
% 2.52/3.49 (assert (forall ((S tptp.set_nat) (T tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat S) T)) T) T)))
% 2.52/3.49 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat S) T)) S) S)))
% 2.52/3.49 (assert (forall ((S tptp.set_nat) (T tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat S) T)) S) S)))
% 2.52/3.49 (assert (forall ((T tptp.set_Pr1261947904930325089at_nat) (S tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat T) (@ (@ tptp.sup_su6327502436637775413at_nat S) T)) T)))
% 2.52/3.49 (assert (forall ((T tptp.set_nat) (S tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat T) (@ (@ tptp.sup_sup_set_nat S) T)) T)))
% 2.52/3.49 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat S) (@ (@ tptp.sup_su6327502436637775413at_nat S) T)) S)))
% 2.52/3.49 (assert (forall ((S tptp.set_nat) (T tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat S) (@ (@ tptp.sup_sup_set_nat S) T)) S)))
% 2.52/3.49 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat S) T)) T) T)))
% 2.52/3.49 (assert (forall ((S tptp.set_nat) (T tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat S) T)) T) T)))
% 2.52/3.49 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat S) T)) S) S)))
% 2.52/3.49 (assert (forall ((S tptp.set_nat) (T tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat S) T)) S) S)))
% 2.52/3.49 (assert (forall ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat) (Q2 tptp.assn) (R tptp.assn)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) As2))) (=> (@ tptp.in_range _let_1) (=> (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H4))) (=> (= (@ (@ tptp.inf_inf_set_nat As2) As4) tptp.bot_bot_set_nat) (=> (@ (@ (@ tptp.relH As2) H2) H4) (=> (@ tptp.in_range (@ _let_1 As2)) (=> (@ (@ tptp.rep_assn Q2) (@ _let_1 As4)) (@ (@ tptp.rep_assn R) (@ _let_1 (@ (@ tptp.sup_sup_set_nat As2) As4))))))))) (@ (@ tptp.rep_assn (@ (@ tptp.wand_assn Q2) R)) _let_1))))))
% 2.52/3.49 (assert (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A3 tptp.set_Pr4532377907799695533_nat_o) (B3 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ _let_1 A3) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.inf_in1906310914598751387_nat_o A3) B3)))))))
% 2.52/3.49 (assert (forall ((C tptp.int) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int2 C))) (=> (@ _let_1 A3) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3)))))))
% 2.52/3.49 (assert (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 A3) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)))))))
% 2.52/3.49 (assert (forall ((C tptp.nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat2 C))) (=> (@ _let_1 A3) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3)))))))
% 2.52/3.49 (assert (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A3 tptp.set_Pr4532377907799695533_nat_o) (B3 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (= (@ _let_1 (@ (@ tptp.inf_in1906310914598751387_nat_o A3) B3)) (and (@ _let_1 A3) (@ _let_1 B3))))))
% 2.52/3.49 (assert (forall ((C tptp.int) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int2 C))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3)) (and (@ _let_1 A3) (@ _let_1 B3))))))
% 2.52/3.49 (assert (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)) (and (@ _let_1 A3) (@ _let_1 B3))))))
% 2.52/3.49 (assert (forall ((C tptp.nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat2 C))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3)) (and (@ _let_1 A3) (@ _let_1 B3))))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3) tptp.top_to4669805908274784177at_nat) (and (= A3 tptp.top_to4669805908274784177at_nat) (= B3 tptp.top_to4669805908274784177at_nat)))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat A3) B3) tptp.top_top_set_nat) (and (= A3 tptp.top_top_set_nat) (= B3 tptp.top_top_set_nat)))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_Product_unit) (B3 tptp.set_Product_unit)) (= (= (@ (@ tptp.inf_in4660618365625256667t_unit A3) B3) tptp.top_to1996260823553986621t_unit) (and (= A3 tptp.top_to1996260823553986621t_unit) (= B3 tptp.top_to1996260823553986621t_unit)))))
% 2.52/3.49 (assert (forall ((P2 tptp.assn) (Q2 tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn (@ (@ tptp.sup_sup_assn P2) Q2)) H2) (or (@ (@ tptp.rep_assn P2) H2) (@ (@ tptp.rep_assn Q2) H2)))))
% 2.52/3.49 (assert (forall ((A Bool) (B Bool)) (= (@ (@ tptp.sup_sup_assn (@ tptp.pure_assn A)) (@ tptp.pure_assn B)) (@ tptp.pure_assn (or A B)))))
% 2.52/3.49 (assert (forall ((As2 tptp.set_nat) (As3 tptp.set_nat) (H2 tptp.heap_e7401611519738050253t_unit) (H5 tptp.heap_e7401611519738050253t_unit)) (= (@ (@ (@ tptp.relH (@ (@ tptp.sup_sup_set_nat As2) As3)) H2) H5) (and (@ (@ (@ tptp.relH As2) H2) H5) (@ (@ (@ tptp.relH As3) H2) H5)))))
% 2.52/3.49 (assert (forall ((P2 tptp.assn) (Q2 tptp.assn) (H2 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) tptp.bot_bot_set_nat))) (= (@ (@ tptp.rep_assn (@ (@ tptp.sup_sup_assn P2) Q2)) _let_1) (or (@ (@ tptp.rep_assn P2) _let_1) (@ (@ tptp.rep_assn Q2) _let_1))))))
% 2.52/3.49 (assert (forall ((As2 tptp.set_nat) (H2 tptp.heap_e7401611519738050253t_unit) (H5 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ tptp.relH As2))) (=> (@ (@ _let_1 H2) H5) (@ (@ _let_1 H5) H2)))))
% 2.52/3.49 (assert (forall ((As2 tptp.set_nat) (H12 tptp.heap_e7401611519738050253t_unit) (H23 tptp.heap_e7401611519738050253t_unit) (H32 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ tptp.relH As2))) (let ((_let_2 (@ _let_1 H12))) (=> (@ _let_2 H23) (=> (@ (@ _let_1 H23) H32) (@ _let_2 H32)))))))
% 2.52/3.49 (assert (forall ((C2 tptp.assn) (A3 tptp.assn) (B3 tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn C2))) (= (@ _let_1 (@ (@ tptp.sup_sup_assn A3) B3)) (@ (@ tptp.sup_sup_assn (@ _let_1 A3)) (@ _let_1 B3))))))
% 2.52/3.49 (assert (forall ((A3 tptp.assn) (B3 tptp.assn) (C2 tptp.assn)) (= (@ (@ tptp.times_times_assn (@ (@ tptp.sup_sup_assn A3) B3)) C2) (@ (@ tptp.sup_sup_assn (@ (@ tptp.times_times_assn A3) C2)) (@ (@ tptp.times_times_assn B3) C2)))))
% 2.52/3.49 (assert (forall ((B3 tptp.assn) (A3 tptp.assn)) (@ (@ tptp.entails B3) (@ (@ tptp.sup_sup_assn A3) B3))))
% 2.52/3.49 (assert (forall ((A3 tptp.assn) (B3 tptp.assn)) (@ (@ tptp.entails A3) (@ (@ tptp.sup_sup_assn A3) B3))))
% 2.52/3.49 (assert (forall ((A3 tptp.assn) (C2 tptp.assn) (B3 tptp.assn)) (let ((_let_1 (@ tptp.entails A3))) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.sup_sup_assn B3) C2))))))
% 2.52/3.49 (assert (forall ((A3 tptp.assn) (B3 tptp.assn) (C2 tptp.assn)) (let ((_let_1 (@ tptp.entails A3))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.sup_sup_assn B3) C2))))))
% 2.52/3.49 (assert (forall ((P2 tptp.assn) (Q2 tptp.assn) (R tptp.assn)) (=> (@ (@ tptp.entails (@ (@ tptp.sup_sup_assn P2) Q2)) R) (@ (@ tptp.entails Q2) R))))
% 2.52/3.49 (assert (forall ((P2 tptp.assn) (Q2 tptp.assn) (R tptp.assn)) (=> (@ (@ tptp.entails (@ (@ tptp.sup_sup_assn P2) Q2)) R) (@ (@ tptp.entails P2) R))))
% 2.52/3.49 (assert (forall ((A3 tptp.assn) (C2 tptp.assn) (B3 tptp.assn)) (=> (@ (@ tptp.entails A3) C2) (=> (@ (@ tptp.entails B3) C2) (@ (@ tptp.entails (@ (@ tptp.sup_sup_assn A3) B3)) C2)))))
% 2.52/3.49 (assert (forall ((A3 tptp.assn) (M tptp.assn) (B3 tptp.assn)) (=> (@ (@ tptp.entailst A3) M) (=> (@ (@ tptp.entailst B3) M) (@ (@ tptp.entailst (@ (@ tptp.sup_sup_assn A3) B3)) M)))))
% 2.52/3.49 (assert (forall ((A3 tptp.assn) (B3 tptp.assn) (C2 tptp.assn)) (=> (@ (@ tptp.entailst (@ (@ tptp.sup_sup_assn A3) B3)) C2) (@ (@ tptp.entailst A3) C2))))
% 2.52/3.49 (assert (forall ((A3 tptp.assn) (B3 tptp.assn) (C2 tptp.assn)) (=> (@ (@ tptp.entailst (@ (@ tptp.sup_sup_assn A3) B3)) C2) (@ (@ tptp.entailst B3) C2))))
% 2.52/3.49 (assert (forall ((A3 tptp.assn) (B3 tptp.assn) (C2 tptp.assn)) (let ((_let_1 (@ tptp.entailst A3))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.sup_sup_assn B3) C2))))))
% 2.52/3.49 (assert (forall ((A3 tptp.assn) (C2 tptp.assn) (B3 tptp.assn)) (let ((_let_1 (@ tptp.entailst A3))) (=> (@ _let_1 C2) (@ _let_1 (@ (@ tptp.sup_sup_assn B3) C2))))))
% 2.52/3.49 (assert (forall ((A3 tptp.assn) (B3 tptp.assn)) (@ (@ tptp.entailst A3) (@ (@ tptp.sup_sup_assn A3) B3))))
% 2.52/3.49 (assert (forall ((B3 tptp.assn) (A3 tptp.assn)) (@ (@ tptp.entailst B3) (@ (@ tptp.sup_sup_assn A3) B3))))
% 2.52/3.49 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.sup_sup_assn tptp.top_top_assn) X) tptp.top_top_assn)))
% 2.52/3.49 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.sup_sup_assn X) tptp.top_top_assn) tptp.top_top_assn)))
% 2.52/3.49 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.sup_sup_assn tptp.bot_bot_assn) X) X)))
% 2.52/3.49 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.sup_sup_assn X) tptp.bot_bot_assn) X)))
% 2.52/3.49 (assert (forall ((As2 tptp.set_nat) (H2 tptp.heap_e7401611519738050253t_unit) (H5 tptp.heap_e7401611519738050253t_unit) (P2 tptp.assn)) (let ((_let_1 (@ tptp.rep_assn P2))) (=> (@ (@ (@ tptp.relH As2) H2) H5) (= (@ _let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) As2)) (@ _let_1 (@ (@ tptp.produc7507926704131184380et_nat H5) As2)))))))
% 2.52/3.49 (assert (forall ((As2 tptp.set_nat) (H2 tptp.heap_e7401611519738050253t_unit) (H5 tptp.heap_e7401611519738050253t_unit)) (=> (@ (@ (@ tptp.relH As2) H2) H5) (@ tptp.in_range (@ (@ tptp.produc7507926704131184380et_nat H5) As2)))))
% 2.52/3.49 (assert (forall ((As2 tptp.set_nat) (H2 tptp.heap_e7401611519738050253t_unit) (H5 tptp.heap_e7401611519738050253t_unit)) (=> (@ (@ (@ tptp.relH As2) H2) H5) (@ tptp.in_range (@ (@ tptp.produc7507926704131184380et_nat H2) As2)))))
% 2.52/3.49 (assert (forall ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (=> (@ tptp.in_range (@ (@ tptp.produc7507926704131184380et_nat H2) As2)) (@ (@ (@ tptp.relH As2) H2) H2))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) tptp.top_to4669805908274784177at_nat) A3)))
% 2.52/3.49 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A3) tptp.top_top_set_nat) A3)))
% 2.52/3.49 (assert (forall ((A3 tptp.set_Product_unit)) (= (@ (@ tptp.inf_in4660618365625256667t_unit A3) tptp.top_to1996260823553986621t_unit) A3)))
% 2.52/3.49 (assert (forall ((B3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.top_to4669805908274784177at_nat) B3) B3)))
% 2.52/3.49 (assert (forall ((B3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat tptp.top_top_set_nat) B3) B3)))
% 2.52/3.49 (assert (forall ((B3 tptp.set_Product_unit)) (= (@ (@ tptp.inf_in4660618365625256667t_unit tptp.top_to1996260823553986621t_unit) B3) B3)))
% 2.52/3.49 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A3))) (let ((_let_2 (@ tptp.inf_in2572325071724192079at_nat B3))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A3))) (let ((_let_2 (@ tptp.inf_inf_set_nat B3))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A3))) (let ((_let_2 (@ _let_1 B3))) (= (@ _let_1 _let_2) _let_2)))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A3))) (let ((_let_2 (@ _let_1 B3))) (= (@ _let_1 _let_2) _let_2)))))
% 2.52/3.49 (assert (= tptp.inf_in2572325071724192079at_nat (lambda ((A4 tptp.set_Pr1261947904930325089at_nat) (B4 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.inf_in2572325071724192079at_nat B4) A4))))
% 2.52/3.49 (assert (= tptp.inf_inf_set_nat (lambda ((A4 tptp.set_nat) (B4 tptp.set_nat)) (@ (@ tptp.inf_inf_set_nat B4) A4))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) A3) A3)))
% 2.52/3.49 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A3) A3) A3)))
% 2.52/3.49 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A3))) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 B3)) C2) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B3) C2))))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A3))) (= (@ (@ tptp.inf_inf_set_nat (@ _let_1 B3)) C2) (@ _let_1 (@ (@ tptp.inf_inf_set_nat B3) C2))))))
% 2.52/3.49 (assert (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A3 tptp.set_Pr4532377907799695533_nat_o) (B3 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ _let_1 (@ (@ tptp.inf_in1906310914598751387_nat_o A3) B3)) (@ _let_1 B3)))))
% 2.52/3.49 (assert (forall ((C tptp.int) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int2 C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3)) (@ _let_1 B3)))))
% 2.52/3.49 (assert (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)) (@ _let_1 B3)))))
% 2.52/3.49 (assert (forall ((C tptp.nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat2 C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3)) (@ _let_1 B3)))))
% 2.52/3.49 (assert (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A3 tptp.set_Pr4532377907799695533_nat_o) (B3 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ _let_1 (@ (@ tptp.inf_in1906310914598751387_nat_o A3) B3)) (@ _let_1 A3)))))
% 2.52/3.49 (assert (forall ((C tptp.int) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int2 C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3)) (@ _let_1 A3)))))
% 2.52/3.49 (assert (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)) (@ _let_1 A3)))))
% 2.52/3.49 (assert (forall ((C tptp.nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat2 C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3)) (@ _let_1 A3)))))
% 2.52/3.49 (assert (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A3 tptp.set_Pr4532377907799695533_nat_o) (B3 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ _let_1 (@ (@ tptp.inf_in1906310914598751387_nat_o A3) B3)) (not (=> (@ _let_1 A3) (not (@ _let_1 B3))))))))
% 2.52/3.49 (assert (forall ((C tptp.int) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int2 C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3)) (not (=> (@ _let_1 A3) (not (@ _let_1 B3))))))))
% 2.52/3.49 (assert (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)) (not (=> (@ _let_1 A3) (not (@ _let_1 B3))))))))
% 2.52/3.49 (assert (forall ((C tptp.nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat2 C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3)) (not (=> (@ _let_1 A3) (not (@ _let_1 B3))))))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3) tptp.bot_bo2099793752762293965at_nat) (forall ((X2 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X2) A3) (forall ((Y2 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat Y2) B3) (not (= X2 Y2)))))))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat A3) B3) tptp.bot_bot_set_nat) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat2 X2) A3) (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member_nat2 Y2) B3) (not (= X2 Y2)))))))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (= (@ (@ tptp.inf_inf_set_int A3) B3) tptp.bot_bot_set_int) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int2 X2) A3) (forall ((Y2 tptp.int)) (=> (@ (@ tptp.member_int2 Y2) B3) (not (= X2 Y2)))))))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) tptp.bot_bo2099793752762293965at_nat) tptp.bot_bo2099793752762293965at_nat)))
% 2.52/3.49 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A3) tptp.bot_bot_set_nat) tptp.bot_bot_set_nat)))
% 2.52/3.49 (assert (forall ((A3 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int A3) tptp.bot_bot_set_int) tptp.bot_bot_set_int)))
% 2.52/3.49 (assert (forall ((B3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bot_bo2099793752762293965at_nat) B3) tptp.bot_bo2099793752762293965at_nat)))
% 2.52/3.49 (assert (forall ((B3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat tptp.bot_bot_set_nat) B3) tptp.bot_bot_set_nat)))
% 2.52/3.49 (assert (forall ((B3 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int tptp.bot_bot_set_int) B3) tptp.bot_bot_set_int)))
% 2.52/3.49 (assert (forall ((A3 tptp.set_Pr4532377907799695533_nat_o) (B3 tptp.set_Pr4532377907799695533_nat_o)) (= (= (@ (@ tptp.inf_in1906310914598751387_nat_o A3) B3) tptp.bot_bo7824918357723582233_nat_o) (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o X2))) (=> (@ _let_1 A3) (not (@ _let_1 B3))))))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3) tptp.bot_bo2099793752762293965at_nat) (forall ((X2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X2))) (=> (@ _let_1 A3) (not (@ _let_1 B3))))))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat A3) B3) tptp.bot_bot_set_nat) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat2 X2))) (=> (@ _let_1 A3) (not (@ _let_1 B3))))))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (= (@ (@ tptp.inf_inf_set_int A3) B3) tptp.bot_bot_set_int) (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.member_int2 X2))) (=> (@ _let_1 A3) (not (@ _let_1 B3))))))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_Pr4532377907799695533_nat_o) (B3 tptp.set_Pr4532377907799695533_nat_o)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o X3))) (=> (@ _let_1 A3) (not (@ _let_1 B3))))) (= (@ (@ tptp.inf_in1906310914598751387_nat_o A3) B3) tptp.bot_bo7824918357723582233_nat_o))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X3 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X3))) (=> (@ _let_1 A3) (not (@ _let_1 B3))))) (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3) tptp.bot_bo2099793752762293965at_nat))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.member_nat2 X3))) (=> (@ _let_1 A3) (not (@ _let_1 B3))))) (= (@ (@ tptp.inf_inf_set_nat A3) B3) tptp.bot_bot_set_nat))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (=> (forall ((X3 tptp.int)) (let ((_let_1 (@ tptp.member_int2 X3))) (=> (@ _let_1 A3) (not (@ _let_1 B3))))) (= (@ (@ tptp.inf_inf_set_int A3) B3) tptp.bot_bot_set_int))))
% 2.52/3.49 (assert (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat B3) C2)) A3) (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat B3) A3)) (@ (@ tptp.sup_su6327502436637775413at_nat C2) A3)))))
% 2.52/3.49 (assert (forall ((B3 tptp.set_nat) (C2 tptp.set_nat) (A3 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat B3) C2)) A3) (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat B3) A3)) (@ (@ tptp.sup_sup_set_nat C2) A3)))))
% 2.52/3.49 (assert (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat B3) C2)) A3) (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat B3) A3)) (@ (@ tptp.inf_in2572325071724192079at_nat C2) A3)))))
% 2.52/3.49 (assert (forall ((B3 tptp.set_nat) (C2 tptp.set_nat) (A3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat B3) C2)) A3) (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat B3) A3)) (@ (@ tptp.inf_inf_set_nat C2) A3)))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.sup_su6327502436637775413at_nat A3))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B3) C2)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 B3)) (@ _let_1 C2))))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A3))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat B3) C2)) (@ (@ tptp.inf_inf_set_nat (@ _let_1 B3)) (@ _let_1 C2))))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A3))) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat B3) C2)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 B3)) (@ _let_1 C2))))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A3))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat B3) C2)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 B3)) (@ _let_1 C2))))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)) (@ (@ tptp.inf_in2572325071724192079at_nat B3) C2))) (@ (@ tptp.inf_in2572325071724192079at_nat C2) A3)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat A3) B3)) (@ (@ tptp.sup_su6327502436637775413at_nat B3) C2))) (@ (@ tptp.sup_su6327502436637775413at_nat C2) A3)))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C2 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat A3) B3)) (@ (@ tptp.inf_inf_set_nat B3) C2))) (@ (@ tptp.inf_inf_set_nat C2) A3)) (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat A3) B3)) (@ (@ tptp.sup_sup_set_nat B3) C2))) (@ (@ tptp.sup_sup_set_nat C2) A3)))))
% 2.52/3.49 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat)) (=> (not (@ (@ (@ tptp.wand_raw X) Xa) Xb)) (not (forall ((H3 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H3) As))) (=> (= Xb _let_1) (and (@ tptp.in_range _let_1) (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H4))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As) As4) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As) H3) H4) (@ tptp.in_range (@ _let_1 As)) (@ X (@ _let_1 As4))) (@ Xa (@ _let_1 (@ (@ tptp.sup_sup_set_nat As) As4))))))))))))))
% 2.52/3.49 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat)) (=> (@ (@ (@ tptp.wand_raw X) Xa) Xb) (not (forall ((H3 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H3) As))) (=> (= Xb _let_1) (not (and (@ tptp.in_range _let_1) (forall ((H6 tptp.heap_e7401611519738050253t_unit) (As5 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H6))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As) As5) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As) H3) H6) (@ tptp.in_range (@ _let_1 As)) (@ X (@ _let_1 As5))) (@ Xa (@ _let_1 (@ (@ tptp.sup_sup_set_nat As) As5)))))))))))))))
% 2.52/3.49 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ (@ (@ tptp.wand_raw X) Xa) Xb) Y) (not (forall ((H3 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H3) As))) (=> (= Xb _let_1) (= Y (not (and (@ tptp.in_range _let_1) (forall ((H7 tptp.heap_e7401611519738050253t_unit) (As6 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H7))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As) As6) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As) H3) H7) (@ tptp.in_range (@ _let_1 As)) (@ X (@ _let_1 As6))) (@ Xa (@ _let_1 (@ (@ tptp.sup_sup_set_nat As) As6))))))))))))))))
% 2.52/3.49 (assert (forall ((P2 (-> tptp.produc3658429121746597890et_nat Bool)) (Q2 (-> tptp.produc3658429121746597890et_nat Bool)) (H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) As2))) (= (@ (@ (@ tptp.wand_raw P2) Q2) _let_1) (and (@ tptp.in_range _let_1) (forall ((H7 tptp.heap_e7401611519738050253t_unit) (As6 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H7))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As2) As6) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As2) H2) H7) (@ tptp.in_range (@ _let_1 As2)) (@ P2 (@ _let_1 As6))) (@ Q2 (@ _let_1 (@ (@ tptp.sup_sup_set_nat As2) As6)))))))))))
% 2.52/3.49 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat)) (=> (not (@ (@ (@ tptp.times_assn_raw X) Xa) Xb)) (not (forall ((H3 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (= Xb (@ (@ tptp.produc7507926704131184380et_nat H3) As)) (exists ((As12 tptp.set_nat) (As23 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H3))) (and (= As (@ (@ tptp.sup_sup_set_nat As12) As23)) (= (@ (@ tptp.inf_inf_set_nat As12) As23) tptp.bot_bot_set_nat) (@ X (@ _let_1 As12)) (@ Xa (@ _let_1 As23)))))))))))
% 2.52/3.49 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat)) (=> (@ (@ (@ tptp.times_assn_raw X) Xa) Xb) (not (forall ((H3 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (= Xb (@ (@ tptp.produc7507926704131184380et_nat H3) As)) (not (exists ((As13 tptp.set_nat) (As24 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H3))) (and (= As (@ (@ tptp.sup_sup_set_nat As13) As24)) (= (@ (@ tptp.inf_inf_set_nat As13) As24) tptp.bot_bot_set_nat) (@ X (@ _let_1 As13)) (@ Xa (@ _let_1 As24))))))))))))
% 2.52/3.49 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ (@ (@ tptp.times_assn_raw X) Xa) Xb) Y) (not (forall ((H3 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (= Xb (@ (@ tptp.produc7507926704131184380et_nat H3) As)) (= Y (not (exists ((As1 tptp.set_nat) (As22 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H3))) (and (= As (@ (@ tptp.sup_sup_set_nat As1) As22)) (= (@ (@ tptp.inf_inf_set_nat As1) As22) tptp.bot_bot_set_nat) (@ X (@ _let_1 As1)) (@ Xa (@ _let_1 As22)))))))))))))
% 2.52/3.49 (assert (forall ((P2 (-> tptp.produc3658429121746597890et_nat Bool)) (Q2 (-> tptp.produc3658429121746597890et_nat Bool)) (H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (= (@ (@ (@ tptp.times_assn_raw P2) Q2) (@ (@ tptp.produc7507926704131184380et_nat H2) As2)) (exists ((As1 tptp.set_nat) (As22 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H2))) (and (= As2 (@ (@ tptp.sup_sup_set_nat As1) As22)) (= (@ (@ tptp.inf_inf_set_nat As1) As22) tptp.bot_bot_set_nat) (@ P2 (@ _let_1 As1)) (@ Q2 (@ _let_1 As22))))))))
% 2.52/3.49 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o X3))) (=> (@ _let_1 A) (not (@ _let_1 B))))) (= (@ (@ tptp.inf_in1906310914598751387_nat_o A) B) tptp.bot_bo7824918357723582233_nat_o))))
% 2.52/3.49 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X3 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X3))) (=> (@ _let_1 A) (not (@ _let_1 B))))) (= (@ (@ tptp.inf_in2572325071724192079at_nat A) B) tptp.bot_bo2099793752762293965at_nat))))
% 2.52/3.49 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.member_nat2 X3))) (=> (@ _let_1 A) (not (@ _let_1 B))))) (= (@ (@ tptp.inf_inf_set_nat A) B) tptp.bot_bot_set_nat))))
% 2.52/3.49 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (forall ((X3 tptp.int)) (let ((_let_1 (@ tptp.member_int2 X3))) (=> (@ _let_1 A) (not (@ _let_1 B))))) (= (@ (@ tptp.inf_inf_set_int A) B) tptp.bot_bot_set_int))))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (=> (= (@ (@ tptp.inf_in2572325071724192079at_nat X) Y) tptp.bot_bo2099793752762293965at_nat) (=> (= (@ (@ tptp.sup_su6327502436637775413at_nat X) Y) tptp.top_to4669805908274784177at_nat) (= (@ tptp.uminus6524753893492686040at_nat X) Y)))))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool))) (=> (= (@ (@ tptp.inf_in3604695632404883862_int_o X) Y) tptp.bot_bo8147686125503663512_int_o) (=> (= (@ (@ tptp.sup_su8463660629351352368_int_o X) Y) tptp.top_to1578927101902068148_int_o) (= (@ tptp.uminus7117520113953359693_int_o X) Y)))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (= (@ (@ tptp.inf_inf_set_nat X) Y) tptp.bot_bot_set_nat) (=> (= (@ (@ tptp.sup_sup_set_nat X) Y) tptp.top_top_set_nat) (= (@ tptp.uminus5710092332889474511et_nat X) Y)))))
% 2.52/3.49 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (= (@ (@ tptp.inf_inf_set_int X) Y) tptp.bot_bot_set_int) (=> (= (@ (@ tptp.sup_sup_set_int X) Y) tptp.top_top_set_int) (= (@ tptp.uminus1532241313380277803et_int X) Y)))))
% 2.52/3.49 (assert (forall ((X tptp.set_Product_unit) (Y tptp.set_Product_unit)) (=> (= (@ (@ tptp.inf_in4660618365625256667t_unit X) Y) tptp.bot_bo3957492148770167129t_unit) (=> (= (@ (@ tptp.sup_su793286257634532545t_unit X) Y) tptp.top_to1996260823553986621t_unit) (= (@ tptp.uminus5944136376168626660t_unit X) Y)))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (= (@ (@ tptp.inf_inf_assn X) Y) tptp.bot_bot_assn) (=> (= (@ (@ tptp.sup_sup_assn X) Y) tptp.top_top_assn) (= (@ tptp.uminus_uminus_assn X) Y)))))
% 2.52/3.49 (assert (forall ((P2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (forall ((As tptp.set_nat) (H3 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H3) As))) (=> (@ P2 _let_1) (@ tptp.in_range _let_1)))) (=> (forall ((As tptp.set_nat) (H3 tptp.heap_e7401611519738050253t_unit) (H4 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H4) As))) (=> (@ P2 (@ (@ tptp.produc7507926704131184380et_nat H3) As)) (=> (@ (@ (@ tptp.relH As) H3) H4) (=> (@ tptp.in_range _let_1) (@ P2 _let_1)))))) (@ tptp.proper P2)))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) (@ tptp.uminus_uminus_int B)) (= A B))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) (@ tptp.uminus_uminus_rat B)) (= A B))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) (@ tptp.uminus1351360451143612070nteger B)) (= A B))))
% 2.52/3.49 (assert (forall ((A tptp.int)) (= (@ tptp.uminus_uminus_int (@ tptp.uminus_uminus_int A)) A)))
% 2.52/3.49 (assert (forall ((A tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ tptp.uminus_uminus_rat A)) A)))
% 2.52/3.49 (assert (forall ((A tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.uminus1351360451143612070nteger A)) A)))
% 2.52/3.49 (assert (forall ((B Bool)) (@ tptp.proper (@ tptp.pure_a825153325127701367it_nat B))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) (@ tptp.uminus6524753893492686040at_nat A3)) tptp.bot_bo2099793752762293965at_nat)))
% 2.52/3.49 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A3) (@ tptp.uminus5710092332889474511et_nat A3)) tptp.bot_bot_set_nat)))
% 2.52/3.49 (assert (forall ((A3 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int A3) (@ tptp.uminus1532241313380277803et_int A3)) tptp.bot_bot_set_int)))
% 2.52/3.49 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ tptp.uminus6524753893492686040at_nat A3)) A3) tptp.bot_bo2099793752762293965at_nat)))
% 2.52/3.49 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ tptp.uminus5710092332889474511et_nat A3)) A3) tptp.bot_bot_set_nat)))
% 2.52/3.49 (assert (forall ((A3 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int (@ tptp.uminus1532241313380277803et_int A3)) A3) tptp.bot_bot_set_int)))
% 2.52/3.49 (assert (forall ((P2 tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn (@ tptp.uminus_uminus_assn P2)) H2) (and (@ tptp.in_range H2) (not (@ (@ tptp.rep_assn P2) H2))))))
% 2.52/3.49 (assert (@ tptp.proper tptp.in_range))
% 2.52/3.49 (assert (forall ((P2 (-> tptp.produc3658429121746597890et_nat Bool)) (Q2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ tptp.proper P2) (=> (@ tptp.proper Q2) (@ tptp.proper (@ (@ tptp.times_assn_raw P2) Q2))))))
% 2.52/3.49 (assert (forall ((P2 (-> tptp.produc3658429121746597890et_nat Bool)) (Q2 (-> tptp.produc3658429121746597890et_nat Bool))) (@ tptp.proper (@ (@ tptp.wand_raw P2) Q2))))
% 2.52/3.49 (assert (@ tptp.proper tptp.one_assn_raw))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ tptp.uminus6524753893492686040at_nat X)) (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)) tptp.bot_bo2099793752762293965at_nat)))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.inf_in3604695632404883862_int_o (@ tptp.uminus7117520113953359693_int_o X)) (@ (@ tptp.inf_in3604695632404883862_int_o X) Y)) tptp.bot_bo8147686125503663512_int_o)))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ tptp.uminus5710092332889474511et_nat X)) (@ (@ tptp.inf_inf_set_nat X) Y)) tptp.bot_bot_set_nat)))
% 2.52/3.49 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int (@ tptp.uminus1532241313380277803et_int X)) (@ (@ tptp.inf_inf_set_int X) Y)) tptp.bot_bot_set_int)))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (@ (@ tptp.inf_inf_assn (@ tptp.uminus_uminus_assn X)) (@ (@ tptp.inf_inf_assn X) Y)) tptp.bot_bot_assn)))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat X) (@ (@ tptp.inf_in2572325071724192079at_nat (@ tptp.uminus6524753893492686040at_nat X)) Y)) tptp.bot_bo2099793752762293965at_nat)))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.inf_in3604695632404883862_int_o X) (@ (@ tptp.inf_in3604695632404883862_int_o (@ tptp.uminus7117520113953359693_int_o X)) Y)) tptp.bot_bo8147686125503663512_int_o)))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X) (@ (@ tptp.inf_inf_set_nat (@ tptp.uminus5710092332889474511et_nat X)) Y)) tptp.bot_bot_set_nat)))
% 2.52/3.49 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int X) (@ (@ tptp.inf_inf_set_int (@ tptp.uminus1532241313380277803et_int X)) Y)) tptp.bot_bot_set_int)))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (@ (@ tptp.inf_inf_assn X) (@ (@ tptp.inf_inf_assn (@ tptp.uminus_uminus_assn X)) Y)) tptp.bot_bot_assn)))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat X) (@ (@ tptp.inf_in2572325071724192079at_nat Y) (@ tptp.uminus6524753893492686040at_nat X))) tptp.bot_bo2099793752762293965at_nat)))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.inf_in3604695632404883862_int_o X) (@ (@ tptp.inf_in3604695632404883862_int_o Y) (@ tptp.uminus7117520113953359693_int_o X))) tptp.bot_bo8147686125503663512_int_o)))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X) (@ (@ tptp.inf_inf_set_nat Y) (@ tptp.uminus5710092332889474511et_nat X))) tptp.bot_bot_set_nat)))
% 2.52/3.49 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int X) (@ (@ tptp.inf_inf_set_int Y) (@ tptp.uminus1532241313380277803et_int X))) tptp.bot_bot_set_int)))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (@ (@ tptp.inf_inf_assn X) (@ (@ tptp.inf_inf_assn Y) (@ tptp.uminus_uminus_assn X))) tptp.bot_bot_assn)))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ tptp.uminus6524753893492686040at_nat X)) X) tptp.bot_bo2099793752762293965at_nat)))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.inf_in3604695632404883862_int_o (@ tptp.uminus7117520113953359693_int_o X)) X) tptp.bot_bo8147686125503663512_int_o)))
% 2.52/3.49 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ tptp.uminus5710092332889474511et_nat X)) X) tptp.bot_bot_set_nat)))
% 2.52/3.49 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int (@ tptp.uminus1532241313380277803et_int X)) X) tptp.bot_bot_set_int)))
% 2.52/3.49 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn (@ tptp.uminus_uminus_assn X)) X) tptp.bot_bot_assn)))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat X) (@ tptp.uminus6524753893492686040at_nat X)) tptp.bot_bo2099793752762293965at_nat)))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.inf_in3604695632404883862_int_o X) (@ tptp.uminus7117520113953359693_int_o X)) tptp.bot_bo8147686125503663512_int_o)))
% 2.52/3.49 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X) (@ tptp.uminus5710092332889474511et_nat X)) tptp.bot_bot_set_nat)))
% 2.52/3.49 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int X) (@ tptp.uminus1532241313380277803et_int X)) tptp.bot_bot_set_int)))
% 2.52/3.49 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn X) (@ tptp.uminus_uminus_assn X)) tptp.bot_bot_assn)))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.uminus6524753893492686040at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ tptp.uminus6524753893492686040at_nat X)) (@ tptp.uminus6524753893492686040at_nat Y)))))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool))) (= (@ tptp.uminus7117520113953359693_int_o (@ (@ tptp.inf_in3604695632404883862_int_o X) Y)) (@ (@ tptp.sup_su8463660629351352368_int_o (@ tptp.uminus7117520113953359693_int_o X)) (@ tptp.uminus7117520113953359693_int_o Y)))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ tptp.uminus5710092332889474511et_nat (@ (@ tptp.inf_inf_set_nat X) Y)) (@ (@ tptp.sup_sup_set_nat (@ tptp.uminus5710092332889474511et_nat X)) (@ tptp.uminus5710092332889474511et_nat Y)))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (@ tptp.uminus_uminus_assn (@ (@ tptp.inf_inf_assn X) Y)) (@ (@ tptp.sup_sup_assn (@ tptp.uminus_uminus_assn X)) (@ tptp.uminus_uminus_assn Y)))))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.uminus6524753893492686040at_nat (@ (@ tptp.sup_su6327502436637775413at_nat X) Y)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ tptp.uminus6524753893492686040at_nat X)) (@ tptp.uminus6524753893492686040at_nat Y)))))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool))) (= (@ tptp.uminus7117520113953359693_int_o (@ (@ tptp.sup_su8463660629351352368_int_o X) Y)) (@ (@ tptp.inf_in3604695632404883862_int_o (@ tptp.uminus7117520113953359693_int_o X)) (@ tptp.uminus7117520113953359693_int_o Y)))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ tptp.uminus5710092332889474511et_nat (@ (@ tptp.sup_sup_set_nat X) Y)) (@ (@ tptp.inf_inf_set_nat (@ tptp.uminus5710092332889474511et_nat X)) (@ tptp.uminus5710092332889474511et_nat Y)))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (@ tptp.uminus_uminus_assn (@ (@ tptp.sup_sup_assn X) Y)) (@ (@ tptp.inf_inf_assn (@ tptp.uminus_uminus_assn X)) (@ tptp.uminus_uminus_assn Y)))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (let ((_let_2 (@ tptp.sup_sup_assn Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 2.52/3.49 (assert (= tptp.sup_sup_assn (lambda ((X2 tptp.assn) (Y2 tptp.assn)) (@ (@ tptp.sup_sup_assn Y2) X2))))
% 2.52/3.49 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.sup_sup_assn X) X) X)))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (= (@ (@ tptp.sup_sup_assn (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup_sup_assn Y) Z))))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ tptp.uminus_uminus_int B) A))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B) (= (@ tptp.uminus_uminus_rat B) A))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) B) (= (@ tptp.uminus1351360451143612070nteger B) A))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= B (@ tptp.uminus_uminus_int A)))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B)) (= B (@ tptp.uminus_uminus_rat A)))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger B)) (= B (@ tptp.uminus1351360451143612070nteger A)))))
% 2.52/3.49 (assert (forall ((Y (-> tptp.produc3658429121746597890et_nat Bool)) (P2 (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o Y) (@ tptp.collec939566748876313656_nat_o tptp.proper)) (=> (forall ((X3 tptp.assn)) (@ P2 (@ tptp.rep_assn X3))) (@ P2 Y)))))
% 2.52/3.49 (assert (forall ((Y (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o Y) (@ tptp.collec939566748876313656_nat_o tptp.proper)) (not (forall ((X3 tptp.assn)) (not (= Y (@ tptp.rep_assn X3))))))))
% 2.52/3.49 (assert (forall ((X tptp.assn)) (@ (@ tptp.member6576561426505652726_nat_o (@ tptp.rep_assn X)) (@ tptp.collec939566748876313656_nat_o tptp.proper))))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) A)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ tptp.uminus6524753893492686040at_nat X)) B)) tptp.bot_bo2099793752762293965at_nat)))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (A (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.inf_in3604695632404883862_int_o (@ (@ tptp.inf_in3604695632404883862_int_o X) A)) (@ (@ tptp.inf_in3604695632404883862_int_o (@ tptp.uminus7117520113953359693_int_o X)) B)) tptp.bot_bo8147686125503663512_int_o)))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.inf_inf_set_nat X) A)) (@ (@ tptp.inf_inf_set_nat (@ tptp.uminus5710092332889474511et_nat X)) B)) tptp.bot_bot_set_nat)))
% 2.52/3.49 (assert (forall ((X tptp.set_int) (A tptp.set_int) (B tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int (@ (@ tptp.inf_inf_set_int X) A)) (@ (@ tptp.inf_inf_set_int (@ tptp.uminus1532241313380277803et_int X)) B)) tptp.bot_bot_set_int)))
% 2.52/3.49 (assert (forall ((X tptp.assn) (A tptp.assn) (B tptp.assn)) (= (@ (@ tptp.inf_inf_assn (@ (@ tptp.inf_inf_assn X) A)) (@ (@ tptp.inf_inf_assn (@ tptp.uminus_uminus_assn X)) B)) tptp.bot_bot_assn)))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.inf_in2572325071724192079at_nat (@ tptp.uminus6524753893492686040at_nat X)) A)) (@ (@ tptp.inf_in2572325071724192079at_nat X) B)) tptp.bot_bo2099793752762293965at_nat)))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (A (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.inf_in3604695632404883862_int_o (@ (@ tptp.inf_in3604695632404883862_int_o (@ tptp.uminus7117520113953359693_int_o X)) A)) (@ (@ tptp.inf_in3604695632404883862_int_o X) B)) tptp.bot_bo8147686125503663512_int_o)))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.inf_inf_set_nat (@ tptp.uminus5710092332889474511et_nat X)) A)) (@ (@ tptp.inf_inf_set_nat X) B)) tptp.bot_bot_set_nat)))
% 2.52/3.49 (assert (forall ((X tptp.set_int) (A tptp.set_int) (B tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int (@ (@ tptp.inf_inf_set_int (@ tptp.uminus1532241313380277803et_int X)) A)) (@ (@ tptp.inf_inf_set_int X) B)) tptp.bot_bot_set_int)))
% 2.52/3.49 (assert (forall ((X tptp.assn) (A tptp.assn) (B tptp.assn)) (= (@ (@ tptp.inf_inf_assn (@ (@ tptp.inf_inf_assn (@ tptp.uminus_uminus_assn X)) A)) (@ (@ tptp.inf_inf_assn X) B)) tptp.bot_bot_assn)))
% 2.52/3.49 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.uminus6524753893492686040at_nat (@ (@ tptp.sup_su6327502436637775413at_nat A3) B3)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ tptp.uminus6524753893492686040at_nat A3)) (@ tptp.uminus6524753893492686040at_nat B3)))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (@ tptp.uminus5710092332889474511et_nat (@ (@ tptp.sup_sup_set_nat A3) B3)) (@ (@ tptp.inf_inf_set_nat (@ tptp.uminus5710092332889474511et_nat A3)) (@ tptp.uminus5710092332889474511et_nat B3)))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.uminus6524753893492686040at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ tptp.uminus6524753893492686040at_nat A3)) (@ tptp.uminus6524753893492686040at_nat B3)))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (@ tptp.uminus5710092332889474511et_nat (@ (@ tptp.inf_inf_set_nat A3) B3)) (@ (@ tptp.sup_sup_set_nat (@ tptp.uminus5710092332889474511et_nat A3)) (@ tptp.uminus5710092332889474511et_nat B3)))))
% 2.52/3.49 (assert (forall ((P2 (-> tptp.produc3658429121746597890et_nat Bool)) (H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) As2))) (=> (@ tptp.proper P2) (=> (@ P2 _let_1) (@ tptp.in_range _let_1))))))
% 2.52/3.49 (assert (forall ((P2 (-> tptp.produc3658429121746597890et_nat Bool)) (As2 tptp.set_nat) (H2 tptp.heap_e7401611519738050253t_unit) (H5 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H5) As2))) (=> (@ tptp.proper P2) (=> (@ (@ (@ tptp.relH As2) H2) H5) (=> (@ tptp.in_range _let_1) (= (@ P2 (@ (@ tptp.produc7507926704131184380et_nat H2) As2)) (@ P2 _let_1))))))))
% 2.52/3.49 (assert (= tptp.proper (lambda ((P (-> tptp.produc3658429121746597890et_nat Bool))) (forall ((H tptp.heap_e7401611519738050253t_unit) (H7 tptp.heap_e7401611519738050253t_unit) (As7 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H7) As7))) (let ((_let_2 (@ (@ tptp.produc7507926704131184380et_nat H) As7))) (let ((_let_3 (@ P _let_2))) (and (=> _let_3 (@ tptp.in_range _let_2)) (=> (and _let_3 (@ (@ (@ tptp.relH As7) H) H7) (@ tptp.in_range _let_1)) (@ P _let_1))))))))))
% 2.52/3.49 (assert (forall ((P2 (-> tptp.produc3658429121746597890et_nat Bool)) (H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat) (H5 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H5) As2))) (=> (@ tptp.proper P2) (=> (@ P2 (@ (@ tptp.produc7507926704131184380et_nat H2) As2)) (=> (@ (@ (@ tptp.relH As2) H2) H5) (=> (@ tptp.in_range _let_1) (@ P2 _let_1))))))))
% 2.52/3.49 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int tptp.one_one_int)) Z) (@ tptp.uminus_uminus_int Z))))
% 2.52/3.49 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) Z) (@ tptp.uminus_uminus_rat Z))))
% 2.52/3.49 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) Z) (@ tptp.uminus1351360451143612070nteger Z))))
% 2.52/3.49 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int Z))))
% 2.52/3.49 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat Z) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat Z))))
% 2.52/3.49 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger Z) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger Z))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A)) B) (@ tptp.uminus_uminus_int (@ (@ tptp.times_times_int A) B)))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat A)) B) (@ tptp.uminus_uminus_rat (@ (@ tptp.times_times_rat A) B)))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.times_3573771949741848930nteger A) B)))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.times_times_int A) B))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) B))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.times_3573771949741848930nteger A) B))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int (@ _let_1 B))))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat (@ _let_1 B))))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ _let_1 B))))))
% 2.52/3.49 (assert (forall ((X tptp.int)) (= (= (@ (@ tptp.times_times_int X) X) tptp.one_one_int) (or (= X tptp.one_one_int) (= X (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 2.52/3.49 (assert (forall ((X tptp.rat)) (= (= (@ (@ tptp.times_times_rat X) X) tptp.one_one_rat) (or (= X tptp.one_one_rat) (= X (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 2.52/3.49 (assert (forall ((X tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger X) X) tptp.one_one_Code_integer) (or (= X tptp.one_one_Code_integer) (= X (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))))
% 2.52/3.49 (assert (not (= tptp.one_one_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 2.52/3.49 (assert (not (= tptp.one_one_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 2.52/3.49 (assert (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.times_times_int A) A) (@ (@ tptp.times_times_int B) B)) (or (= A B) (= A (@ tptp.uminus_uminus_int B))))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) A) (@ (@ tptp.times_times_rat B) B)) (or (= A B) (= A (@ tptp.uminus_uminus_rat B))))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger A) A) (@ (@ tptp.times_3573771949741848930nteger B) B)) (or (= A B) (= A (@ tptp.uminus1351360451143612070nteger B))))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.times_times_int A) (@ tptp.uminus_uminus_int B)))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.times_times_rat A) (@ tptp.uminus_uminus_rat B)))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.times_3573771949741848930nteger A) (@ tptp.uminus1351360451143612070nteger B)))))
% 2.52/3.49 (assert (@ (@ (@ (@ (@ tptp.boolea949959532490082519at_nat tptp.inf_in2572325071724192079at_nat) tptp.sup_su6327502436637775413at_nat) tptp.uminus6524753893492686040at_nat) tptp.bot_bo2099793752762293965at_nat) tptp.top_to4669805908274784177at_nat))
% 2.52/3.49 (assert (@ (@ (@ (@ (@ tptp.boolea1849928419393854478_int_o tptp.inf_in3604695632404883862_int_o) tptp.sup_su8463660629351352368_int_o) tptp.uminus7117520113953359693_int_o) tptp.bot_bo8147686125503663512_int_o) tptp.top_to1578927101902068148_int_o))
% 2.52/3.49 (assert (@ (@ (@ (@ (@ tptp.boolea778851993438741648et_nat tptp.inf_inf_set_nat) tptp.sup_sup_set_nat) tptp.uminus5710092332889474511et_nat) tptp.bot_bot_set_nat) tptp.top_top_set_nat))
% 2.52/3.49 (assert (@ (@ (@ (@ (@ tptp.boolea5824373010784320748et_int tptp.inf_inf_set_int) tptp.sup_sup_set_int) tptp.uminus1532241313380277803et_int) tptp.bot_bot_set_int) tptp.top_top_set_int))
% 2.52/3.49 (assert (@ (@ (@ (@ (@ tptp.boolea3191171876098928227t_unit tptp.inf_in4660618365625256667t_unit) tptp.sup_su793286257634532545t_unit) tptp.uminus5944136376168626660t_unit) tptp.bot_bo3957492148770167129t_unit) tptp.top_to1996260823553986621t_unit))
% 2.52/3.49 (assert (@ (@ (@ (@ (@ tptp.boolea5875918072483028530a_assn tptp.inf_inf_assn) tptp.sup_sup_assn) tptp.uminus_uminus_assn) tptp.bot_bot_assn) tptp.top_top_assn))
% 2.52/3.49 (assert (= tptp.wand_assn (lambda ((P tptp.assn) (Q tptp.assn)) (@ tptp.abs_assn (@ (@ tptp.wand_raw (@ tptp.rep_assn P)) (@ tptp.rep_assn Q))))))
% 2.52/3.49 (assert (forall ((X tptp.assn)) (= (@ tptp.abs_assn (@ tptp.rep_assn X)) X)))
% 2.52/3.49 (assert (forall ((P2 (-> tptp.produc3658429121746597890et_nat Bool)) (Pr tptp.assn)) (=> (forall ((H3 tptp.produc3658429121746597890et_nat)) (= (@ P2 H3) (@ (@ tptp.rep_assn Pr) H3))) (= Pr (@ tptp.abs_assn P2)))))
% 2.52/3.49 (assert (forall ((P2 (-> tptp.produc3658429121746597890et_nat Bool)) (Pr tptp.assn)) (=> (forall ((H3 tptp.produc3658429121746597890et_nat)) (= (@ P2 H3) (@ (@ tptp.rep_assn Pr) H3))) (= (@ tptp.abs_assn P2) Pr))))
% 2.52/3.49 (assert (= tptp.pure_assn (lambda ((B2 Bool)) (@ tptp.abs_assn (@ tptp.pure_a825153325127701367it_nat B2)))))
% 2.52/3.49 (assert (forall ((X tptp.assn)) (not (forall ((Y3 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (= X (@ tptp.abs_assn Y3)) (not (@ (@ tptp.member6576561426505652726_nat_o Y3) (@ tptp.collec939566748876313656_nat_o tptp.proper))))))))
% 2.52/3.49 (assert (forall ((P2 (-> tptp.assn Bool)) (X tptp.assn)) (=> (forall ((Y3 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o Y3) (@ tptp.collec939566748876313656_nat_o tptp.proper)) (@ P2 (@ tptp.abs_assn Y3)))) (@ P2 X))))
% 2.52/3.49 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Y (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.collec939566748876313656_nat_o tptp.proper))) (=> (@ (@ tptp.member6576561426505652726_nat_o X) _let_1) (=> (@ (@ tptp.member6576561426505652726_nat_o Y) _let_1) (= (= (@ tptp.abs_assn X) (@ tptp.abs_assn Y)) (= X Y)))))))
% 2.52/3.49 (assert (forall ((Y (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o Y) (@ tptp.collec939566748876313656_nat_o tptp.proper)) (= (@ tptp.rep_assn (@ tptp.abs_assn Y)) Y))))
% 2.52/3.49 (assert (= tptp.top_top_assn (@ tptp.abs_assn tptp.in_range)))
% 2.52/3.49 (assert (= tptp.one_one_assn (@ tptp.abs_assn tptp.one_assn_raw)))
% 2.52/3.49 (assert (= tptp.times_times_assn (lambda ((P tptp.assn) (Q tptp.assn)) (@ tptp.abs_assn (@ (@ tptp.times_assn_raw (@ tptp.rep_assn P)) (@ tptp.rep_assn Q))))))
% 2.52/3.49 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ tptp.neg_nu5851722552734809277nc_int _let_1) _let_1)))
% 2.52/3.49 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ tptp.neg_nu5219082963157363817nc_rat _let_1) _let_1)))
% 2.52/3.49 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ tptp.neg_nu5831290666863070958nteger _let_1) _let_1)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.produc6575502325842934193n_assn tptp.set_nat))) (= (@ (@ tptp.list_c6061723043370948915sn_nat F2) tptp.nil_Pr5671120429643327159n_assn) tptp.bot_bot_set_nat)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.int tptp.set_nat))) (= (@ (@ tptp.list_c3451693981498911948nt_nat F2) tptp.nil_int) tptp.bot_bot_set_nat)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.nat tptp.set_nat))) (= (@ (@ tptp.list_c2452340269597857392at_nat F2) tptp.nil_nat) tptp.bot_bot_set_nat)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.produc6575502325842934193n_assn tptp.set_int))) (= (@ (@ tptp.list_c6059232572861898639sn_int F2) tptp.nil_Pr5671120429643327159n_assn) tptp.bot_bot_set_int)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.int tptp.set_int))) (= (@ (@ tptp.list_c3449203510989861672nt_int F2) tptp.nil_int) tptp.bot_bot_set_int)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.nat tptp.set_int))) (= (@ (@ tptp.list_c2449849799088807116at_int F2) tptp.nil_nat) tptp.bot_bot_set_int)))
% 2.52/3.49 (assert (forall ((B Bool) (H2 tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn (@ tptp.pure_assn B)) H2) (and (= (@ tptp.produc8586169260539613262et_nat H2) tptp.bot_bot_set_nat) B))))
% 2.52/3.49 (assert (@ (@ (@ tptp.type_d3909072315231072503_nat_o tptp.rep_assn) tptp.abs_assn) (@ tptp.collec939566748876313656_nat_o tptp.proper)))
% 2.52/3.49 (assert (= (@ tptp.neg_nu7757733837767384882nteger tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 2.52/3.49 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat tptp.one_one_rat) tptp.one_one_rat))
% 2.52/3.49 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.one_one_int) tptp.one_one_int))
% 2.52/3.49 (assert (= (@ tptp.linord2612477271533052124et_int tptp.bot_bot_set_int) tptp.nil_int))
% 2.52/3.49 (assert (= (@ tptp.linord2614967742042102400et_nat tptp.bot_bot_set_nat) tptp.nil_nat))
% 2.52/3.49 (assert (= tptp.top_to5722533637347664993n_assn (@ tptp.coset_703488708621576356n_assn tptp.nil_Pr5671120429643327159n_assn)))
% 2.52/3.49 (assert (= tptp.top_top_set_int (@ tptp.coset_int tptp.nil_int)))
% 2.52/3.49 (assert (= tptp.top_top_set_nat (@ tptp.coset_nat tptp.nil_nat)))
% 2.52/3.49 (assert (= tptp.top_to1996260823553986621t_unit (@ tptp.coset_Product_unit tptp.nil_Product_unit)))
% 2.52/3.49 (assert (forall ((H2 tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn tptp.one_one_assn) H2) (= (@ tptp.produc8586169260539613262et_nat H2) tptp.bot_bot_set_nat))))
% 2.52/3.49 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 2.52/3.49 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 2.52/3.49 (assert (= (@ tptp.neg_nu7757733837767384882nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 2.52/3.49 (assert (forall ((A3 tptp.set_int)) (=> (@ tptp.finite_finite_int A3) (= (= (@ tptp.linord2612477271533052124et_int A3) tptp.nil_int) (= A3 tptp.bot_bot_set_int)))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A3) (= (= (@ tptp.linord2614967742042102400et_nat A3) tptp.nil_nat) (= A3 tptp.bot_bot_set_nat)))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.nat tptp.set_nat)) (X (-> tptp.nat tptp.nat))) (= (@ (@ tptp.list_c2452340269597857392at_nat F2) (@ (@ tptp.map_nat_nat X) tptp.nil_nat)) tptp.bot_bot_set_nat)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.assn tptp.set_nat)) (X (-> tptp.produc6575502325842934193n_assn tptp.assn))) (= (@ (@ tptp.list_c1844713377658005960sn_nat F2) (@ (@ tptp.map_Pr8991440229025900053n_assn X) tptp.nil_Pr5671120429643327159n_assn)) tptp.bot_bot_set_nat)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.nat tptp.set_int)) (X (-> tptp.nat tptp.nat))) (= (@ (@ tptp.list_c2449849799088807116at_int F2) (@ (@ tptp.map_nat_nat X) tptp.nil_nat)) tptp.bot_bot_set_int)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.assn tptp.set_int)) (X (-> tptp.produc6575502325842934193n_assn tptp.assn))) (= (@ (@ tptp.list_c1842222907148955684sn_int F2) (@ (@ tptp.map_Pr8991440229025900053n_assn X) tptp.nil_Pr5671120429643327159n_assn)) tptp.bot_bot_set_int)))
% 2.52/3.49 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn)) (= (@ (@ tptp.nths_P5537322223065504949n_assn Xs) tptp.bot_bot_set_nat) tptp.nil_Pr5671120429643327159n_assn)))
% 2.52/3.49 (assert (forall ((Xs tptp.list_int)) (= (@ (@ tptp.nths_int Xs) tptp.bot_bot_set_nat) tptp.nil_int)))
% 2.52/3.49 (assert (forall ((Xs tptp.list_nat)) (= (@ (@ tptp.nths_nat Xs) tptp.bot_bot_set_nat) tptp.nil_nat)))
% 2.52/3.49 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.zero_zero_int) tptp.one_one_int))
% 2.52/3.49 (assert (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 2.52/3.49 (assert (= (@ tptp.neg_nu5831290666863070958nteger tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer))
% 2.52/3.49 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3) tptp.bot_bo2099793752762293965at_nat) (@ (@ tptp.ord_le3146513528884898305at_nat A3) (@ tptp.uminus6524753893492686040at_nat B3)))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (= (@ (@ tptp.inf_inf_set_int A3) B3) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int A3) (@ tptp.uminus1532241313380277803et_int B3)))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat A3) B3) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat A3) (@ tptp.uminus5710092332889474511et_nat B3)))))
% 2.52/3.49 (assert (forall ((X tptp.nat) (Y tptp.nat)) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ tptp.measures_nat tptp.nil_nat_nat)))))
% 2.52/3.49 (assert (forall ((X tptp.int) (Y tptp.int)) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) (@ tptp.measures_int tptp.nil_int_nat)))))
% 2.52/3.49 (assert (forall ((P5 tptp.set_Pr1261947904930325089at_nat) (Q4 tptp.set_Pr1261947904930325089at_nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat P5) (@ (@ tptp.sup_su6327502436637775413at_nat Q4) R2)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat P5) (@ tptp.uminus6524753893492686040at_nat Q4))) R2))))
% 2.52/3.49 (assert (forall ((P5 (-> tptp.product_prod_int_int Bool)) (Q4 (-> tptp.product_prod_int_int Bool)) (R2 (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.ord_le8369615600986905444_int_o P5) (@ (@ tptp.sup_su8463660629351352368_int_o Q4) R2)) (@ (@ tptp.ord_le8369615600986905444_int_o (@ (@ tptp.inf_in3604695632404883862_int_o P5) (@ tptp.uminus7117520113953359693_int_o Q4))) R2))))
% 2.52/3.49 (assert (forall ((P5 tptp.assn) (Q4 tptp.assn) (R2 tptp.assn)) (= (@ (@ tptp.ord_less_eq_assn P5) (@ (@ tptp.sup_sup_assn Q4) R2)) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn P5) (@ tptp.uminus_uminus_assn Q4))) R2))))
% 2.52/3.49 (assert (forall ((P5 tptp.set_nat) (Q4 tptp.set_nat) (R2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat P5) (@ (@ tptp.sup_sup_set_nat Q4) R2)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat P5) (@ tptp.uminus5710092332889474511et_nat Q4))) R2))))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) (@ tptp.uminus6524753893492686040at_nat Y))) Z) (@ (@ tptp.ord_le3146513528884898305at_nat X) (@ (@ tptp.sup_su6327502436637775413at_nat Y) Z)))))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool)) (Z (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.ord_le8369615600986905444_int_o (@ (@ tptp.inf_in3604695632404883862_int_o X) (@ tptp.uminus7117520113953359693_int_o Y))) Z) (@ (@ tptp.ord_le8369615600986905444_int_o X) (@ (@ tptp.sup_su8463660629351352368_int_o Y) Z)))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (= (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn X) (@ tptp.uminus_uminus_assn Y))) Z) (@ (@ tptp.ord_less_eq_assn X) (@ (@ tptp.sup_sup_assn Y) Z)))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X) (@ tptp.uminus5710092332889474511et_nat Y))) Z) (@ (@ tptp.ord_less_eq_set_nat X) (@ (@ tptp.sup_sup_set_nat Y) Z)))))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)) Z) (@ (@ tptp.ord_le3146513528884898305at_nat X) (@ (@ tptp.sup_su6327502436637775413at_nat (@ tptp.uminus6524753893492686040at_nat Y)) Z)))))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool)) (Z (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.ord_le8369615600986905444_int_o (@ (@ tptp.inf_in3604695632404883862_int_o X) Y)) Z) (@ (@ tptp.ord_le8369615600986905444_int_o X) (@ (@ tptp.sup_su8463660629351352368_int_o (@ tptp.uminus7117520113953359693_int_o Y)) Z)))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (= (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn X) Y)) Z) (@ (@ tptp.ord_less_eq_assn X) (@ (@ tptp.sup_sup_assn (@ tptp.uminus_uminus_assn Y)) Z)))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X) Y)) Z) (@ (@ tptp.ord_less_eq_set_nat X) (@ (@ tptp.sup_sup_set_nat (@ tptp.uminus5710092332889474511et_nat Y)) Z)))))
% 2.52/3.49 (assert (= tptp.relH (lambda ((As7 tptp.set_nat) (H tptp.heap_e7401611519738050253t_unit) (H7 tptp.heap_e7401611519738050253t_unit)) (and (@ tptp.in_range (@ (@ tptp.produc7507926704131184380et_nat H) As7)) (@ tptp.in_range (@ (@ tptp.produc7507926704131184380et_nat H7) As7)) (forall ((T2 tptp.typerep) (X2 tptp.nat)) (=> (@ (@ tptp.member_nat2 X2) As7) (and (= (@ (@ (@ tptp.refs_Product_unit H) T2) X2) (@ (@ (@ tptp.refs_Product_unit H7) T2) X2)) (= (@ (@ (@ tptp.arrays_Product_unit H) T2) X2) (@ (@ (@ tptp.arrays_Product_unit H7) T2) X2)))))))))
% 2.52/3.49 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) C) (@ (@ tptp.times_times_rat B) C)) (or (= C tptp.zero_zero_rat) (= A B)))))
% 2.52/3.49 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.times_times_nat A) C) (@ (@ tptp.times_times_nat B) C)) (or (= C tptp.zero_zero_nat) (= A B)))))
% 2.52/3.49 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (= (@ (@ tptp.times_times_int A) C) (@ (@ tptp.times_times_int B) C)) (or (= C tptp.zero_zero_int) (= A B)))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger A) C) (@ (@ tptp.times_3573771949741848930nteger B) C)) (or (= C tptp.zero_z3403309356797280102nteger) (= A B)))))
% 2.52/3.49 (assert (forall ((A tptp.code_natural) (C tptp.code_natural) (B tptp.code_natural)) (= (= (@ (@ tptp.times_2397367101498566445atural A) C) (@ (@ tptp.times_2397367101498566445atural B) C)) (or (= C tptp.zero_z2226904508553997617atural) (= A B)))))
% 2.52/3.49 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_rat) (= A B))))))
% 2.52/3.49 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_nat) (= A B))))))
% 2.52/3.49 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_int) (= A B))))))
% 2.52/3.49 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_z3403309356797280102nteger) (= A B))))))
% 2.52/3.49 (assert (forall ((C tptp.code_natural) (A tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_z2226904508553997617atural) (= A B))))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) B) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))))
% 2.52/3.49 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat) (or (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.times_times_int A) B) tptp.zero_zero_int) (or (= A tptp.zero_zero_int) (= B tptp.zero_zero_int)))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger A) B) tptp.zero_z3403309356797280102nteger) (or (= A tptp.zero_z3403309356797280102nteger) (= B tptp.zero_z3403309356797280102nteger)))))
% 2.52/3.49 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (= (@ (@ tptp.times_2397367101498566445atural A) B) tptp.zero_z2226904508553997617atural) (or (= A tptp.zero_z2226904508553997617atural) (= B tptp.zero_z2226904508553997617atural)))))
% 2.52/3.49 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 2.52/3.49 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 2.52/3.49 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 2.52/3.49 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger A) tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)))
% 2.52/3.49 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.times_2397367101498566445atural A) tptp.zero_z2226904508553997617atural) tptp.zero_z2226904508553997617atural)))
% 2.52/3.49 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)))
% 2.52/3.49 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 2.52/3.49 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 2.52/3.49 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger tptp.zero_z3403309356797280102nteger) A) tptp.zero_z3403309356797280102nteger)))
% 2.52/3.49 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.times_2397367101498566445atural tptp.zero_z2226904508553997617atural) A) tptp.zero_z2226904508553997617atural)))
% 2.52/3.49 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) B))))
% 2.52/3.49 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.ord_less_eq_rat A) B))))
% 2.52/3.49 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_eq_int A) B))))
% 2.52/3.49 (assert (= (@ tptp.uminus_uminus_int tptp.zero_zero_int) tptp.zero_zero_int))
% 2.52/3.49 (assert (= (@ tptp.uminus_uminus_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 2.52/3.49 (assert (= (@ tptp.uminus1351360451143612070nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 2.52/3.49 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.uminus_uminus_int A)) (= tptp.zero_zero_int A))))
% 2.52/3.49 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat A)) (= tptp.zero_zero_rat A))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger A)) (= tptp.zero_z3403309356797280102nteger A))))
% 2.52/3.49 (assert (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 2.52/3.49 (assert (forall ((A tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 2.52/3.49 (assert (forall ((A tptp.int)) (= (= A (@ tptp.uminus_uminus_int A)) (= A tptp.zero_zero_int))))
% 2.52/3.49 (assert (forall ((A tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat A)) (= A tptp.zero_zero_rat))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger A)) (= A tptp.zero_z3403309356797280102nteger))))
% 2.52/3.49 (assert (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) A) (= A tptp.zero_zero_int))))
% 2.52/3.49 (assert (forall ((A tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) A) (= A tptp.zero_zero_rat))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) A) (= A tptp.zero_z3403309356797280102nteger))))
% 2.52/3.49 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B) C)) (and (@ _let_1 B) (@ _let_1 C))))))
% 2.52/3.49 (assert (forall ((A (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool)) (C (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.ord_le8369615600986905444_int_o A))) (= (@ _let_1 (@ (@ tptp.inf_in3604695632404883862_int_o B) C)) (and (@ _let_1 B) (@ _let_1 C))))))
% 2.52/3.49 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn A))) (= (@ _let_1 (@ (@ tptp.inf_inf_assn B) C)) (and (@ _let_1 B) (@ _let_1 C))))))
% 2.52/3.49 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat B) C)) (and (@ _let_1 B) (@ _let_1 C))))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (= (@ _let_1 (@ (@ tptp.inf_inf_rat B) C)) (and (@ _let_1 B) (@ _let_1 C))))))
% 2.52/3.49 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (= (@ _let_1 (@ (@ tptp.inf_inf_nat B) C)) (and (@ _let_1 B) (@ _let_1 C))))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (= (@ _let_1 (@ (@ tptp.inf_inf_int B) C)) (and (@ _let_1 B) (@ _let_1 C))))))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat X))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z)) (and (@ _let_1 Y) (@ _let_1 Z))))))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool)) (Z (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.ord_le8369615600986905444_int_o X))) (= (@ _let_1 (@ (@ tptp.inf_in3604695632404883862_int_o Y) Z)) (and (@ _let_1 Y) (@ _let_1 Z))))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn X))) (= (@ _let_1 (@ (@ tptp.inf_inf_assn Y) Z)) (and (@ _let_1 Y) (@ _let_1 Z))))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y) Z)) (and (@ _let_1 Y) (@ _let_1 Z))))))
% 2.52/3.49 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_rat Y) Z)) (and (@ _let_1 Y) (@ _let_1 Z))))))
% 2.52/3.49 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z)) (and (@ _let_1 Y) (@ _let_1 Z))))))
% 2.52/3.49 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (= (@ _let_1 (@ (@ tptp.inf_inf_int Y) Z)) (and (@ _let_1 Y) (@ _let_1 Z))))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (= (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.sup_sup_assn X) Y)) Z) (and (@ (@ tptp.ord_less_eq_assn X) Z) (@ (@ tptp.ord_less_eq_assn Y) Z)))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat X) Y)) Z) (and (@ (@ tptp.ord_less_eq_set_nat X) Z) (@ (@ tptp.ord_less_eq_set_nat Y) Z)))))
% 2.52/3.49 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat X) Y)) Z) (and (@ (@ tptp.ord_less_eq_rat X) Z) (@ (@ tptp.ord_less_eq_rat Y) Z)))))
% 2.52/3.49 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat X) Y)) Z) (and (@ (@ tptp.ord_less_eq_nat X) Z) (@ (@ tptp.ord_less_eq_nat Y) Z)))))
% 2.52/3.49 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int X) Y)) Z) (and (@ (@ tptp.ord_less_eq_int X) Z) (@ (@ tptp.ord_less_eq_int Y) Z)))))
% 2.52/3.49 (assert (forall ((B tptp.assn) (C tptp.assn) (A tptp.assn)) (= (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.sup_sup_assn B) C)) A) (and (@ (@ tptp.ord_less_eq_assn B) A) (@ (@ tptp.ord_less_eq_assn C) A)))))
% 2.52/3.49 (assert (forall ((B tptp.set_nat) (C tptp.set_nat) (A tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat B) C)) A) (and (@ (@ tptp.ord_less_eq_set_nat B) A) (@ (@ tptp.ord_less_eq_set_nat C) A)))))
% 2.52/3.49 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat B) C)) A) (and (@ (@ tptp.ord_less_eq_rat B) A) (@ (@ tptp.ord_less_eq_rat C) A)))))
% 2.52/3.49 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat B) C)) A) (and (@ (@ tptp.ord_less_eq_nat B) A) (@ (@ tptp.ord_less_eq_nat C) A)))))
% 2.52/3.49 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int B) C)) A) (and (@ (@ tptp.ord_less_eq_int B) A) (@ (@ tptp.ord_less_eq_int C) A)))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn)) (Xs tptp.list_P8527749157015355191n_assn)) (= (= (@ (@ tptp.map_Pr7925354932063753860n_assn F2) Xs) tptp.nil_Pr5671120429643327159n_assn) (= Xs tptp.nil_Pr5671120429643327159n_assn))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.int tptp.produc6575502325842934193n_assn)) (Xs tptp.list_int)) (= (= (@ (@ tptp.map_in4427992030928829247n_assn F2) Xs) tptp.nil_Pr5671120429643327159n_assn) (= Xs tptp.nil_int))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.nat tptp.produc6575502325842934193n_assn)) (Xs tptp.list_nat)) (= (= (@ (@ tptp.map_na2667955367175718043n_assn F2) Xs) tptp.nil_Pr5671120429643327159n_assn) (= Xs tptp.nil_nat))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.produc6575502325842934193n_assn tptp.int)) (Xs tptp.list_P8527749157015355191n_assn)) (= (= (@ (@ tptp.map_Pr7568062423562401049sn_int F2) Xs) tptp.nil_int) (= Xs tptp.nil_Pr5671120429643327159n_assn))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.int tptp.int)) (Xs tptp.list_int)) (= (= (@ (@ tptp.map_int_int F2) Xs) tptp.nil_int) (= Xs tptp.nil_int))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.nat tptp.int)) (Xs tptp.list_nat)) (= (= (@ (@ tptp.map_nat_int F2) Xs) tptp.nil_int) (= Xs tptp.nil_nat))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.produc6575502325842934193n_assn tptp.nat)) (Xs tptp.list_P8527749157015355191n_assn)) (= (= (@ (@ tptp.map_Pr7570552894071451325sn_nat F2) Xs) tptp.nil_nat) (= Xs tptp.nil_Pr5671120429643327159n_assn))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.int tptp.nat)) (Xs tptp.list_int)) (= (= (@ (@ tptp.map_int_nat F2) Xs) tptp.nil_nat) (= Xs tptp.nil_int))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (Xs tptp.list_nat)) (= (= (@ (@ tptp.map_nat_nat F2) Xs) tptp.nil_nat) (= Xs tptp.nil_nat))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.produc6575502325842934193n_assn tptp.assn)) (Xs tptp.list_P8527749157015355191n_assn)) (= (= (@ (@ tptp.map_Pr8991440229025900053n_assn F2) Xs) tptp.nil_assn) (= Xs tptp.nil_Pr5671120429643327159n_assn))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn)) (Xs tptp.list_P8527749157015355191n_assn)) (= (= tptp.nil_Pr5671120429643327159n_assn (@ (@ tptp.map_Pr7925354932063753860n_assn F2) Xs)) (= Xs tptp.nil_Pr5671120429643327159n_assn))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.int tptp.produc6575502325842934193n_assn)) (Xs tptp.list_int)) (= (= tptp.nil_Pr5671120429643327159n_assn (@ (@ tptp.map_in4427992030928829247n_assn F2) Xs)) (= Xs tptp.nil_int))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.nat tptp.produc6575502325842934193n_assn)) (Xs tptp.list_nat)) (= (= tptp.nil_Pr5671120429643327159n_assn (@ (@ tptp.map_na2667955367175718043n_assn F2) Xs)) (= Xs tptp.nil_nat))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.produc6575502325842934193n_assn tptp.int)) (Xs tptp.list_P8527749157015355191n_assn)) (= (= tptp.nil_int (@ (@ tptp.map_Pr7568062423562401049sn_int F2) Xs)) (= Xs tptp.nil_Pr5671120429643327159n_assn))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.int tptp.int)) (Xs tptp.list_int)) (= (= tptp.nil_int (@ (@ tptp.map_int_int F2) Xs)) (= Xs tptp.nil_int))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.nat tptp.int)) (Xs tptp.list_nat)) (= (= tptp.nil_int (@ (@ tptp.map_nat_int F2) Xs)) (= Xs tptp.nil_nat))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.produc6575502325842934193n_assn tptp.nat)) (Xs tptp.list_P8527749157015355191n_assn)) (= (= tptp.nil_nat (@ (@ tptp.map_Pr7570552894071451325sn_nat F2) Xs)) (= Xs tptp.nil_Pr5671120429643327159n_assn))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.int tptp.nat)) (Xs tptp.list_int)) (= (= tptp.nil_nat (@ (@ tptp.map_int_nat F2) Xs)) (= Xs tptp.nil_int))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (Xs tptp.list_nat)) (= (= tptp.nil_nat (@ (@ tptp.map_nat_nat F2) Xs)) (= Xs tptp.nil_nat))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.produc6575502325842934193n_assn tptp.assn)) (Xs tptp.list_P8527749157015355191n_assn)) (= (= tptp.nil_assn (@ (@ tptp.map_Pr8991440229025900053n_assn F2) Xs)) (= Xs tptp.nil_Pr5671120429643327159n_assn))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn)) (A tptp.list_P8527749157015355191n_assn)) (= (= (@ (@ tptp.map_Pr7925354932063753860n_assn F2) A) tptp.nil_Pr5671120429643327159n_assn) (= A tptp.nil_Pr5671120429643327159n_assn))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.int tptp.produc6575502325842934193n_assn)) (A tptp.list_int)) (= (= (@ (@ tptp.map_in4427992030928829247n_assn F2) A) tptp.nil_Pr5671120429643327159n_assn) (= A tptp.nil_int))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.nat tptp.produc6575502325842934193n_assn)) (A tptp.list_nat)) (= (= (@ (@ tptp.map_na2667955367175718043n_assn F2) A) tptp.nil_Pr5671120429643327159n_assn) (= A tptp.nil_nat))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.produc6575502325842934193n_assn tptp.int)) (A tptp.list_P8527749157015355191n_assn)) (= (= (@ (@ tptp.map_Pr7568062423562401049sn_int F2) A) tptp.nil_int) (= A tptp.nil_Pr5671120429643327159n_assn))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.int tptp.int)) (A tptp.list_int)) (= (= (@ (@ tptp.map_int_int F2) A) tptp.nil_int) (= A tptp.nil_int))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.nat tptp.int)) (A tptp.list_nat)) (= (= (@ (@ tptp.map_nat_int F2) A) tptp.nil_int) (= A tptp.nil_nat))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.produc6575502325842934193n_assn tptp.nat)) (A tptp.list_P8527749157015355191n_assn)) (= (= (@ (@ tptp.map_Pr7570552894071451325sn_nat F2) A) tptp.nil_nat) (= A tptp.nil_Pr5671120429643327159n_assn))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.int tptp.nat)) (A tptp.list_int)) (= (= (@ (@ tptp.map_int_nat F2) A) tptp.nil_nat) (= A tptp.nil_int))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (A tptp.list_nat)) (= (= (@ (@ tptp.map_nat_nat F2) A) tptp.nil_nat) (= A tptp.nil_nat))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.produc6575502325842934193n_assn tptp.assn)) (A tptp.list_P8527749157015355191n_assn)) (= (= (@ (@ tptp.map_Pr8991440229025900053n_assn F2) A) tptp.nil_assn) (= A tptp.nil_Pr5671120429643327159n_assn))))
% 2.52/3.49 (assert (forall ((C2 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat C2))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)) (and (@ _let_1 A3) (@ _let_1 B3))))))
% 2.52/3.49 (assert (forall ((C2 tptp.set_nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C2))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3)) (and (@ _let_1 A3) (@ _let_1 B3))))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.nths_P5537322223065504949n_assn tptp.nil_Pr5671120429643327159n_assn) A3) tptp.nil_Pr5671120429643327159n_assn)))
% 2.52/3.49 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.nths_int tptp.nil_int) A3) tptp.nil_int)))
% 2.52/3.49 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.nths_nat tptp.nil_nat) A3) tptp.nil_nat)))
% 2.52/3.49 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger))))
% 2.52/3.49 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 2.52/3.49 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 2.52/3.49 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A))))
% 2.52/3.49 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 2.52/3.49 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (= (@ _let_1 (@ tptp.uminus_uminus_rat A)) (@ _let_1 tptp.zero_zero_rat)))))
% 2.52/3.49 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (= (@ _let_1 (@ tptp.uminus_uminus_int A)) (@ _let_1 tptp.zero_zero_int)))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 2.52/3.49 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) A) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A))))
% 2.52/3.49 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) A) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) C) C) (or (= C tptp.zero_zero_rat) (= A tptp.one_one_rat)))))
% 2.52/3.49 (assert (forall ((A tptp.int) (C tptp.int)) (= (= (@ (@ tptp.times_times_int A) C) C) (or (= C tptp.zero_zero_int) (= A tptp.one_one_int)))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer) (C tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger A) C) C) (or (= C tptp.zero_z3403309356797280102nteger) (= A tptp.one_one_Code_integer)))))
% 2.52/3.49 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (= C (@ (@ tptp.times_times_rat B) C)) (or (= C tptp.zero_zero_rat) (= B tptp.one_one_rat)))))
% 2.52/3.49 (assert (forall ((C tptp.int) (B tptp.int)) (= (= C (@ (@ tptp.times_times_int B) C)) (or (= C tptp.zero_zero_int) (= B tptp.one_one_int)))))
% 2.52/3.49 (assert (forall ((C tptp.code_integer) (B tptp.code_integer)) (= (= C (@ (@ tptp.times_3573771949741848930nteger B) C)) (or (= C tptp.zero_z3403309356797280102nteger) (= B tptp.one_one_Code_integer)))))
% 2.52/3.49 (assert (forall ((C tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.times_times_rat C) A) C) (or (= C tptp.zero_zero_rat) (= A tptp.one_one_rat)))))
% 2.52/3.49 (assert (forall ((C tptp.int) (A tptp.int)) (= (= (@ (@ tptp.times_times_int C) A) C) (or (= C tptp.zero_zero_int) (= A tptp.one_one_int)))))
% 2.52/3.49 (assert (forall ((C tptp.code_integer) (A tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger C) A) C) (or (= C tptp.zero_z3403309356797280102nteger) (= A tptp.one_one_Code_integer)))))
% 2.52/3.49 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (= C (@ (@ tptp.times_times_rat C) B)) (or (= C tptp.zero_zero_rat) (= B tptp.one_one_rat)))))
% 2.52/3.49 (assert (forall ((C tptp.int) (B tptp.int)) (= (= C (@ (@ tptp.times_times_int C) B)) (or (= C tptp.zero_zero_int) (= B tptp.one_one_int)))))
% 2.52/3.49 (assert (forall ((C tptp.code_integer) (B tptp.code_integer)) (= (= C (@ (@ tptp.times_3573771949741848930nteger C) B)) (or (= C tptp.zero_z3403309356797280102nteger) (= B tptp.one_one_Code_integer)))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_int)) (=> (not (@ tptp.finite_finite_int A3)) (= (@ tptp.linord2612477271533052124et_int A3) tptp.nil_int))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat A3)) (= (@ tptp.linord2614967742042102400et_nat A3) tptp.nil_nat))))
% 2.52/3.49 (assert (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (Xs tptp.list_nat) (I tptp.set_nat)) (let ((_let_1 (@ tptp.map_nat_nat F2))) (= (@ (@ tptp.nths_nat (@ _let_1 Xs)) I) (@ _let_1 (@ (@ tptp.nths_nat Xs) I))))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.produc6575502325842934193n_assn tptp.assn)) (Xs tptp.list_P8527749157015355191n_assn) (I tptp.set_nat)) (let ((_let_1 (@ tptp.map_Pr8991440229025900053n_assn F2))) (= (@ (@ tptp.nths_assn (@ _let_1 Xs)) I) (@ _let_1 (@ (@ tptp.nths_P5537322223065504949n_assn Xs) I))))))
% 2.52/3.49 (assert (forall ((X tptp.nat)) (= (= tptp.zero_zero_nat X) (= X tptp.zero_zero_nat))))
% 2.52/3.49 (assert (forall ((X tptp.int)) (= (= tptp.zero_zero_int X) (= X tptp.zero_zero_int))))
% 2.52/3.49 (assert (forall ((X tptp.rat)) (= (= tptp.zero_zero_rat X) (= X tptp.zero_zero_rat))))
% 2.52/3.49 (assert (forall ((X tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger X) (= X tptp.zero_z3403309356797280102nteger))))
% 2.52/3.49 (assert (forall ((X tptp.code_natural)) (= (= tptp.zero_z2226904508553997617atural X) (= X tptp.zero_z2226904508553997617atural))))
% 2.52/3.49 (assert (forall ((X tptp.produc2732055786443039994et_nat)) (not (forall ((P4 (-> tptp.produc3658429121746597890et_nat Bool)) (Q5 (-> tptp.produc3658429121746597890et_nat Bool)) (H3 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (not (= X (@ (@ tptp.produc2245416461498447860et_nat P4) (@ (@ tptp.produc5001842942810119800et_nat Q5) (@ (@ tptp.produc7507926704131184380et_nat H3) As)))))))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A)) (@ _let_1 B)))))))
% 2.52/3.49 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural C))) (=> (@ (@ tptp.ord_le1926595141338095240atural A) B) (=> (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) C) (@ (@ tptp.ord_le1926595141338095240atural (@ _let_1 A)) (@ _let_1 B)))))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 2.52/3.49 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)))))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger)))))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.times_times_rat A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)))))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.times_times_int A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int)))))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger B) A)) tptp.zero_z3403309356797280102nteger)))))
% 2.52/3.49 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) A) (=> (@ (@ tptp.ord_le1926595141338095240atural B) tptp.zero_z2226904508553997617atural) (@ (@ tptp.ord_le1926595141338095240atural (@ (@ tptp.times_2397367101498566445atural B) A)) tptp.zero_z2226904508553997617atural)))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat B) A)) tptp.zero_zero_rat)))))
% 2.52/3.49 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat B) A)) tptp.zero_zero_nat)))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int B) A)) tptp.zero_zero_int)))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.zero_z3403309356797280102nteger)))))
% 2.52/3.49 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (@ (@ tptp.ord_le1926595141338095240atural A) tptp.zero_z2226904508553997617atural) (=> (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) B) (@ (@ tptp.ord_le1926595141338095240atural (@ (@ tptp.times_2397367101498566445atural A) B)) tptp.zero_z2226904508553997617atural)))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))))
% 2.52/3.49 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.zero_z3403309356797280102nteger)))))
% 2.52/3.49 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) A) (=> (@ (@ tptp.ord_le1926595141338095240atural B) tptp.zero_z2226904508553997617atural) (@ (@ tptp.ord_le1926595141338095240atural (@ (@ tptp.times_2397367101498566445atural A) B)) tptp.zero_z2226904508553997617atural)))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))))
% 2.52/3.49 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A) B)))))))
% 2.52/3.49 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_2397367101498566445atural A) B)))))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_rat A) B)))))))
% 2.52/3.49 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_nat A) B)))))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_int A) B)))))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger)) (and (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (@ _let_1 B))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.zero_z3403309356797280102nteger)))))
% 2.52/3.49 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_le1926595141338095240atural B) tptp.zero_z2226904508553997617atural)) (and (@ (@ tptp.ord_le1926595141338095240atural A) tptp.zero_z2226904508553997617atural) (@ _let_1 B))) (@ (@ tptp.ord_le1926595141338095240atural (@ (@ tptp.times_2397367101498566445atural A) B)) tptp.zero_z2226904508553997617atural)))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ _let_1 B))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))))
% 2.52/3.49 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat)) (and (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (@ _let_1 B))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ _let_1 B))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.zero_z3403309356797280102nteger) (or (and (@ _let_1 A) (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger)) (and (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (@ _let_1 B)))))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ _let_1 B)))))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ _let_1 B)))))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 2.52/3.49 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (=> (@ (@ tptp.ord_le1926595141338095240atural A) B) (=> (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) C) (@ (@ tptp.ord_le1926595141338095240atural (@ (@ tptp.times_2397367101498566445atural A) C)) (@ (@ tptp.times_2397367101498566445atural B) C))))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 2.52/3.49 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C))))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 2.52/3.49 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 2.52/3.49 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 2.52/3.49 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A)) (@ _let_1 B)))))))
% 2.52/3.49 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural C))) (=> (@ (@ tptp.ord_le1926595141338095240atural A) B) (=> (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) C) (@ (@ tptp.ord_le1926595141338095240atural (@ _let_1 A)) (@ _let_1 B)))))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 2.52/3.49 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)))))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.times_3573771949741848930nteger A) B))))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B))))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) B))))))
% 2.52/3.49 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A)) (@ _let_1 B)))))))
% 2.52/3.49 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 2.52/3.49 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)))))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger))) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A) B))))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat))) (@ _let_1 (@ (@ tptp.times_times_rat A) B))))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int))) (@ _let_1 (@ (@ tptp.times_times_int A) B))))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.times_3573771949741848930nteger A) A))))
% 2.52/3.49 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) A))))
% 2.52/3.49 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) A))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D2)))))))))
% 2.52/3.49 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural) (D2 tptp.code_natural)) (let ((_let_1 (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural))) (=> (@ (@ tptp.ord_le1926595141338095240atural A) B) (=> (@ (@ tptp.ord_le1926595141338095240atural C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_le1926595141338095240atural (@ (@ tptp.times_2397367101498566445atural A) C)) (@ (@ tptp.times_2397367101498566445atural B) D2)))))))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D2)))))))))
% 2.52/3.49 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D2)))))))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D2)))))))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) D2) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D2)))))))))
% 2.52/3.49 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural) (D2 tptp.code_natural)) (let ((_let_1 (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural))) (=> (@ (@ tptp.ord_le1926595141338095240atural A) B) (=> (@ (@ tptp.ord_le1926595141338095240atural C) D2) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_le1926595141338095240atural (@ (@ tptp.times_2397367101498566445atural A) C)) (@ (@ tptp.times_2397367101498566445atural B) D2)))))))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D2) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D2)))))))))
% 2.52/3.49 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D2) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D2)))))))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D2) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D2)))))))))
% 2.52/3.49 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 2.52/3.49 (assert (not (@ (@ tptp.ord_le1926595141338095240atural tptp.one_one_Code_natural) tptp.zero_z2226904508553997617atural)))
% 2.52/3.49 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 2.52/3.49 (assert (not (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 2.52/3.49 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.zero_zero_int)))
% 2.52/3.49 (assert (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer))
% 2.52/3.49 (assert (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) tptp.one_one_Code_natural))
% 2.52/3.49 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 2.52/3.49 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 2.52/3.49 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 2.52/3.49 (assert (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer))
% 2.52/3.49 (assert (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) tptp.one_one_Code_natural))
% 2.52/3.49 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 2.52/3.49 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 2.52/3.49 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 2.52/3.49 (assert (forall ((C tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.one_one_Code_integer) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) A)))))
% 2.52/3.49 (assert (forall ((C tptp.code_natural) (A tptp.code_natural)) (=> (@ (@ tptp.ord_le1926595141338095240atural C) tptp.one_one_Code_natural) (=> (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) A) (@ (@ tptp.ord_le1926595141338095240atural (@ (@ tptp.times_2397367101498566445atural A) C)) A)))))
% 2.52/3.49 (assert (forall ((C tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.one_one_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) A)))))
% 2.52/3.49 (assert (forall ((C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) tptp.one_one_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) A)))))
% 2.52/3.49 (assert (forall ((C tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.one_one_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) A)))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.one_one_Code_integer) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.one_one_Code_integer))))))
% 2.52/3.49 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (@ (@ tptp.ord_le1926595141338095240atural A) tptp.one_one_Code_natural) (=> (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) B) (=> (@ (@ tptp.ord_le1926595141338095240atural B) tptp.one_one_Code_natural) (@ (@ tptp.ord_le1926595141338095240atural (@ (@ tptp.times_2397367101498566445atural A) B)) tptp.one_one_Code_natural))))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.one_one_rat))))))
% 2.52/3.49 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B)) tptp.one_one_nat))))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int B) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.one_one_int))))))
% 2.52/3.49 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_le3102999989581377725nteger Y) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger X) Y)) X)))))))
% 2.52/3.49 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X) Y)) X)))))))
% 2.52/3.49 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X) Y)) X)))))))
% 2.52/3.49 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_le3102999989581377725nteger Y) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger Y) X)) X)))))))
% 2.52/3.49 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Y) X)) X)))))))
% 2.52/3.49 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int Y) X)) X)))))))
% 2.52/3.49 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 2.52/3.49 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 2.52/3.49 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 2.52/3.49 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 2.52/3.49 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 2.52/3.49 (assert (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn))) (= (@ (@ tptp.map_Pr7925354932063753860n_assn F2) tptp.nil_Pr5671120429643327159n_assn) tptp.nil_Pr5671120429643327159n_assn)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.produc6575502325842934193n_assn tptp.int))) (= (@ (@ tptp.map_Pr7568062423562401049sn_int F2) tptp.nil_Pr5671120429643327159n_assn) tptp.nil_int)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.produc6575502325842934193n_assn tptp.nat))) (= (@ (@ tptp.map_Pr7570552894071451325sn_nat F2) tptp.nil_Pr5671120429643327159n_assn) tptp.nil_nat)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.int tptp.produc6575502325842934193n_assn))) (= (@ (@ tptp.map_in4427992030928829247n_assn F2) tptp.nil_int) tptp.nil_Pr5671120429643327159n_assn)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.int tptp.int))) (= (@ (@ tptp.map_int_int F2) tptp.nil_int) tptp.nil_int)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.int tptp.nat))) (= (@ (@ tptp.map_int_nat F2) tptp.nil_int) tptp.nil_nat)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.nat tptp.produc6575502325842934193n_assn))) (= (@ (@ tptp.map_na2667955367175718043n_assn F2) tptp.nil_nat) tptp.nil_Pr5671120429643327159n_assn)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.nat tptp.int))) (= (@ (@ tptp.map_nat_int F2) tptp.nil_nat) tptp.nil_int)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.nat tptp.nat))) (= (@ (@ tptp.map_nat_nat F2) tptp.nil_nat) tptp.nil_nat)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.produc6575502325842934193n_assn tptp.assn))) (= (@ (@ tptp.map_Pr8991440229025900053n_assn F2) tptp.nil_Pr5671120429643327159n_assn) tptp.nil_assn)))
% 2.52/3.49 (assert (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 2.52/3.49 (assert (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.one_one_rat))
% 2.52/3.49 (assert (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.one_one_nat))
% 2.52/3.49 (assert (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.one_one_int))
% 2.52/3.49 (assert (forall ((X tptp.produc6197004810343482825et_nat)) (not (forall ((B5 Bool) (H3 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (not (= X (@ (@ tptp.produc3762353314782720579et_nat B5) (@ (@ tptp.produc7507926704131184380et_nat H3) As))))))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le3102999989581377725nteger B) (@ tptp.uminus1351360451143612070nteger A)))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.ord_less_eq_rat B) (@ tptp.uminus_uminus_rat A)))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.ord_less_eq_int B) (@ tptp.uminus_uminus_int A)))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) A))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) A))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B)) A))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)))))
% 2.52/3.49 (assert (forall ((B tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B) C) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) C))))
% 2.52/3.49 (assert (forall ((B (-> tptp.product_prod_int_int Bool)) (C (-> tptp.product_prod_int_int Bool)) (A (-> tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le8369615600986905444_int_o B) C) (@ (@ tptp.ord_le8369615600986905444_int_o (@ (@ tptp.inf_in3604695632404883862_int_o A) B)) C))))
% 2.52/3.49 (assert (forall ((B tptp.assn) (C tptp.assn) (A tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn B) C) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn A) B)) C))))
% 2.52/3.49 (assert (forall ((B tptp.set_nat) (C tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B) C) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) C))))
% 2.52/3.49 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat A) B)) C))))
% 2.52/3.49 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) C))))
% 2.52/3.49 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A) B)) C))))
% 2.52/3.49 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A) C) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) C))))
% 2.52/3.49 (assert (forall ((A (-> tptp.product_prod_int_int Bool)) (C (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le8369615600986905444_int_o A) C) (@ (@ tptp.ord_le8369615600986905444_int_o (@ (@ tptp.inf_in3604695632404883862_int_o A) B)) C))))
% 2.52/3.49 (assert (forall ((A tptp.assn) (C tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A) C) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn A) B)) C))))
% 2.52/3.49 (assert (forall ((A tptp.set_nat) (C tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) C) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) C))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat A) B)) C))))
% 2.52/3.49 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) C))))
% 2.52/3.49 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A) B)) C))))
% 2.52/3.49 (assert (= tptp.ord_le3146513528884898305at_nat (lambda ((B2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2) B2))))
% 2.52/3.49 (assert (= tptp.ord_le8369615600986905444_int_o (lambda ((B2 (-> tptp.product_prod_int_int Bool)) (A2 (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.inf_in3604695632404883862_int_o A2) B2) B2))))
% 2.52/3.49 (assert (= tptp.ord_less_eq_assn (lambda ((B2 tptp.assn) (A2 tptp.assn)) (= (@ (@ tptp.inf_inf_assn A2) B2) B2))))
% 2.52/3.49 (assert (= tptp.ord_less_eq_set_nat (lambda ((B2 tptp.set_nat) (A2 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A2) B2) B2))))
% 2.52/3.49 (assert (= tptp.ord_less_eq_rat (lambda ((B2 tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.inf_inf_rat A2) B2) B2))))
% 2.52/3.49 (assert (= tptp.ord_less_eq_nat (lambda ((B2 tptp.nat) (A2 tptp.nat)) (= (@ (@ tptp.inf_inf_nat A2) B2) B2))))
% 2.52/3.49 (assert (= tptp.ord_less_eq_int (lambda ((B2 tptp.int) (A2 tptp.int)) (= (@ (@ tptp.inf_inf_int A2) B2) B2))))
% 2.52/3.49 (assert (= tptp.ord_le3146513528884898305at_nat (lambda ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2) A2))))
% 2.52/3.49 (assert (= tptp.ord_le8369615600986905444_int_o (lambda ((A2 (-> tptp.product_prod_int_int Bool)) (B2 (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.inf_in3604695632404883862_int_o A2) B2) A2))))
% 2.52/3.49 (assert (= tptp.ord_less_eq_assn (lambda ((A2 tptp.assn) (B2 tptp.assn)) (= (@ (@ tptp.inf_inf_assn A2) B2) A2))))
% 2.52/3.49 (assert (= tptp.ord_less_eq_set_nat (lambda ((A2 tptp.set_nat) (B2 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A2) B2) A2))))
% 2.52/3.49 (assert (= tptp.ord_less_eq_rat (lambda ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.inf_inf_rat A2) B2) A2))))
% 2.52/3.49 (assert (= tptp.ord_less_eq_nat (lambda ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.inf_inf_nat A2) B2) A2))))
% 2.52/3.49 (assert (= tptp.ord_less_eq_int (lambda ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.inf_inf_int A2) B2) A2))))
% 2.52/3.49 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) B)))
% 2.52/3.49 (assert (forall ((A (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool))) (@ (@ tptp.ord_le8369615600986905444_int_o (@ (@ tptp.inf_in3604695632404883862_int_o A) B)) B)))
% 2.52/3.49 (assert (forall ((A tptp.assn) (B tptp.assn)) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn A) B)) B)))
% 2.52/3.49 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) B)))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat A) B)) B)))
% 2.52/3.49 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) B)))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A) B)) B)))
% 2.52/3.49 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) A)))
% 2.52/3.49 (assert (forall ((A (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool))) (@ (@ tptp.ord_le8369615600986905444_int_o (@ (@ tptp.inf_in3604695632404883862_int_o A) B)) A)))
% 2.52/3.49 (assert (forall ((A tptp.assn) (B tptp.assn)) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn A) B)) A)))
% 2.52/3.49 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) A)))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat A) B)) A)))
% 2.52/3.49 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) A)))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A) B)) A)))
% 2.52/3.49 (assert (= tptp.ord_le3146513528884898305at_nat (lambda ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (= A2 (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2)))))
% 2.52/3.49 (assert (= tptp.ord_le8369615600986905444_int_o (lambda ((A2 (-> tptp.product_prod_int_int Bool)) (B2 (-> tptp.product_prod_int_int Bool))) (= A2 (@ (@ tptp.inf_in3604695632404883862_int_o A2) B2)))))
% 2.52/3.49 (assert (= tptp.ord_less_eq_assn (lambda ((A2 tptp.assn) (B2 tptp.assn)) (= A2 (@ (@ tptp.inf_inf_assn A2) B2)))))
% 2.52/3.49 (assert (= tptp.ord_less_eq_set_nat (lambda ((A2 tptp.set_nat) (B2 tptp.set_nat)) (= A2 (@ (@ tptp.inf_inf_set_nat A2) B2)))))
% 2.52/3.49 (assert (= tptp.ord_less_eq_rat (lambda ((A2 tptp.rat) (B2 tptp.rat)) (= A2 (@ (@ tptp.inf_inf_rat A2) B2)))))
% 2.52/3.49 (assert (= tptp.ord_less_eq_nat (lambda ((A2 tptp.nat) (B2 tptp.nat)) (= A2 (@ (@ tptp.inf_inf_nat A2) B2)))))
% 2.52/3.49 (assert (= tptp.ord_less_eq_int (lambda ((A2 tptp.int) (B2 tptp.int)) (= A2 (@ (@ tptp.inf_inf_int A2) B2)))))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z)))))))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool)) (Z (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.ord_le8369615600986905444_int_o X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.inf_in3604695632404883862_int_o Y) Z)))))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.inf_inf_assn Y) Z)))))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y) Z)))))))
% 2.52/3.49 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.inf_inf_rat Y) Z)))))))
% 2.52/3.49 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z)))))))
% 2.52/3.49 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.inf_inf_int Y) Z)))))))
% 2.52/3.49 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B) C)))))))
% 2.52/3.49 (assert (forall ((A (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool)) (C (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.ord_le8369615600986905444_int_o A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.inf_in3604695632404883862_int_o B) C)))))))
% 2.52/3.49 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.inf_inf_assn B) C)))))))
% 2.52/3.49 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.inf_inf_set_nat B) C)))))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.inf_inf_rat B) C)))))))
% 2.52/3.49 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.inf_inf_nat B) C)))))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.inf_inf_int B) C)))))))
% 2.52/3.49 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A))) (=> (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))))
% 2.52/3.49 (assert (forall ((A (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool)) (C (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.ord_le8369615600986905444_int_o A))) (=> (@ _let_1 (@ (@ tptp.inf_in3604695632404883862_int_o B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))))
% 2.52/3.49 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_assn B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))))
% 2.52/3.49 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_rat B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))))
% 2.52/3.49 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_nat B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_int B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))))
% 2.52/3.49 (assert (forall ((Y tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat Y) X) (= (@ (@ tptp.inf_in2572325071724192079at_nat X) Y) Y))))
% 2.52/3.49 (assert (forall ((Y (-> tptp.product_prod_int_int Bool)) (X (-> tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le8369615600986905444_int_o Y) X) (= (@ (@ tptp.inf_in3604695632404883862_int_o X) Y) Y))))
% 2.52/3.49 (assert (forall ((Y tptp.assn) (X tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn Y) X) (= (@ (@ tptp.inf_inf_assn X) Y) Y))))
% 2.52/3.49 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (= (@ (@ tptp.inf_inf_set_nat X) Y) Y))))
% 2.52/3.49 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (= (@ (@ tptp.inf_inf_rat X) Y) Y))))
% 2.52/3.49 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.inf_inf_nat X) Y) Y))))
% 2.52/3.49 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= (@ (@ tptp.inf_inf_int X) Y) Y))))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat X) Y) (= (@ (@ tptp.inf_in2572325071724192079at_nat X) Y) X))))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le8369615600986905444_int_o X) Y) (= (@ (@ tptp.inf_in3604695632404883862_int_o X) Y) X))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X) Y) (= (@ (@ tptp.inf_inf_assn X) Y) X))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (= (@ (@ tptp.inf_inf_set_nat X) Y) X))))
% 2.52/3.49 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (= (@ (@ tptp.inf_inf_rat X) Y) X))))
% 2.52/3.49 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (@ (@ tptp.inf_inf_nat X) Y) X))))
% 2.52/3.49 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (@ (@ tptp.inf_inf_int X) Y) X))))
% 2.52/3.49 (assert (forall ((B tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B) A) (= (@ (@ tptp.inf_in2572325071724192079at_nat A) B) B))))
% 2.52/3.49 (assert (forall ((B (-> tptp.product_prod_int_int Bool)) (A (-> tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le8369615600986905444_int_o B) A) (= (@ (@ tptp.inf_in3604695632404883862_int_o A) B) B))))
% 2.52/3.49 (assert (forall ((B tptp.assn) (A tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn B) A) (= (@ (@ tptp.inf_inf_assn A) B) B))))
% 2.52/3.49 (assert (forall ((B tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (= (@ (@ tptp.inf_inf_set_nat A) B) B))))
% 2.52/3.49 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.inf_inf_rat A) B) B))))
% 2.52/3.49 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.inf_inf_nat A) B) B))))
% 2.52/3.49 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.inf_inf_int A) B) B))))
% 2.52/3.49 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A) B) (= (@ (@ tptp.inf_in2572325071724192079at_nat A) B) A))))
% 2.52/3.49 (assert (forall ((A (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le8369615600986905444_int_o A) B) (= (@ (@ tptp.inf_in3604695632404883862_int_o A) B) A))))
% 2.52/3.49 (assert (forall ((A tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A) B) (= (@ (@ tptp.inf_inf_assn A) B) A))))
% 2.52/3.49 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (= (@ (@ tptp.inf_inf_set_nat A) B) A))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= (@ (@ tptp.inf_inf_rat A) B) A))))
% 2.52/3.49 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.inf_inf_nat A) B) A))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (= (@ (@ tptp.inf_inf_int A) B) A))))
% 2.52/3.49 (assert (= tptp.ord_le3146513528884898305at_nat (lambda ((X2 tptp.set_Pr1261947904930325089at_nat) (Y2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat X2) Y2) X2))))
% 2.52/3.49 (assert (= tptp.ord_le8369615600986905444_int_o (lambda ((X2 (-> tptp.product_prod_int_int Bool)) (Y2 (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.inf_in3604695632404883862_int_o X2) Y2) X2))))
% 2.52/3.49 (assert (= tptp.ord_less_eq_assn (lambda ((X2 tptp.assn) (Y2 tptp.assn)) (= (@ (@ tptp.inf_inf_assn X2) Y2) X2))))
% 2.52/3.49 (assert (= tptp.ord_less_eq_set_nat (lambda ((X2 tptp.set_nat) (Y2 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X2) Y2) X2))))
% 2.52/3.49 (assert (= tptp.ord_less_eq_rat (lambda ((X2 tptp.rat) (Y2 tptp.rat)) (= (@ (@ tptp.inf_inf_rat X2) Y2) X2))))
% 2.52/3.49 (assert (= tptp.ord_less_eq_nat (lambda ((X2 tptp.nat) (Y2 tptp.nat)) (= (@ (@ tptp.inf_inf_nat X2) Y2) X2))))
% 2.52/3.49 (assert (= tptp.ord_less_eq_int (lambda ((X2 tptp.int) (Y2 tptp.int)) (= (@ (@ tptp.inf_inf_int X2) Y2) X2))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat)) (X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X3 tptp.set_Pr1261947904930325089at_nat) (Y3 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ F2 X3) Y3)) X3)) (=> (forall ((X3 tptp.set_Pr1261947904930325089at_nat) (Y3 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ F2 X3) Y3)) Y3)) (=> (forall ((X3 tptp.set_Pr1261947904930325089at_nat) (Y3 tptp.set_Pr1261947904930325089at_nat) (Z2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat X3))) (=> (@ _let_1 Y3) (=> (@ _let_1 Z2) (@ _let_1 (@ (@ F2 Y3) Z2)))))) (= (@ (@ tptp.inf_in2572325071724192079at_nat X) Y) (@ (@ F2 X) Y)))))))
% 2.52/3.49 (assert (forall ((F2 (-> (-> tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool) tptp.product_prod_int_int Bool)) (X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool))) (=> (forall ((X3 (-> tptp.product_prod_int_int Bool)) (Y3 (-> tptp.product_prod_int_int Bool))) (@ (@ tptp.ord_le8369615600986905444_int_o (@ (@ F2 X3) Y3)) X3)) (=> (forall ((X3 (-> tptp.product_prod_int_int Bool)) (Y3 (-> tptp.product_prod_int_int Bool))) (@ (@ tptp.ord_le8369615600986905444_int_o (@ (@ F2 X3) Y3)) Y3)) (=> (forall ((X3 (-> tptp.product_prod_int_int Bool)) (Y3 (-> tptp.product_prod_int_int Bool)) (Z2 (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.ord_le8369615600986905444_int_o X3))) (=> (@ _let_1 Y3) (=> (@ _let_1 Z2) (@ _let_1 (@ (@ F2 Y3) Z2)))))) (= (@ (@ tptp.inf_in3604695632404883862_int_o X) Y) (@ (@ F2 X) Y)))))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.assn tptp.assn tptp.assn)) (X tptp.assn) (Y tptp.assn)) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (@ (@ tptp.ord_less_eq_assn (@ (@ F2 X3) Y3)) X3)) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (@ (@ tptp.ord_less_eq_assn (@ (@ F2 X3) Y3)) Y3)) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn) (Z2 tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn X3))) (=> (@ _let_1 Y3) (=> (@ _let_1 Z2) (@ _let_1 (@ (@ F2 Y3) Z2)))))) (= (@ (@ tptp.inf_inf_assn X) Y) (@ (@ F2 X) Y)))))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.set_nat tptp.set_nat tptp.set_nat)) (X tptp.set_nat) (Y tptp.set_nat)) (=> (forall ((X3 tptp.set_nat) (Y3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ F2 X3) Y3)) X3)) (=> (forall ((X3 tptp.set_nat) (Y3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ F2 X3) Y3)) Y3)) (=> (forall ((X3 tptp.set_nat) (Y3 tptp.set_nat) (Z2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X3))) (=> (@ _let_1 Y3) (=> (@ _let_1 Z2) (@ _let_1 (@ (@ F2 Y3) Z2)))))) (= (@ (@ tptp.inf_inf_set_nat X) Y) (@ (@ F2 X) Y)))))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.rat tptp.rat tptp.rat)) (X tptp.rat) (Y tptp.rat)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ F2 X3) Y3)) X3)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ F2 X3) Y3)) Y3)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat) (Z2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X3))) (=> (@ _let_1 Y3) (=> (@ _let_1 Z2) (@ _let_1 (@ (@ F2 Y3) Z2)))))) (= (@ (@ tptp.inf_inf_rat X) Y) (@ (@ F2 X) Y)))))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.nat tptp.nat tptp.nat)) (X tptp.nat) (Y tptp.nat)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ F2 X3) Y3)) X3)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ F2 X3) Y3)) Y3)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X3))) (=> (@ _let_1 Y3) (=> (@ _let_1 Z2) (@ _let_1 (@ (@ F2 Y3) Z2)))))) (= (@ (@ tptp.inf_inf_nat X) Y) (@ (@ F2 X) Y)))))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.int tptp.int tptp.int)) (X tptp.int) (Y tptp.int)) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ F2 X3) Y3)) X3)) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ F2 X3) Y3)) Y3)) (=> (forall ((X3 tptp.int) (Y3 tptp.int) (Z2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X3))) (=> (@ _let_1 Y3) (=> (@ _let_1 Z2) (@ _let_1 (@ (@ F2 Y3) Z2)))))) (= (@ (@ tptp.inf_inf_int X) Y) (@ (@ F2 X) Y)))))))
% 2.52/3.49 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (=> (= A (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) (@ (@ tptp.ord_le3146513528884898305at_nat A) B))))
% 2.52/3.49 (assert (forall ((A (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool))) (=> (= A (@ (@ tptp.inf_in3604695632404883862_int_o A) B)) (@ (@ tptp.ord_le8369615600986905444_int_o A) B))))
% 2.52/3.49 (assert (forall ((A tptp.assn) (B tptp.assn)) (=> (= A (@ (@ tptp.inf_inf_assn A) B)) (@ (@ tptp.ord_less_eq_assn A) B))))
% 2.52/3.49 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (= A (@ (@ tptp.inf_inf_set_nat A) B)) (@ (@ tptp.ord_less_eq_set_nat A) B))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= A (@ (@ tptp.inf_inf_rat A) B)) (@ (@ tptp.ord_less_eq_rat A) B))))
% 2.52/3.49 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= A (@ (@ tptp.inf_inf_nat A) B)) (@ (@ tptp.ord_less_eq_nat A) B))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= A (@ (@ tptp.inf_inf_int A) B)) (@ (@ tptp.ord_less_eq_int A) B))))
% 2.52/3.49 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A) B) (= A (@ (@ tptp.inf_in2572325071724192079at_nat A) B)))))
% 2.52/3.49 (assert (forall ((A (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le8369615600986905444_int_o A) B) (= A (@ (@ tptp.inf_in3604695632404883862_int_o A) B)))))
% 2.52/3.49 (assert (forall ((A tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A) B) (= A (@ (@ tptp.inf_inf_assn A) B)))))
% 2.52/3.49 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (= A (@ (@ tptp.inf_inf_set_nat A) B)))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= A (@ (@ tptp.inf_inf_rat A) B)))))
% 2.52/3.49 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= A (@ (@ tptp.inf_inf_nat A) B)))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (= A (@ (@ tptp.inf_inf_int A) B)))))
% 2.52/3.49 (assert (forall ((B tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B) X) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) X))))
% 2.52/3.49 (assert (forall ((B (-> tptp.product_prod_int_int Bool)) (X (-> tptp.product_prod_int_int Bool)) (A (-> tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le8369615600986905444_int_o B) X) (@ (@ tptp.ord_le8369615600986905444_int_o (@ (@ tptp.inf_in3604695632404883862_int_o A) B)) X))))
% 2.52/3.49 (assert (forall ((B tptp.assn) (X tptp.assn) (A tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn B) X) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn A) B)) X))))
% 2.52/3.49 (assert (forall ((B tptp.set_nat) (X tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B) X) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) X))))
% 2.52/3.49 (assert (forall ((B tptp.rat) (X tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) X) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat A) B)) X))))
% 2.52/3.49 (assert (forall ((B tptp.nat) (X tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) X) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) X))))
% 2.52/3.49 (assert (forall ((B tptp.int) (X tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) X) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A) B)) X))))
% 2.52/3.49 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A) X) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) X))))
% 2.52/3.49 (assert (forall ((A (-> tptp.product_prod_int_int Bool)) (X (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le8369615600986905444_int_o A) X) (@ (@ tptp.ord_le8369615600986905444_int_o (@ (@ tptp.inf_in3604695632404883862_int_o A) B)) X))))
% 2.52/3.49 (assert (forall ((A tptp.assn) (X tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A) X) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn A) B)) X))))
% 2.52/3.49 (assert (forall ((A tptp.set_nat) (X tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) X) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) X))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (X tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) X) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat A) B)) X))))
% 2.52/3.49 (assert (forall ((A tptp.nat) (X tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) X) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) X))))
% 2.52/3.49 (assert (forall ((A tptp.int) (X tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) X) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A) B)) X))))
% 2.52/3.49 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (D2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A) C) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B) D2) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) (@ (@ tptp.inf_in2572325071724192079at_nat C) D2))))))
% 2.52/3.49 (assert (forall ((A (-> tptp.product_prod_int_int Bool)) (C (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool)) (D2 (-> tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le8369615600986905444_int_o A) C) (=> (@ (@ tptp.ord_le8369615600986905444_int_o B) D2) (@ (@ tptp.ord_le8369615600986905444_int_o (@ (@ tptp.inf_in3604695632404883862_int_o A) B)) (@ (@ tptp.inf_in3604695632404883862_int_o C) D2))))))
% 2.52/3.49 (assert (forall ((A tptp.assn) (C tptp.assn) (B tptp.assn) (D2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A) C) (=> (@ (@ tptp.ord_less_eq_assn B) D2) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn A) B)) (@ (@ tptp.inf_inf_assn C) D2))))))
% 2.52/3.49 (assert (forall ((A tptp.set_nat) (C tptp.set_nat) (B tptp.set_nat) (D2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) C) (=> (@ (@ tptp.ord_less_eq_set_nat B) D2) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) (@ (@ tptp.inf_inf_set_nat C) D2))))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) C) (=> (@ (@ tptp.ord_less_eq_rat B) D2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat A) B)) (@ (@ tptp.inf_inf_rat C) D2))))))
% 2.52/3.49 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) C) (=> (@ (@ tptp.ord_less_eq_nat B) D2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) (@ (@ tptp.inf_inf_nat C) D2))))))
% 2.52/3.49 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) C) (=> (@ (@ tptp.ord_less_eq_int B) D2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A) B)) (@ (@ tptp.inf_inf_int C) D2))))))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat X))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A) B)))))))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (A (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.ord_le8369615600986905444_int_o X))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.inf_in3604695632404883862_int_o A) B)))))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (A tptp.assn) (B tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn X))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.inf_inf_assn A) B)))))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B)))))))
% 2.52/3.49 (assert (forall ((X tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.inf_inf_rat A) B)))))))
% 2.52/3.49 (assert (forall ((X tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.inf_inf_nat A) B)))))))
% 2.52/3.49 (assert (forall ((X tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.inf_inf_int A) B)))))))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat X))) (=> (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) (not (=> (@ _let_1 A) (not (@ _let_1 B))))))))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (A (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.ord_le8369615600986905444_int_o X))) (=> (@ _let_1 (@ (@ tptp.inf_in3604695632404883862_int_o A) B)) (not (=> (@ _let_1 A) (not (@ _let_1 B))))))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (A tptp.assn) (B tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn X))) (=> (@ _let_1 (@ (@ tptp.inf_inf_assn A) B)) (not (=> (@ _let_1 A) (not (@ _let_1 B))))))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B)) (not (=> (@ _let_1 A) (not (@ _let_1 B))))))))
% 2.52/3.49 (assert (forall ((X tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X))) (=> (@ _let_1 (@ (@ tptp.inf_inf_rat A) B)) (not (=> (@ _let_1 A) (not (@ _let_1 B))))))))
% 2.52/3.49 (assert (forall ((X tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 (@ (@ tptp.inf_inf_nat A) B)) (not (=> (@ _let_1 A) (not (@ _let_1 B))))))))
% 2.52/3.49 (assert (forall ((X tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (=> (@ _let_1 (@ (@ tptp.inf_inf_int A) B)) (not (=> (@ _let_1 A) (not (@ _let_1 B))))))))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)) Y)))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool))) (@ (@ tptp.ord_le8369615600986905444_int_o (@ (@ tptp.inf_in3604695632404883862_int_o X) Y)) Y)))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn)) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn X) Y)) Y)))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X) Y)) Y)))
% 2.52/3.49 (assert (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat X) Y)) Y)))
% 2.52/3.49 (assert (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat X) Y)) Y)))
% 2.52/3.49 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int X) Y)) Y)))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)) X)))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool))) (@ (@ tptp.ord_le8369615600986905444_int_o (@ (@ tptp.inf_in3604695632404883862_int_o X) Y)) X)))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn)) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn X) Y)) X)))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X) Y)) X)))
% 2.52/3.49 (assert (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat X) Y)) X)))
% 2.52/3.49 (assert (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat X) Y)) X)))
% 2.52/3.49 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int X) Y)) X)))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)) X)))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool))) (@ (@ tptp.ord_le8369615600986905444_int_o (@ (@ tptp.inf_in3604695632404883862_int_o X) Y)) X)))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn)) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn X) Y)) X)))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X) Y)) X)))
% 2.52/3.49 (assert (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat X) Y)) X)))
% 2.52/3.49 (assert (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat X) Y)) X)))
% 2.52/3.49 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int X) Y)) X)))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)) Y)))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool))) (@ (@ tptp.ord_le8369615600986905444_int_o (@ (@ tptp.inf_in3604695632404883862_int_o X) Y)) Y)))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn)) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn X) Y)) Y)))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X) Y)) Y)))
% 2.52/3.49 (assert (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat X) Y)) Y)))
% 2.52/3.49 (assert (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat X) Y)) Y)))
% 2.52/3.49 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int X) Y)) Y)))
% 2.52/3.49 (assert (forall ((Y tptp.assn) (X tptp.assn)) (@ (@ tptp.ord_less_eq_assn Y) (@ (@ tptp.sup_sup_assn X) Y))))
% 2.52/3.49 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat Y) (@ (@ tptp.sup_sup_set_nat X) Y))))
% 2.52/3.49 (assert (forall ((Y tptp.rat) (X tptp.rat)) (@ (@ tptp.ord_less_eq_rat Y) (@ (@ tptp.sup_sup_rat X) Y))))
% 2.52/3.49 (assert (forall ((Y tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y) (@ (@ tptp.sup_sup_nat X) Y))))
% 2.52/3.49 (assert (forall ((Y tptp.int) (X tptp.int)) (@ (@ tptp.ord_less_eq_int Y) (@ (@ tptp.sup_sup_int X) Y))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn)) (@ (@ tptp.ord_less_eq_assn X) (@ (@ tptp.sup_sup_assn X) Y))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X) (@ (@ tptp.sup_sup_set_nat X) Y))))
% 2.52/3.49 (assert (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.sup_sup_rat X) Y))))
% 2.52/3.49 (assert (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.sup_sup_nat X) Y))))
% 2.52/3.49 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.sup_sup_int X) Y))))
% 2.52/3.49 (assert (forall ((A tptp.assn) (B tptp.assn) (X tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.sup_sup_assn A) B)) X) (not (=> (@ (@ tptp.ord_less_eq_assn A) X) (not (@ (@ tptp.ord_less_eq_assn B) X)))))))
% 2.52/3.49 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat A) B)) X) (not (=> (@ (@ tptp.ord_less_eq_set_nat A) X) (not (@ (@ tptp.ord_less_eq_set_nat B) X)))))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat A) B)) X) (not (=> (@ (@ tptp.ord_less_eq_rat A) X) (not (@ (@ tptp.ord_less_eq_rat B) X)))))))
% 2.52/3.49 (assert (forall ((A tptp.nat) (B tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat A) B)) X) (not (=> (@ (@ tptp.ord_less_eq_nat A) X) (not (@ (@ tptp.ord_less_eq_nat B) X)))))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int A) B)) X) (not (=> (@ (@ tptp.ord_less_eq_int A) X) (not (@ (@ tptp.ord_less_eq_int B) X)))))))
% 2.52/3.49 (assert (forall ((A tptp.assn) (X tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A) X) (=> (@ (@ tptp.ord_less_eq_assn B) X) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.sup_sup_assn A) B)) X)))))
% 2.52/3.49 (assert (forall ((A tptp.set_nat) (X tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) X) (=> (@ (@ tptp.ord_less_eq_set_nat B) X) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat A) B)) X)))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (X tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) X) (=> (@ (@ tptp.ord_less_eq_rat B) X) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat A) B)) X)))))
% 2.52/3.49 (assert (forall ((A tptp.nat) (X tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) X) (=> (@ (@ tptp.ord_less_eq_nat B) X) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat A) B)) X)))))
% 2.52/3.49 (assert (forall ((A tptp.int) (X tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) X) (=> (@ (@ tptp.ord_less_eq_int B) X) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int A) B)) X)))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn)) (@ (@ tptp.ord_less_eq_assn X) (@ (@ tptp.sup_sup_assn X) Y))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X) (@ (@ tptp.sup_sup_set_nat X) Y))))
% 2.52/3.49 (assert (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.sup_sup_rat X) Y))))
% 2.52/3.49 (assert (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.sup_sup_nat X) Y))))
% 2.52/3.49 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.sup_sup_int X) Y))))
% 2.52/3.49 (assert (forall ((Y tptp.assn) (X tptp.assn)) (@ (@ tptp.ord_less_eq_assn Y) (@ (@ tptp.sup_sup_assn X) Y))))
% 2.52/3.49 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat Y) (@ (@ tptp.sup_sup_set_nat X) Y))))
% 2.52/3.49 (assert (forall ((Y tptp.rat) (X tptp.rat)) (@ (@ tptp.ord_less_eq_rat Y) (@ (@ tptp.sup_sup_rat X) Y))))
% 2.52/3.49 (assert (forall ((Y tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y) (@ (@ tptp.sup_sup_nat X) Y))))
% 2.52/3.49 (assert (forall ((Y tptp.int) (X tptp.int)) (@ (@ tptp.ord_less_eq_int Y) (@ (@ tptp.sup_sup_int X) Y))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (A tptp.assn) (B tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn X))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_assn A) B))))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B))))))
% 2.52/3.49 (assert (forall ((X tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_rat A) B))))))
% 2.52/3.49 (assert (forall ((X tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_nat A) B))))))
% 2.52/3.49 (assert (forall ((X tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_int A) B))))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (B tptp.assn) (A tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn X))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_assn A) B))))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (B tptp.set_nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B))))))
% 2.52/3.49 (assert (forall ((X tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_rat A) B))))))
% 2.52/3.49 (assert (forall ((X tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_nat A) B))))))
% 2.52/3.49 (assert (forall ((X tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_int A) B))))))
% 2.52/3.49 (assert (forall ((C tptp.assn) (A tptp.assn) (D2 tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn C) A) (=> (@ (@ tptp.ord_less_eq_assn D2) B) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.sup_sup_assn C) D2)) (@ (@ tptp.sup_sup_assn A) B))))))
% 2.52/3.49 (assert (forall ((C tptp.set_nat) (A tptp.set_nat) (D2 tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat C) A) (=> (@ (@ tptp.ord_less_eq_set_nat D2) B) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat C) D2)) (@ (@ tptp.sup_sup_set_nat A) B))))))
% 2.52/3.49 (assert (forall ((C tptp.rat) (A tptp.rat) (D2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) A) (=> (@ (@ tptp.ord_less_eq_rat D2) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat C) D2)) (@ (@ tptp.sup_sup_rat A) B))))))
% 2.52/3.49 (assert (forall ((C tptp.nat) (A tptp.nat) (D2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) A) (=> (@ (@ tptp.ord_less_eq_nat D2) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat C) D2)) (@ (@ tptp.sup_sup_nat A) B))))))
% 2.52/3.49 (assert (forall ((C tptp.int) (A tptp.int) (D2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) A) (=> (@ (@ tptp.ord_less_eq_int D2) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int C) D2)) (@ (@ tptp.sup_sup_int A) B))))))
% 2.52/3.49 (assert (forall ((A tptp.assn) (C tptp.assn) (B tptp.assn) (D2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A) C) (=> (@ (@ tptp.ord_less_eq_assn B) D2) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.sup_sup_assn A) B)) (@ (@ tptp.sup_sup_assn C) D2))))))
% 2.52/3.49 (assert (forall ((A tptp.set_nat) (C tptp.set_nat) (B tptp.set_nat) (D2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) C) (=> (@ (@ tptp.ord_less_eq_set_nat B) D2) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat A) B)) (@ (@ tptp.sup_sup_set_nat C) D2))))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) C) (=> (@ (@ tptp.ord_less_eq_rat B) D2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat A) B)) (@ (@ tptp.sup_sup_rat C) D2))))))
% 2.52/3.49 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) C) (=> (@ (@ tptp.ord_less_eq_nat B) D2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat A) B)) (@ (@ tptp.sup_sup_nat C) D2))))))
% 2.52/3.49 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) C) (=> (@ (@ tptp.ord_less_eq_int B) D2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int A) B)) (@ (@ tptp.sup_sup_int C) D2))))))
% 2.52/3.49 (assert (forall ((Y tptp.assn) (X tptp.assn) (Z tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn Y) X) (=> (@ (@ tptp.ord_less_eq_assn Z) X) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.sup_sup_assn Y) Z)) X)))))
% 2.52/3.49 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat) (Z tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (=> (@ (@ tptp.ord_less_eq_set_nat Z) X) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat Y) Z)) X)))))
% 2.52/3.49 (assert (forall ((Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (=> (@ (@ tptp.ord_less_eq_rat Z) X) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat Y) Z)) X)))))
% 2.52/3.49 (assert (forall ((Y tptp.nat) (X tptp.nat) (Z tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (=> (@ (@ tptp.ord_less_eq_nat Z) X) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat Y) Z)) X)))))
% 2.52/3.49 (assert (forall ((Y tptp.int) (X tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (=> (@ (@ tptp.ord_less_eq_int Z) X) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int Y) Z)) X)))))
% 2.52/3.49 (assert (= tptp.ord_less_eq_assn (lambda ((X2 tptp.assn) (Y2 tptp.assn)) (= (@ (@ tptp.sup_sup_assn X2) Y2) Y2))))
% 2.52/3.49 (assert (= tptp.ord_less_eq_set_nat (lambda ((X2 tptp.set_nat) (Y2 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat X2) Y2) Y2))))
% 2.52/3.49 (assert (= tptp.ord_less_eq_rat (lambda ((X2 tptp.rat) (Y2 tptp.rat)) (= (@ (@ tptp.sup_sup_rat X2) Y2) Y2))))
% 2.52/3.49 (assert (= tptp.ord_less_eq_nat (lambda ((X2 tptp.nat) (Y2 tptp.nat)) (= (@ (@ tptp.sup_sup_nat X2) Y2) Y2))))
% 2.52/3.49 (assert (= tptp.ord_less_eq_int (lambda ((X2 tptp.int) (Y2 tptp.int)) (= (@ (@ tptp.sup_sup_int X2) Y2) Y2))))
% 2.52/3.49 (assert (forall ((B tptp.assn) (A tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn B) A) (= A (@ (@ tptp.sup_sup_assn A) B)))))
% 2.52/3.49 (assert (forall ((B tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (= A (@ (@ tptp.sup_sup_set_nat A) B)))))
% 2.52/3.49 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= A (@ (@ tptp.sup_sup_rat A) B)))))
% 2.52/3.49 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A (@ (@ tptp.sup_sup_nat A) B)))))
% 2.52/3.49 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A (@ (@ tptp.sup_sup_int A) B)))))
% 2.52/3.49 (assert (forall ((A tptp.assn) (B tptp.assn)) (=> (= A (@ (@ tptp.sup_sup_assn A) B)) (@ (@ tptp.ord_less_eq_assn B) A))))
% 2.52/3.49 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (= A (@ (@ tptp.sup_sup_set_nat A) B)) (@ (@ tptp.ord_less_eq_set_nat B) A))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= A (@ (@ tptp.sup_sup_rat A) B)) (@ (@ tptp.ord_less_eq_rat B) A))))
% 2.52/3.49 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= A (@ (@ tptp.sup_sup_nat A) B)) (@ (@ tptp.ord_less_eq_nat B) A))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= A (@ (@ tptp.sup_sup_int A) B)) (@ (@ tptp.ord_less_eq_int B) A))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.assn tptp.assn tptp.assn)) (X tptp.assn) (Y tptp.assn)) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (@ (@ tptp.ord_less_eq_assn X3) (@ (@ F2 X3) Y3))) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (@ (@ tptp.ord_less_eq_assn Y3) (@ (@ F2 X3) Y3))) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn) (Z2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn Y3) X3) (=> (@ (@ tptp.ord_less_eq_assn Z2) X3) (@ (@ tptp.ord_less_eq_assn (@ (@ F2 Y3) Z2)) X3)))) (= (@ (@ tptp.sup_sup_assn X) Y) (@ (@ F2 X) Y)))))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.set_nat tptp.set_nat tptp.set_nat)) (X tptp.set_nat) (Y tptp.set_nat)) (=> (forall ((X3 tptp.set_nat) (Y3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X3) (@ (@ F2 X3) Y3))) (=> (forall ((X3 tptp.set_nat) (Y3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat Y3) (@ (@ F2 X3) Y3))) (=> (forall ((X3 tptp.set_nat) (Y3 tptp.set_nat) (Z2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y3) X3) (=> (@ (@ tptp.ord_less_eq_set_nat Z2) X3) (@ (@ tptp.ord_less_eq_set_nat (@ (@ F2 Y3) Z2)) X3)))) (= (@ (@ tptp.sup_sup_set_nat X) Y) (@ (@ F2 X) Y)))))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.rat tptp.rat tptp.rat)) (X tptp.rat) (Y tptp.rat)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat X3) (@ (@ F2 X3) Y3))) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat Y3) (@ (@ F2 X3) Y3))) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat) (Z2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y3) X3) (=> (@ (@ tptp.ord_less_eq_rat Z2) X3) (@ (@ tptp.ord_less_eq_rat (@ (@ F2 Y3) Z2)) X3)))) (= (@ (@ tptp.sup_sup_rat X) Y) (@ (@ F2 X) Y)))))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.nat tptp.nat tptp.nat)) (X tptp.nat) (Y tptp.nat)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X3) (@ (@ F2 X3) Y3))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y3) (@ (@ F2 X3) Y3))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat) (Z2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y3) X3) (=> (@ (@ tptp.ord_less_eq_nat Z2) X3) (@ (@ tptp.ord_less_eq_nat (@ (@ F2 Y3) Z2)) X3)))) (= (@ (@ tptp.sup_sup_nat X) Y) (@ (@ F2 X) Y)))))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.int tptp.int tptp.int)) (X tptp.int) (Y tptp.int)) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (@ (@ tptp.ord_less_eq_int X3) (@ (@ F2 X3) Y3))) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (@ (@ tptp.ord_less_eq_int Y3) (@ (@ F2 X3) Y3))) (=> (forall ((X3 tptp.int) (Y3 tptp.int) (Z2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y3) X3) (=> (@ (@ tptp.ord_less_eq_int Z2) X3) (@ (@ tptp.ord_less_eq_int (@ (@ F2 Y3) Z2)) X3)))) (= (@ (@ tptp.sup_sup_int X) Y) (@ (@ F2 X) Y)))))))
% 2.52/3.49 (assert (forall ((B tptp.assn) (A tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn B) A) (= (@ (@ tptp.sup_sup_assn A) B) A))))
% 2.52/3.49 (assert (forall ((B tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (= (@ (@ tptp.sup_sup_set_nat A) B) A))))
% 2.52/3.49 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.sup_sup_rat A) B) A))))
% 2.52/3.49 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.sup_sup_nat A) B) A))))
% 2.52/3.49 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.sup_sup_int A) B) A))))
% 2.52/3.49 (assert (forall ((A tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A) B) (= (@ (@ tptp.sup_sup_assn A) B) B))))
% 2.52/3.49 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (= (@ (@ tptp.sup_sup_set_nat A) B) B))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= (@ (@ tptp.sup_sup_rat A) B) B))))
% 2.52/3.49 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.sup_sup_nat A) B) B))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (= (@ (@ tptp.sup_sup_int A) B) B))))
% 2.52/3.49 (assert (forall ((Y tptp.assn) (X tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn Y) X) (= (@ (@ tptp.sup_sup_assn X) Y) X))))
% 2.52/3.49 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (= (@ (@ tptp.sup_sup_set_nat X) Y) X))))
% 2.52/3.49 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (= (@ (@ tptp.sup_sup_rat X) Y) X))))
% 2.52/3.49 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.sup_sup_nat X) Y) X))))
% 2.52/3.49 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= (@ (@ tptp.sup_sup_int X) Y) X))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X) Y) (= (@ (@ tptp.sup_sup_assn X) Y) Y))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (= (@ (@ tptp.sup_sup_set_nat X) Y) Y))))
% 2.52/3.49 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (= (@ (@ tptp.sup_sup_rat X) Y) Y))))
% 2.52/3.49 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (@ (@ tptp.sup_sup_nat X) Y) Y))))
% 2.52/3.49 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (@ (@ tptp.sup_sup_int X) Y) Y))))
% 2.52/3.49 (assert (forall ((B tptp.assn) (C tptp.assn) (A tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.sup_sup_assn B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_assn B) A) (not (@ (@ tptp.ord_less_eq_assn C) A)))))))
% 2.52/3.49 (assert (forall ((B tptp.set_nat) (C tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (not (@ (@ tptp.ord_less_eq_set_nat C) A)))))))
% 2.52/3.49 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_rat B) A) (not (@ (@ tptp.ord_less_eq_rat C) A)))))))
% 2.52/3.49 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_nat B) A) (not (@ (@ tptp.ord_less_eq_nat C) A)))))))
% 2.52/3.49 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_int B) A) (not (@ (@ tptp.ord_less_eq_int C) A)))))))
% 2.52/3.49 (assert (forall ((B tptp.assn) (A tptp.assn) (C tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn B) A) (=> (@ (@ tptp.ord_less_eq_assn C) A) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.sup_sup_assn B) C)) A)))))
% 2.52/3.49 (assert (forall ((B tptp.set_nat) (A tptp.set_nat) (C tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (=> (@ (@ tptp.ord_less_eq_set_nat C) A) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat B) C)) A)))))
% 2.52/3.49 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat B) C)) A)))))
% 2.52/3.49 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat B) C)) A)))))
% 2.52/3.49 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int C) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int B) C)) A)))))
% 2.52/3.49 (assert (= tptp.ord_less_eq_assn (lambda ((B2 tptp.assn) (A2 tptp.assn)) (= A2 (@ (@ tptp.sup_sup_assn A2) B2)))))
% 2.52/3.49 (assert (= tptp.ord_less_eq_set_nat (lambda ((B2 tptp.set_nat) (A2 tptp.set_nat)) (= A2 (@ (@ tptp.sup_sup_set_nat A2) B2)))))
% 2.52/3.49 (assert (= tptp.ord_less_eq_rat (lambda ((B2 tptp.rat) (A2 tptp.rat)) (= A2 (@ (@ tptp.sup_sup_rat A2) B2)))))
% 2.52/3.49 (assert (= tptp.ord_less_eq_nat (lambda ((B2 tptp.nat) (A2 tptp.nat)) (= A2 (@ (@ tptp.sup_sup_nat A2) B2)))))
% 2.52/3.49 (assert (= tptp.ord_less_eq_int (lambda ((B2 tptp.int) (A2 tptp.int)) (= A2 (@ (@ tptp.sup_sup_int A2) B2)))))
% 2.52/3.49 (assert (forall ((A tptp.assn) (B tptp.assn)) (@ (@ tptp.ord_less_eq_assn A) (@ (@ tptp.sup_sup_assn A) B))))
% 2.52/3.49 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A) (@ (@ tptp.sup_sup_set_nat A) B))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.sup_sup_rat A) B))))
% 2.52/3.49 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.sup_sup_nat A) B))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.sup_sup_int A) B))))
% 2.52/3.49 (assert (forall ((B tptp.assn) (A tptp.assn)) (@ (@ tptp.ord_less_eq_assn B) (@ (@ tptp.sup_sup_assn A) B))))
% 2.52/3.49 (assert (forall ((B tptp.set_nat) (A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat B) (@ (@ tptp.sup_sup_set_nat A) B))))
% 2.52/3.49 (assert (forall ((B tptp.rat) (A tptp.rat)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.sup_sup_rat A) B))))
% 2.52/3.49 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_nat B) (@ (@ tptp.sup_sup_nat A) B))))
% 2.52/3.49 (assert (forall ((B tptp.int) (A tptp.int)) (@ (@ tptp.ord_less_eq_int B) (@ (@ tptp.sup_sup_int A) B))))
% 2.52/3.49 (assert (= tptp.ord_less_eq_assn (lambda ((B2 tptp.assn) (A2 tptp.assn)) (= (@ (@ tptp.sup_sup_assn A2) B2) A2))))
% 2.52/3.49 (assert (= tptp.ord_less_eq_set_nat (lambda ((B2 tptp.set_nat) (A2 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A2) B2) A2))))
% 2.52/3.49 (assert (= tptp.ord_less_eq_rat (lambda ((B2 tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.sup_sup_rat A2) B2) A2))))
% 2.52/3.49 (assert (= tptp.ord_less_eq_nat (lambda ((B2 tptp.nat) (A2 tptp.nat)) (= (@ (@ tptp.sup_sup_nat A2) B2) A2))))
% 2.52/3.49 (assert (= tptp.ord_less_eq_int (lambda ((B2 tptp.int) (A2 tptp.int)) (= (@ (@ tptp.sup_sup_int A2) B2) A2))))
% 2.52/3.49 (assert (= tptp.ord_less_eq_assn (lambda ((A2 tptp.assn) (B2 tptp.assn)) (= (@ (@ tptp.sup_sup_assn A2) B2) B2))))
% 2.52/3.49 (assert (= tptp.ord_less_eq_set_nat (lambda ((A2 tptp.set_nat) (B2 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A2) B2) B2))))
% 2.52/3.49 (assert (= tptp.ord_less_eq_rat (lambda ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.sup_sup_rat A2) B2) B2))))
% 2.52/3.49 (assert (= tptp.ord_less_eq_nat (lambda ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.sup_sup_nat A2) B2) B2))))
% 2.52/3.49 (assert (= tptp.ord_less_eq_int (lambda ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.sup_sup_int A2) B2) B2))))
% 2.52/3.49 (assert (forall ((C tptp.assn) (A tptp.assn) (B tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_assn A) B))))))
% 2.52/3.49 (assert (forall ((C tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B))))))
% 2.52/3.49 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_rat A) B))))))
% 2.52/3.49 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_nat A) B))))))
% 2.52/3.49 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_int A) B))))))
% 2.52/3.49 (assert (forall ((C tptp.assn) (B tptp.assn) (A tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_assn A) B))))))
% 2.52/3.49 (assert (forall ((C tptp.set_nat) (B tptp.set_nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B))))))
% 2.52/3.49 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_rat A) B))))))
% 2.52/3.49 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_nat A) B))))))
% 2.52/3.49 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_int A) B))))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (P2 (-> tptp.int Bool)) (Q2 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_set_int A3) B3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int2 X3) A3) (=> (@ P2 X3) (@ Q2 X3)))) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int A3) (@ tptp.collect_int P2))) (@ (@ tptp.inf_inf_set_int B3) (@ tptp.collect_int Q2)))))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_Pr4532377907799695533_nat_o) (B3 tptp.set_Pr4532377907799695533_nat_o) (P2 (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool)) (Q2 (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o A3) B3) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o X3) A3) (=> (@ P2 X3) (@ Q2 X3)))) (@ (@ tptp.ord_le2965882846123202637_nat_o (@ (@ tptp.inf_in1906310914598751387_nat_o A3) (@ tptp.collec939566748876313656_nat_o P2))) (@ (@ tptp.inf_in1906310914598751387_nat_o B3) (@ tptp.collec939566748876313656_nat_o Q2)))))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_list_nat) (B3 tptp.set_list_nat) (P2 (-> tptp.list_nat Bool)) (Q2 (-> tptp.list_nat Bool))) (=> (@ (@ tptp.ord_le6045566169113846134st_nat A3) B3) (=> (forall ((X3 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X3) A3) (=> (@ P2 X3) (@ Q2 X3)))) (@ (@ tptp.ord_le6045566169113846134st_nat (@ (@ tptp.inf_inf_set_list_nat A3) (@ tptp.collect_list_nat P2))) (@ (@ tptp.inf_inf_set_list_nat B3) (@ tptp.collect_list_nat Q2)))))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (P2 (-> tptp.product_prod_nat_nat Bool)) (Q2 (-> tptp.product_prod_nat_nat Bool))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A3) B3) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) A3) (=> (@ P2 X3) (@ Q2 X3)))) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A3) (@ tptp.collec3392354462482085612at_nat P2))) (@ (@ tptp.inf_in2572325071724192079at_nat B3) (@ tptp.collec3392354462482085612at_nat Q2)))))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (P2 (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat2 X3) A3) (=> (@ P2 X3) (@ Q2 X3)))) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A3) (@ tptp.collect_nat P2))) (@ (@ tptp.inf_inf_set_nat B3) (@ tptp.collect_nat Q2)))))))
% 2.52/3.49 (assert (forall ((C2 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat C2))) (=> (@ _let_1 A3) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)))))))
% 2.52/3.49 (assert (forall ((C2 tptp.set_nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C2))) (=> (@ _let_1 A3) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3)))))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A3) B3) (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3) A3))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B3) (= (@ (@ tptp.inf_inf_set_nat A3) B3) A3))))
% 2.52/3.49 (assert (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B3) A3) (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3) B3))))
% 2.52/3.49 (assert (forall ((B3 tptp.set_nat) (A3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B3) A3) (= (@ (@ tptp.inf_inf_set_nat A3) B3) B3))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)) B3)))
% 2.52/3.49 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A3) B3)) B3)))
% 2.52/3.49 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)) A3)))
% 2.52/3.49 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A3) B3)) A3)))
% 2.52/3.49 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (D tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A3) C2) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B3) D) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)) (@ (@ tptp.inf_in2572325071724192079at_nat C2) D))))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_nat) (C2 tptp.set_nat) (B3 tptp.set_nat) (D tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A3) C2) (=> (@ (@ tptp.ord_less_eq_set_nat B3) D) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A3) B3)) (@ (@ tptp.inf_inf_set_nat C2) D))))))
% 2.52/3.49 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (S2 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat B3))) (let ((_let_2 (@ tptp.inf_in2572325071724192079at_nat A3))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat S) S2) (=> (= (@ _let_2 S2) (@ _let_1 S2)) (= (@ _let_2 S) (@ _let_1 S))))))))
% 2.52/3.49 (assert (forall ((S tptp.set_nat) (S2 tptp.set_nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat B3))) (let ((_let_2 (@ tptp.inf_inf_set_nat A3))) (=> (@ (@ tptp.ord_less_eq_set_nat S) S2) (=> (= (@ _let_2 S2) (@ _let_1 S2)) (= (@ _let_2 S) (@ _let_1 S))))))))
% 2.52/3.49 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ (@ tptp.times_times_rat A) C) (@ (@ tptp.times_times_rat B) C)) (= A B)))))
% 2.52/3.49 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (= (= (@ (@ tptp.times_times_nat A) C) (@ (@ tptp.times_times_nat B) C)) (= A B)))))
% 2.52/3.49 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (=> (not (= C tptp.zero_zero_int)) (= (= (@ (@ tptp.times_times_int A) C) (@ (@ tptp.times_times_int B) C)) (= A B)))))
% 2.52/3.49 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (= (= (@ (@ tptp.times_3573771949741848930nteger A) C) (@ (@ tptp.times_3573771949741848930nteger B) C)) (= A B)))))
% 2.52/3.49 (assert (forall ((C tptp.code_natural) (A tptp.code_natural) (B tptp.code_natural)) (=> (not (= C tptp.zero_z2226904508553997617atural)) (= (= (@ (@ tptp.times_2397367101498566445atural A) C) (@ (@ tptp.times_2397367101498566445atural B) C)) (= A B)))))
% 2.52/3.49 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 2.52/3.49 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (not (= C tptp.zero_zero_nat)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 2.52/3.49 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 2.52/3.49 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 2.52/3.49 (assert (forall ((C tptp.code_natural) (A tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural C))) (=> (not (= C tptp.zero_z2226904508553997617atural)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (not (= (@ (@ tptp.times_times_rat A) B) tptp.zero_zero_rat))))))
% 2.52/3.49 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (not (= B tptp.zero_zero_nat)) (not (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat))))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (not (= B tptp.zero_zero_int)) (not (= (@ (@ tptp.times_times_int A) B) tptp.zero_zero_int))))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (not (= (@ (@ tptp.times_3573771949741848930nteger A) B) tptp.zero_z3403309356797280102nteger))))))
% 2.52/3.49 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (not (= A tptp.zero_z2226904508553997617atural)) (=> (not (= B tptp.zero_z2226904508553997617atural)) (not (= (@ (@ tptp.times_2397367101498566445atural A) B) tptp.zero_z2226904508553997617atural))))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ (@ tptp.times_times_rat A) B) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))))
% 2.52/3.49 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat) (or (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.times_times_int A) B) tptp.zero_zero_int) (or (= A tptp.zero_zero_int) (= B tptp.zero_zero_int)))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.times_3573771949741848930nteger A) B) tptp.zero_z3403309356797280102nteger) (or (= A tptp.zero_z3403309356797280102nteger) (= B tptp.zero_z3403309356797280102nteger)))))
% 2.52/3.49 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (= (@ (@ tptp.times_2397367101498566445atural A) B) tptp.zero_z2226904508553997617atural) (or (= A tptp.zero_z2226904508553997617atural) (= B tptp.zero_z2226904508553997617atural)))))
% 2.52/3.49 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= (@ (@ tptp.times_times_rat A) B) tptp.zero_zero_rat)) (and (not (= A tptp.zero_zero_rat)) (not (= B tptp.zero_zero_rat))))))
% 2.52/3.49 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat)) (and (not (= A tptp.zero_zero_nat)) (not (= B tptp.zero_zero_nat))))))
% 2.52/3.49 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= (@ (@ tptp.times_times_int A) B) tptp.zero_zero_int)) (and (not (= A tptp.zero_zero_int)) (not (= B tptp.zero_zero_int))))))
% 2.52/3.49 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (not (= (@ (@ tptp.times_3573771949741848930nteger A) B) tptp.zero_z3403309356797280102nteger)) (and (not (= A tptp.zero_z3403309356797280102nteger)) (not (= B tptp.zero_z3403309356797280102nteger))))))
% 2.52/3.49 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (not (= (@ (@ tptp.times_2397367101498566445atural A) B) tptp.zero_z2226904508553997617atural)) (and (not (= A tptp.zero_z2226904508553997617atural)) (not (= B tptp.zero_z2226904508553997617atural))))))
% 2.52/3.49 (assert (not (= tptp.zero_zero_nat tptp.one_one_nat)))
% 2.52/3.49 (assert (not (= tptp.zero_zero_int tptp.one_one_int)))
% 2.52/3.49 (assert (not (= tptp.zero_zero_rat tptp.one_one_rat)))
% 2.52/3.49 (assert (not (= tptp.zero_z3403309356797280102nteger tptp.one_one_Code_integer)))
% 2.52/3.49 (assert (not (= tptp.zero_z2226904508553997617atural tptp.one_one_Code_natural)))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (Xs tptp.list_nat)) (let ((_let_1 (@ tptp.map_nat_nat F2))) (= (@ tptp.rotate1_nat (@ _let_1 Xs)) (@ _let_1 (@ tptp.rotate1_nat Xs))))))
% 2.52/3.49 (assert (forall ((F2 (-> tptp.produc6575502325842934193n_assn tptp.assn)) (Xs tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ tptp.map_Pr8991440229025900053n_assn F2))) (= (@ tptp.rotate1_assn (@ _let_1 Xs)) (@ _let_1 (@ tptp.rotate328796349445179396n_assn Xs))))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (=> (= (@ tptp.linord2614967742042102400et_nat A3) (@ tptp.linord2614967742042102400et_nat B3)) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_nat B3) (= A3 B3))))))
% 2.52/3.49 (assert (= tptp.ord_less_eq_assn (lambda ((A2 tptp.assn) (B2 tptp.assn)) (= A2 (@ (@ tptp.inf_inf_assn A2) B2)))))
% 2.52/3.49 (assert (forall ((Bs tptp.set_nat) (H2 tptp.heap_e7401611519738050253t_unit) (H5 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (=> (@ (@ (@ tptp.relH Bs) H2) H5) (=> (@ (@ tptp.ord_less_eq_set_nat As2) Bs) (@ (@ (@ tptp.relH As2) H2) H5)))))
% 2.52/3.49 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 2.52/3.49 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 2.52/3.49 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 2.52/3.49 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 2.52/3.49 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 2.52/3.49 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 Y)) (@ _let_1 Z))) (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat Y) Z))))))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool)) (Z (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.inf_in3604695632404883862_int_o X))) (@ (@ tptp.ord_le8369615600986905444_int_o (@ (@ tptp.sup_su8463660629351352368_int_o (@ _let_1 Y)) (@ _let_1 Z))) (@ _let_1 (@ (@ tptp.sup_su8463660629351352368_int_o Y) Z))))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.sup_sup_assn (@ _let_1 Y)) (@ _let_1 Z))) (@ _let_1 (@ (@ tptp.sup_sup_assn Y) Z))))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat (@ _let_1 Y)) (@ _let_1 Z))) (@ _let_1 (@ (@ tptp.sup_sup_set_nat Y) Z))))))
% 2.52/3.49 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.inf_inf_rat X))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat (@ _let_1 Y)) (@ _let_1 Z))) (@ _let_1 (@ (@ tptp.sup_sup_rat Y) Z))))))
% 2.52/3.49 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat (@ _let_1 Y)) (@ _let_1 Z))) (@ _let_1 (@ (@ tptp.sup_sup_nat Y) Z))))))
% 2.52/3.49 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.inf_inf_int X))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int (@ _let_1 Y)) (@ _let_1 Z))) (@ _let_1 (@ (@ tptp.sup_sup_int Y) Z))))))
% 2.52/3.49 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.sup_su6327502436637775413at_nat X))) (@ (@ tptp.ord_le3146513528884898305at_nat (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z))) (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 2.52/3.49 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool)) (Z (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.sup_su8463660629351352368_int_o X))) (@ (@ tptp.ord_le8369615600986905444_int_o (@ _let_1 (@ (@ tptp.inf_in3604695632404883862_int_o Y) Z))) (@ (@ tptp.inf_in3604695632404883862_int_o (@ _let_1 Y)) (@ _let_1 Z))))))
% 2.52/3.49 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (@ (@ tptp.ord_less_eq_assn (@ _let_1 (@ (@ tptp.inf_inf_assn Y) Z))) (@ (@ tptp.inf_inf_assn (@ _let_1 Y)) (@ _let_1 Z))))))
% 2.52/3.49 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y) Z))) (@ (@ tptp.inf_inf_set_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 2.52/3.49 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.sup_sup_rat X))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 (@ (@ tptp.inf_inf_rat Y) Z))) (@ (@ tptp.inf_inf_rat (@ _let_1 Y)) (@ _let_1 Z))))))
% 2.52/3.49 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z))) (@ (@ tptp.inf_inf_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 2.52/3.49 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.sup_sup_int X))) (@ (@ tptp.ord_less_eq_int (@ _let_1 (@ (@ tptp.inf_inf_int Y) Z))) (@ (@ tptp.inf_inf_int (@ _let_1 Y)) (@ _let_1 Z))))))
% 2.52/3.49 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (A5 tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A) A5) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B) B6) (=> (= (@ (@ tptp.inf_in2572325071724192079at_nat A5) B6) tptp.bot_bo2099793752762293965at_nat) (= (@ (@ tptp.inf_in2572325071724192079at_nat A) B) tptp.bot_bo2099793752762293965at_nat))))))
% 2.52/3.49 (assert (forall ((A tptp.set_int) (A5 tptp.set_int) (B tptp.set_int) (B6 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) A5) (=> (@ (@ tptp.ord_less_eq_set_int B) B6) (=> (= (@ (@ tptp.inf_inf_set_int A5) B6) tptp.bot_bot_set_int) (= (@ (@ tptp.inf_inf_set_int A) B) tptp.bot_bot_set_int))))))
% 2.52/3.49 (assert (forall ((A tptp.set_nat) (A5 tptp.set_nat) (B tptp.set_nat) (B6 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) A5) (=> (@ (@ tptp.ord_less_eq_set_nat B) B6) (=> (= (@ (@ tptp.inf_inf_set_nat A5) B6) tptp.bot_bot_set_nat) (= (@ (@ tptp.inf_inf_set_nat A) B) tptp.bot_bot_set_nat))))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A3))) (= (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 B3)) C2) (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat B3) C2))) (@ (@ tptp.ord_le3146513528884898305at_nat C2) A3)))))
% 2.52/3.49 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A3))) (= (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 B3)) C2) (@ _let_1 (@ (@ tptp.sup_sup_set_nat B3) C2))) (@ (@ tptp.ord_less_eq_set_nat C2) A3)))))
% 2.52/3.49 (assert (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 2.52/3.50 (assert (not (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 2.52/3.50 (assert (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 2.52/3.50 (assert (forall ((As2 tptp.set_nat) (As3 tptp.set_nat) (H2 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H2))) (=> (@ (@ tptp.ord_less_eq_set_nat As2) As3) (=> (@ tptp.in_range (@ _let_1 As3)) (@ tptp.in_range (@ _let_1 As2)))))))
% 2.52/3.50 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.inf_in2572325071724192079at_nat X) Y) tptp.bot_bo2099793752762293965at_nat) (@ (@ tptp.ord_le3146513528884898305at_nat X) (@ tptp.uminus6524753893492686040at_nat Y)))))
% 2.52/3.50 (assert (forall ((X (-> tptp.product_prod_int_int Bool)) (Y (-> tptp.product_prod_int_int Bool))) (= (= (@ (@ tptp.inf_in3604695632404883862_int_o X) Y) tptp.bot_bo8147686125503663512_int_o) (@ (@ tptp.ord_le8369615600986905444_int_o X) (@ tptp.uminus7117520113953359693_int_o Y)))))
% 2.52/3.50 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (= (@ (@ tptp.inf_inf_set_int X) Y) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int X) (@ tptp.uminus1532241313380277803et_int Y)))))
% 2.52/3.50 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (= (@ (@ tptp.inf_inf_assn X) Y) tptp.bot_bot_assn) (@ (@ tptp.ord_less_eq_assn X) (@ tptp.uminus_uminus_assn Y)))))
% 2.52/3.50 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat X) Y) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat X) (@ tptp.uminus5710092332889474511et_nat Y)))))
% 2.52/3.50 (assert (forall ((F4 tptp.set_Pr1261947904930325089at_nat) (G2 tptp.set_Pr1261947904930325089at_nat)) (=> (or (@ tptp.finite6177210948735845034at_nat F4) (@ tptp.finite6177210948735845034at_nat G2)) (@ tptp.finite6177210948735845034at_nat (@ (@ tptp.inf_in2572325071724192079at_nat F4) G2)))))
% 2.52/3.50 (assert (forall ((F4 tptp.set_nat) (G2 tptp.set_nat)) (=> (or (@ tptp.finite_finite_nat F4) (@ tptp.finite_finite_nat G2)) (@ tptp.finite_finite_nat (@ (@ tptp.inf_inf_set_nat F4) G2)))))
% 2.52/3.50 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat)) (=> (not (@ (@ (@ tptp.wand_raw X) Xa) Xb)) (=> (@ (@ tptp.accp_P1862375125659990705et_nat tptp.wand_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) Xb))) (not (forall ((H3 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H3) As))) (=> (= Xb _let_1) (=> (@ (@ tptp.accp_P1862375125659990705et_nat tptp.wand_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) _let_1))) (and (@ tptp.in_range _let_1) (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H4))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As) As4) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As) H3) H4) (@ tptp.in_range (@ _let_1 As)) (@ X (@ _let_1 As4))) (@ Xa (@ _let_1 (@ (@ tptp.sup_sup_set_nat As) As4))))))))))))))))
% 2.52/3.50 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat)) (=> (@ (@ (@ tptp.wand_raw X) Xa) Xb) (=> (@ (@ tptp.accp_P1862375125659990705et_nat tptp.wand_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) Xb))) (not (forall ((H3 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H3) As))) (=> (= Xb _let_1) (=> (@ (@ tptp.accp_P1862375125659990705et_nat tptp.wand_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) _let_1))) (not (and (@ tptp.in_range _let_1) (forall ((H6 tptp.heap_e7401611519738050253t_unit) (As5 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H6))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As) As5) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As) H3) H6) (@ tptp.in_range (@ _let_1 As)) (@ X (@ _let_1 As5))) (@ Xa (@ _let_1 (@ (@ tptp.sup_sup_set_nat As) As5)))))))))))))))))
% 2.52/3.50 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ (@ (@ tptp.wand_raw X) Xa) Xb) Y) (=> (@ (@ tptp.accp_P1862375125659990705et_nat tptp.wand_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) Xb))) (not (forall ((H3 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H3) As))) (=> (= Xb _let_1) (=> (= Y (and (@ tptp.in_range _let_1) (forall ((H7 tptp.heap_e7401611519738050253t_unit) (As6 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H7))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As) As6) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As) H3) H7) (@ tptp.in_range (@ _let_1 As)) (@ X (@ _let_1 As6))) (@ Xa (@ _let_1 (@ (@ tptp.sup_sup_set_nat As) As6)))))))) (not (@ (@ tptp.accp_P1862375125659990705et_nat tptp.wand_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) _let_1)))))))))))))
% 2.52/3.50 (assert (forall ((P2 tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn P2) tptp.top_top_assn)) H2) (not (forall ((H4 tptp.produc3658429121746597890et_nat)) (=> (= (@ tptp.produc1824681642469235216et_nat H4) (@ tptp.produc1824681642469235216et_nat H2)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.produc8586169260539613262et_nat H4)) (@ tptp.produc8586169260539613262et_nat H2)) (not (@ (@ tptp.rep_assn P2) H4)))))))))
% 2.52/3.50 (assert (= tptp.map_nat_nat tptp.map_tailrec_nat_nat))
% 2.52/3.50 (assert (= tptp.map_Pr8991440229025900053n_assn tptp.map_ta2194206859901583947n_assn))
% 2.52/3.50 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ (@ (@ tptp.times_assn_raw X) Xa) Xb) Y) (=> (@ (@ tptp.accp_P1862375125659990705et_nat tptp.times_assn_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) Xb))) (not (forall ((H3 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H3) As))) (=> (= Xb _let_1) (=> (= Y (exists ((As1 tptp.set_nat) (As22 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H3))) (and (= As (@ (@ tptp.sup_sup_set_nat As1) As22)) (= (@ (@ tptp.inf_inf_set_nat As1) As22) tptp.bot_bot_set_nat) (@ X (@ _let_1 As1)) (@ Xa (@ _let_1 As22)))))) (not (@ (@ tptp.accp_P1862375125659990705et_nat tptp.times_assn_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) _let_1)))))))))))))
% 2.52/3.50 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat)) (=> (@ (@ (@ tptp.times_assn_raw X) Xa) Xb) (=> (@ (@ tptp.accp_P1862375125659990705et_nat tptp.times_assn_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) Xb))) (not (forall ((H3 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H3) As))) (=> (= Xb _let_1) (=> (@ (@ tptp.accp_P1862375125659990705et_nat tptp.times_assn_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) _let_1))) (not (exists ((As13 tptp.set_nat) (As24 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H3))) (and (= As (@ (@ tptp.sup_sup_set_nat As13) As24)) (= (@ (@ tptp.inf_inf_set_nat As13) As24) tptp.bot_bot_set_nat) (@ X (@ _let_1 As13)) (@ Xa (@ _let_1 As24)))))))))))))))
% 2.52/3.50 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat)) (=> (not (@ (@ (@ tptp.times_assn_raw X) Xa) Xb)) (=> (@ (@ tptp.accp_P1862375125659990705et_nat tptp.times_assn_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) Xb))) (not (forall ((H3 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H3) As))) (=> (= Xb _let_1) (=> (@ (@ tptp.accp_P1862375125659990705et_nat tptp.times_assn_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) _let_1))) (exists ((As12 tptp.set_nat) (As23 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H3))) (and (= As (@ (@ tptp.sup_sup_set_nat As12) As23)) (= (@ (@ tptp.inf_inf_set_nat As12) As23) tptp.bot_bot_set_nat) (@ X (@ _let_1 As12)) (@ Xa (@ _let_1 As23))))))))))))))
% 2.52/3.50 (assert (forall ((C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger C) (@ (@ tptp.times_3573771949741848930nteger C) B)) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) B)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.one_one_Code_integer))))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.times_times_rat C) B)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.one_one_rat))))))
% 2.52/3.50 (assert (forall ((C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.times_times_int C) B)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.one_one_int))))))
% 2.52/3.50 (assert (forall ((X21 tptp.int) (X22 tptp.list_int) (Y21 tptp.int) (Y22 tptp.list_int)) (= (= (@ (@ tptp.cons_int X21) X22) (@ (@ tptp.cons_int Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))))
% 2.52/3.50 (assert (forall ((X21 tptp.nat) (X22 tptp.list_nat) (Y21 tptp.nat) (Y22 tptp.list_nat)) (= (= (@ (@ tptp.cons_nat X21) X22) (@ (@ tptp.cons_nat Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))))
% 2.52/3.50 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 2.52/3.50 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_int A) B))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.ord_less_rat A) B))))
% 2.52/3.50 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) B))))
% 2.52/3.50 (assert (forall ((P2 (-> tptp.int Bool)) (X tptp.int) (Xs tptp.list_int)) (let ((_let_1 (@ tptp.list_ex_int P2))) (= (@ _let_1 (@ (@ tptp.cons_int X) Xs)) (or (@ P2 X) (@ _let_1 Xs))))))
% 2.52/3.50 (assert (forall ((P2 (-> tptp.nat Bool)) (X tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ tptp.list_ex_nat P2))) (= (@ _let_1 (@ (@ tptp.cons_nat X) Xs)) (or (@ P2 X) (@ _let_1 Xs))))))
% 2.52/3.50 (assert (forall ((X tptp.nat) (Y tptp.nat) (F2 (-> tptp.nat tptp.nat)) (Fs tptp.list_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)))) (let ((_let_2 (@ F2 Y))) (let ((_let_3 (@ F2 X))) (= (@ _let_1 (@ tptp.measures_nat (@ (@ tptp.cons_nat_nat F2) Fs))) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ _let_1 (@ tptp.measures_nat Fs))))))))))
% 2.52/3.50 (assert (forall ((X tptp.int) (Y tptp.int) (F2 (-> tptp.int tptp.nat)) (Fs tptp.list_int_nat)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)))) (let ((_let_2 (@ F2 Y))) (let ((_let_3 (@ F2 X))) (= (@ _let_1 (@ tptp.measures_int (@ (@ tptp.cons_int_nat F2) Fs))) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ _let_1 (@ tptp.measures_int Fs))))))))))
% 2.52/3.50 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 2.52/3.50 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))
% 2.52/3.50 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) A) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) A) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 2.52/3.50 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (= (@ _let_1 (@ tptp.uminus_uminus_int A)) (@ _let_1 tptp.zero_zero_int)))))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (= (@ _let_1 (@ tptp.uminus_uminus_rat A)) (@ _let_1 tptp.zero_zero_rat)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 2.52/3.50 (assert (forall ((X tptp.int) (Xs tptp.list_int) (Y tptp.nat) (Ys tptp.list_nat)) (= (@ (@ tptp.zip_int_nat (@ (@ tptp.cons_int X) Xs)) (@ (@ tptp.cons_nat Y) Ys)) (@ (@ tptp.cons_P7512249878480867347nt_nat (@ (@ tptp.product_Pair_int_nat X) Y)) (@ (@ tptp.zip_int_nat Xs) Ys)))))
% 2.52/3.50 (assert (forall ((X tptp.nat) (Xs tptp.list_nat) (Y tptp.int) (Ys tptp.list_int)) (= (@ (@ tptp.zip_nat_int (@ (@ tptp.cons_nat X) Xs)) (@ (@ tptp.cons_int Y) Ys)) (@ (@ tptp.cons_P2335045147070616083at_int (@ (@ tptp.product_Pair_nat_int X) Y)) (@ (@ tptp.zip_nat_int Xs) Ys)))))
% 2.52/3.50 (assert (forall ((X tptp.heap_e7401611519738050253t_unit) (Xs tptp.list_h2745205591237434579t_unit) (Y tptp.set_nat) (Ys tptp.list_set_nat)) (= (@ (@ tptp.zip_he6711929980790699996et_nat (@ (@ tptp.cons_h4161061858534515843t_unit X) Xs)) (@ (@ tptp.cons_set_nat Y) Ys)) (@ (@ tptp.cons_P2869003950965171916et_nat (@ (@ tptp.produc7507926704131184380et_nat X) Y)) (@ (@ tptp.zip_he6711929980790699996et_nat Xs) Ys)))))
% 2.52/3.50 (assert (forall ((X tptp.nat) (Xs tptp.list_nat) (Y tptp.nat) (Ys tptp.list_nat)) (= (@ (@ tptp.zip_nat_nat (@ (@ tptp.cons_nat X) Xs)) (@ (@ tptp.cons_nat Y) Ys)) (@ (@ tptp.cons_P6512896166579812791at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ (@ tptp.zip_nat_nat Xs) Ys)))))
% 2.52/3.50 (assert (forall ((X tptp.int) (Xs tptp.list_int) (Y tptp.int) (Ys tptp.list_int)) (= (@ (@ tptp.zip_int_int (@ (@ tptp.cons_int X) Xs)) (@ (@ tptp.cons_int Y) Ys)) (@ (@ tptp.cons_P3334398858971670639nt_int (@ (@ tptp.product_Pair_int_int X) Y)) (@ (@ tptp.zip_int_int Xs) Ys)))))
% 2.52/3.50 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xs tptp.list_P7985473006766602707_nat_o) (Y tptp.produc3658429121746597890et_nat) (Ys tptp.list_P9062070895058802706et_nat)) (= (@ (@ tptp.zip_Pr7134870689397686104et_nat (@ (@ tptp.cons_P6219271836124797827_nat_o X) Xs)) (@ (@ tptp.cons_P2869003950965171916et_nat Y) Ys)) (@ (@ tptp.cons_P3419706843779801160et_nat (@ (@ tptp.produc5001842942810119800et_nat X) Y)) (@ (@ tptp.zip_Pr7134870689397686104et_nat Xs) Ys)))))
% 2.52/3.50 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xs tptp.list_P7985473006766602707_nat_o) (Y tptp.produc3925858234332021118et_nat) (Ys tptp.list_P2321686559999237006et_nat)) (= (@ (@ tptp.zip_Pr8136144321567152340et_nat (@ (@ tptp.cons_P6219271836124797827_nat_o X) Xs)) (@ (@ tptp.cons_P3419706843779801160et_nat Y) Ys)) (@ (@ tptp.cons_P6329468272379687876et_nat (@ (@ tptp.produc2245416461498447860et_nat X) Y)) (@ (@ tptp.zip_Pr8136144321567152340et_nat Xs) Ys)))))
% 2.52/3.50 (assert (forall ((Zs tptp.list_P9062070895058802706et_nat)) (= (@ (@ tptp.zip_he6711929980790699996et_nat (@ (@ tptp.map_Pr7042224834074979589t_unit tptp.produc1824681642469235216et_nat) Zs)) (@ (@ tptp.map_Pr4871828589360411470et_nat tptp.produc8586169260539613262et_nat) Zs)) Zs)))
% 2.52/3.50 (assert (forall ((Zs tptp.list_P5707943133018811711nt_int)) (= (@ (@ tptp.zip_int_int (@ (@ tptp.map_Pr6494458893431244577nt_int tptp.product_fst_int_int) Zs)) (@ (@ tptp.map_Pr6494458893431244577nt_int tptp.product_snd_int_int) Zs)) Zs)))
% 2.52/3.50 (assert (forall ((Zs tptp.list_P8527749157015355191n_assn)) (= (@ (@ tptp.zip_assn_assn (@ (@ tptp.map_Pr8991440229025900053n_assn tptp.produc9167289414957590229n_assn) Zs)) (@ (@ tptp.map_Pr8991440229025900053n_assn tptp.produc2051961928117032727n_assn) Zs)) Zs)))
% 2.52/3.50 (assert (forall ((A3 tptp.set_nat) (X tptp.produc6575502325842934193n_assn)) (let ((_let_1 (@ (@ tptp.cons_P2971678138204555879n_assn X) tptp.nil_Pr5671120429643327159n_assn))) (let ((_let_2 (@ (@ tptp.nths_P5537322223065504949n_assn _let_1) A3))) (let ((_let_3 (@ (@ tptp.member_nat2 tptp.zero_zero_nat) A3))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 tptp.nil_Pr5671120429643327159n_assn))))))))
% 2.52/3.50 (assert (forall ((A3 tptp.set_nat) (X tptp.int)) (let ((_let_1 (@ (@ tptp.cons_int X) tptp.nil_int))) (let ((_let_2 (@ (@ tptp.nths_int _let_1) A3))) (let ((_let_3 (@ (@ tptp.member_nat2 tptp.zero_zero_nat) A3))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 tptp.nil_int))))))))
% 2.52/3.50 (assert (forall ((A3 tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.cons_nat X) tptp.nil_nat))) (let ((_let_2 (@ (@ tptp.nths_nat _let_1) A3))) (let ((_let_3 (@ (@ tptp.member_nat2 tptp.zero_zero_nat) A3))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 tptp.nil_nat))))))))
% 2.52/3.50 (assert (= tptp.ord_less_assn (lambda ((A2 tptp.assn) (B2 tptp.assn)) (and (@ (@ tptp.ord_less_eq_assn A2) B2) (not (= A2 B2))))))
% 2.52/3.50 (assert (forall ((X tptp.int) (Xs tptp.list_int)) (not (= (@ (@ tptp.cons_int X) Xs) Xs))))
% 2.52/3.50 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (not (= (@ (@ tptp.cons_nat X) Xs) Xs))))
% 2.52/3.50 (assert (forall ((X tptp.list_l6351802567095793725n_assn)) (=> (not (= X tptp.nil_li5476096274760905021n_assn)) (=> (forall ((Xss tptp.list_l6351802567095793725n_assn)) (not (= X (@ (@ tptp.cons_l2423627976422276333n_assn tptp.nil_Pr5671120429643327159n_assn) Xss)))) (not (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn) (Xss tptp.list_l6351802567095793725n_assn)) (not (= X (@ (@ tptp.cons_l2423627976422276333n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)) Xss)))))))))
% 2.52/3.50 (assert (forall ((X tptp.list_list_int)) (=> (not (= X tptp.nil_list_int)) (=> (forall ((Xss tptp.list_list_int)) (not (= X (@ (@ tptp.cons_list_int tptp.nil_int) Xss)))) (not (forall ((X3 tptp.int) (Xs2 tptp.list_int) (Xss tptp.list_list_int)) (not (= X (@ (@ tptp.cons_list_int (@ (@ tptp.cons_int X3) Xs2)) Xss)))))))))
% 2.52/3.50 (assert (forall ((X tptp.list_list_nat)) (=> (not (= X tptp.nil_list_nat)) (=> (forall ((Xss tptp.list_list_nat)) (not (= X (@ (@ tptp.cons_list_nat tptp.nil_nat) Xss)))) (not (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Xss tptp.list_list_nat)) (not (= X (@ (@ tptp.cons_list_nat (@ (@ tptp.cons_nat X3) Xs2)) Xss)))))))))
% 2.52/3.50 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_nat) (Xy tptp.product_prod_int_nat) (Xys tptp.list_P8198026277950538467nt_nat)) (=> (= (@ (@ tptp.zip_int_nat Xs) Ys) (@ (@ tptp.cons_P7512249878480867347nt_nat Xy) Xys)) (not (forall ((X3 tptp.int) (Xs3 tptp.list_int)) (=> (= Xs (@ (@ tptp.cons_int X3) Xs3)) (forall ((Y3 tptp.nat) (Ys2 tptp.list_nat)) (=> (= Ys (@ (@ tptp.cons_nat Y3) Ys2)) (=> (= Xy (@ (@ tptp.product_Pair_int_nat X3) Y3)) (not (= Xys (@ (@ tptp.zip_int_nat Xs3) Ys2))))))))))))
% 2.52/3.50 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_int) (Xy tptp.product_prod_nat_int) (Xys tptp.list_P3521021558325789923at_int)) (=> (= (@ (@ tptp.zip_nat_int Xs) Ys) (@ (@ tptp.cons_P2335045147070616083at_int Xy) Xys)) (not (forall ((X3 tptp.nat) (Xs3 tptp.list_nat)) (=> (= Xs (@ (@ tptp.cons_nat X3) Xs3)) (forall ((Y3 tptp.int) (Ys2 tptp.list_int)) (=> (= Ys (@ (@ tptp.cons_int Y3) Ys2)) (=> (= Xy (@ (@ tptp.product_Pair_nat_int X3) Y3)) (not (= Xys (@ (@ tptp.zip_nat_int Xs3) Ys2))))))))))))
% 2.52/3.50 (assert (forall ((Xs tptp.list_h2745205591237434579t_unit) (Ys tptp.list_set_nat) (Xy tptp.produc3658429121746597890et_nat) (Xys tptp.list_P9062070895058802706et_nat)) (=> (= (@ (@ tptp.zip_he6711929980790699996et_nat Xs) Ys) (@ (@ tptp.cons_P2869003950965171916et_nat Xy) Xys)) (not (forall ((X3 tptp.heap_e7401611519738050253t_unit) (Xs3 tptp.list_h2745205591237434579t_unit)) (=> (= Xs (@ (@ tptp.cons_h4161061858534515843t_unit X3) Xs3)) (forall ((Y3 tptp.set_nat) (Ys2 tptp.list_set_nat)) (=> (= Ys (@ (@ tptp.cons_set_nat Y3) Ys2)) (=> (= Xy (@ (@ tptp.produc7507926704131184380et_nat X3) Y3)) (not (= Xys (@ (@ tptp.zip_he6711929980790699996et_nat Xs3) Ys2))))))))))))
% 2.52/3.50 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (Xy tptp.product_prod_nat_nat) (Xys tptp.list_P6011104703257516679at_nat)) (=> (= (@ (@ tptp.zip_nat_nat Xs) Ys) (@ (@ tptp.cons_P6512896166579812791at_nat Xy) Xys)) (not (forall ((X3 tptp.nat) (Xs3 tptp.list_nat)) (=> (= Xs (@ (@ tptp.cons_nat X3) Xs3)) (forall ((Y3 tptp.nat) (Ys2 tptp.list_nat)) (=> (= Ys (@ (@ tptp.cons_nat Y3) Ys2)) (=> (= Xy (@ (@ tptp.product_Pair_nat_nat X3) Y3)) (not (= Xys (@ (@ tptp.zip_nat_nat Xs3) Ys2))))))))))))
% 2.52/3.50 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int) (Xy tptp.product_prod_int_int) (Xys tptp.list_P5707943133018811711nt_int)) (=> (= (@ (@ tptp.zip_int_int Xs) Ys) (@ (@ tptp.cons_P3334398858971670639nt_int Xy) Xys)) (not (forall ((X3 tptp.int) (Xs3 tptp.list_int)) (=> (= Xs (@ (@ tptp.cons_int X3) Xs3)) (forall ((Y3 tptp.int) (Ys2 tptp.list_int)) (=> (= Ys (@ (@ tptp.cons_int Y3) Ys2)) (=> (= Xy (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (= Xys (@ (@ tptp.zip_int_int Xs3) Ys2))))))))))))
% 2.52/3.50 (assert (forall ((Xs tptp.list_P7985473006766602707_nat_o) (Ys tptp.list_P9062070895058802706et_nat) (Xy tptp.produc3925858234332021118et_nat) (Xys tptp.list_P2321686559999237006et_nat)) (=> (= (@ (@ tptp.zip_Pr7134870689397686104et_nat Xs) Ys) (@ (@ tptp.cons_P3419706843779801160et_nat Xy) Xys)) (not (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Xs3 tptp.list_P7985473006766602707_nat_o)) (=> (= Xs (@ (@ tptp.cons_P6219271836124797827_nat_o X3) Xs3)) (forall ((Y3 tptp.produc3658429121746597890et_nat) (Ys2 tptp.list_P9062070895058802706et_nat)) (=> (= Ys (@ (@ tptp.cons_P2869003950965171916et_nat Y3) Ys2)) (=> (= Xy (@ (@ tptp.produc5001842942810119800et_nat X3) Y3)) (not (= Xys (@ (@ tptp.zip_Pr7134870689397686104et_nat Xs3) Ys2))))))))))))
% 2.52/3.50 (assert (forall ((Xs tptp.list_P7985473006766602707_nat_o) (Ys tptp.list_P2321686559999237006et_nat) (Xy tptp.produc2732055786443039994et_nat) (Xys tptp.list_P362550909693114634et_nat)) (=> (= (@ (@ tptp.zip_Pr8136144321567152340et_nat Xs) Ys) (@ (@ tptp.cons_P6329468272379687876et_nat Xy) Xys)) (not (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Xs3 tptp.list_P7985473006766602707_nat_o)) (=> (= Xs (@ (@ tptp.cons_P6219271836124797827_nat_o X3) Xs3)) (forall ((Y3 tptp.produc3925858234332021118et_nat) (Ys2 tptp.list_P2321686559999237006et_nat)) (=> (= Ys (@ (@ tptp.cons_P3419706843779801160et_nat Y3) Ys2)) (=> (= Xy (@ (@ tptp.produc2245416461498447860et_nat X3) Y3)) (not (= Xys (@ (@ tptp.zip_Pr8136144321567152340et_nat Xs3) Ys2))))))))))))
% 2.52/3.50 (assert (forall ((Xs tptp.list_P9062070895058802706et_nat) (Ys tptp.list_P9062070895058802706et_nat)) (let ((_let_1 (@ tptp.map_Pr4871828589360411470et_nat tptp.produc8586169260539613262et_nat))) (let ((_let_2 (@ tptp.map_Pr7042224834074979589t_unit tptp.produc1824681642469235216et_nat))) (=> (= (@ _let_2 Xs) (@ _let_2 Ys)) (=> (= (@ _let_1 Xs) (@ _let_1 Ys)) (= Xs Ys)))))))
% 2.52/3.50 (assert (forall ((Xs tptp.list_P5707943133018811711nt_int) (Ys tptp.list_P5707943133018811711nt_int)) (let ((_let_1 (@ tptp.map_Pr6494458893431244577nt_int tptp.product_snd_int_int))) (let ((_let_2 (@ tptp.map_Pr6494458893431244577nt_int tptp.product_fst_int_int))) (=> (= (@ _let_2 Xs) (@ _let_2 Ys)) (=> (= (@ _let_1 Xs) (@ _let_1 Ys)) (= Xs Ys)))))))
% 2.52/3.50 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ tptp.map_Pr8991440229025900053n_assn tptp.produc2051961928117032727n_assn))) (let ((_let_2 (@ tptp.map_Pr8991440229025900053n_assn tptp.produc9167289414957590229n_assn))) (=> (= (@ _let_2 Xs) (@ _let_2 Ys)) (=> (= (@ _let_1 Xs) (@ _let_1 Ys)) (= Xs Ys)))))))
% 2.52/3.50 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (not (= N tptp.zero_zero_nat)))))
% 2.52/3.50 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (not (= N tptp.zero_zero_nat)))))
% 2.52/3.50 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 2.52/3.50 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 2.52/3.50 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) tptp.one_one_Code_integer)))
% 2.52/3.50 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.one_one_rat)))
% 2.52/3.50 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.one_one_nat)))
% 2.52/3.50 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.one_one_int)))
% 2.52/3.50 (assert (forall ((L tptp.list_P8527749157015355191n_assn)) (=> (not (= L tptp.nil_Pr5671120429643327159n_assn)) (not (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn)) (not (= L (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2))))))))
% 2.52/3.50 (assert (forall ((L tptp.list_int)) (=> (not (= L tptp.nil_int)) (not (forall ((X3 tptp.int) (Xs2 tptp.list_int)) (not (= L (@ (@ tptp.cons_int X3) Xs2))))))))
% 2.52/3.50 (assert (forall ((L tptp.list_nat)) (=> (not (= L tptp.nil_nat)) (not (forall ((X3 tptp.nat) (Xs2 tptp.list_nat)) (not (= L (@ (@ tptp.cons_nat X3) Xs2))))))))
% 2.52/3.50 (assert (forall ((P2 (-> tptp.list_P8527749157015355191n_assn tptp.list_P8527749157015355191n_assn Bool)) (W1 tptp.list_P8527749157015355191n_assn) (W2 tptp.list_P8527749157015355191n_assn)) (=> (@ (@ P2 tptp.nil_Pr5671120429643327159n_assn) tptp.nil_Pr5671120429643327159n_assn) (=> (forall ((E tptp.produc6575502325842934193n_assn) (W12 tptp.list_P8527749157015355191n_assn) (W22 tptp.list_P8527749157015355191n_assn)) (=> (@ (@ P2 W12) W22) (@ (@ P2 (@ (@ tptp.cons_P2971678138204555879n_assn E) W12)) W22))) (=> (forall ((E tptp.produc6575502325842934193n_assn) (W13 tptp.list_P8527749157015355191n_assn) (W23 tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ P2 W13))) (=> (@ _let_1 W23) (@ _let_1 (@ (@ tptp.cons_P2971678138204555879n_assn E) W23))))) (@ (@ P2 W1) W2))))))
% 2.52/3.50 (assert (forall ((P2 (-> tptp.list_P8527749157015355191n_assn tptp.list_int Bool)) (W1 tptp.list_P8527749157015355191n_assn) (W2 tptp.list_int)) (=> (@ (@ P2 tptp.nil_Pr5671120429643327159n_assn) tptp.nil_int) (=> (forall ((E tptp.produc6575502325842934193n_assn) (W12 tptp.list_P8527749157015355191n_assn) (W22 tptp.list_int)) (=> (@ (@ P2 W12) W22) (@ (@ P2 (@ (@ tptp.cons_P2971678138204555879n_assn E) W12)) W22))) (=> (forall ((E tptp.int) (W13 tptp.list_P8527749157015355191n_assn) (W23 tptp.list_int)) (let ((_let_1 (@ P2 W13))) (=> (@ _let_1 W23) (@ _let_1 (@ (@ tptp.cons_int E) W23))))) (@ (@ P2 W1) W2))))))
% 2.52/3.50 (assert (forall ((P2 (-> tptp.list_P8527749157015355191n_assn tptp.list_nat Bool)) (W1 tptp.list_P8527749157015355191n_assn) (W2 tptp.list_nat)) (=> (@ (@ P2 tptp.nil_Pr5671120429643327159n_assn) tptp.nil_nat) (=> (forall ((E tptp.produc6575502325842934193n_assn) (W12 tptp.list_P8527749157015355191n_assn) (W22 tptp.list_nat)) (=> (@ (@ P2 W12) W22) (@ (@ P2 (@ (@ tptp.cons_P2971678138204555879n_assn E) W12)) W22))) (=> (forall ((E tptp.nat) (W13 tptp.list_P8527749157015355191n_assn) (W23 tptp.list_nat)) (let ((_let_1 (@ P2 W13))) (=> (@ _let_1 W23) (@ _let_1 (@ (@ tptp.cons_nat E) W23))))) (@ (@ P2 W1) W2))))))
% 2.52/3.50 (assert (forall ((P2 (-> tptp.list_int tptp.list_P8527749157015355191n_assn Bool)) (W1 tptp.list_int) (W2 tptp.list_P8527749157015355191n_assn)) (=> (@ (@ P2 tptp.nil_int) tptp.nil_Pr5671120429643327159n_assn) (=> (forall ((E tptp.int) (W12 tptp.list_int) (W22 tptp.list_P8527749157015355191n_assn)) (=> (@ (@ P2 W12) W22) (@ (@ P2 (@ (@ tptp.cons_int E) W12)) W22))) (=> (forall ((E tptp.produc6575502325842934193n_assn) (W13 tptp.list_int) (W23 tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ P2 W13))) (=> (@ _let_1 W23) (@ _let_1 (@ (@ tptp.cons_P2971678138204555879n_assn E) W23))))) (@ (@ P2 W1) W2))))))
% 2.52/3.50 (assert (forall ((P2 (-> tptp.list_int tptp.list_int Bool)) (W1 tptp.list_int) (W2 tptp.list_int)) (=> (@ (@ P2 tptp.nil_int) tptp.nil_int) (=> (forall ((E tptp.int) (W12 tptp.list_int) (W22 tptp.list_int)) (=> (@ (@ P2 W12) W22) (@ (@ P2 (@ (@ tptp.cons_int E) W12)) W22))) (=> (forall ((E tptp.int) (W13 tptp.list_int) (W23 tptp.list_int)) (let ((_let_1 (@ P2 W13))) (=> (@ _let_1 W23) (@ _let_1 (@ (@ tptp.cons_int E) W23))))) (@ (@ P2 W1) W2))))))
% 2.52/3.50 (assert (forall ((P2 (-> tptp.list_int tptp.list_nat Bool)) (W1 tptp.list_int) (W2 tptp.list_nat)) (=> (@ (@ P2 tptp.nil_int) tptp.nil_nat) (=> (forall ((E tptp.int) (W12 tptp.list_int) (W22 tptp.list_nat)) (=> (@ (@ P2 W12) W22) (@ (@ P2 (@ (@ tptp.cons_int E) W12)) W22))) (=> (forall ((E tptp.nat) (W13 tptp.list_int) (W23 tptp.list_nat)) (let ((_let_1 (@ P2 W13))) (=> (@ _let_1 W23) (@ _let_1 (@ (@ tptp.cons_nat E) W23))))) (@ (@ P2 W1) W2))))))
% 2.52/3.50 (assert (forall ((P2 (-> tptp.list_nat tptp.list_P8527749157015355191n_assn Bool)) (W1 tptp.list_nat) (W2 tptp.list_P8527749157015355191n_assn)) (=> (@ (@ P2 tptp.nil_nat) tptp.nil_Pr5671120429643327159n_assn) (=> (forall ((E tptp.nat) (W12 tptp.list_nat) (W22 tptp.list_P8527749157015355191n_assn)) (=> (@ (@ P2 W12) W22) (@ (@ P2 (@ (@ tptp.cons_nat E) W12)) W22))) (=> (forall ((E tptp.produc6575502325842934193n_assn) (W13 tptp.list_nat) (W23 tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ P2 W13))) (=> (@ _let_1 W23) (@ _let_1 (@ (@ tptp.cons_P2971678138204555879n_assn E) W23))))) (@ (@ P2 W1) W2))))))
% 2.52/3.50 (assert (forall ((P2 (-> tptp.list_nat tptp.list_int Bool)) (W1 tptp.list_nat) (W2 tptp.list_int)) (=> (@ (@ P2 tptp.nil_nat) tptp.nil_int) (=> (forall ((E tptp.nat) (W12 tptp.list_nat) (W22 tptp.list_int)) (=> (@ (@ P2 W12) W22) (@ (@ P2 (@ (@ tptp.cons_nat E) W12)) W22))) (=> (forall ((E tptp.int) (W13 tptp.list_nat) (W23 tptp.list_int)) (let ((_let_1 (@ P2 W13))) (=> (@ _let_1 W23) (@ _let_1 (@ (@ tptp.cons_int E) W23))))) (@ (@ P2 W1) W2))))))
% 2.52/3.50 (assert (forall ((P2 (-> tptp.list_nat tptp.list_nat Bool)) (W1 tptp.list_nat) (W2 tptp.list_nat)) (=> (@ (@ P2 tptp.nil_nat) tptp.nil_nat) (=> (forall ((E tptp.nat) (W12 tptp.list_nat) (W22 tptp.list_nat)) (=> (@ (@ P2 W12) W22) (@ (@ P2 (@ (@ tptp.cons_nat E) W12)) W22))) (=> (forall ((E tptp.nat) (W13 tptp.list_nat) (W23 tptp.list_nat)) (let ((_let_1 (@ P2 W13))) (=> (@ _let_1 W23) (@ _let_1 (@ (@ tptp.cons_nat E) W23))))) (@ (@ P2 W1) W2))))))
% 2.52/3.50 (assert (forall ((P2 (-> tptp.list_P8527749157015355191n_assn Bool)) (Xs tptp.list_P8527749157015355191n_assn)) (=> (@ P2 tptp.nil_Pr5671120429643327159n_assn) (=> (forall ((X3 tptp.produc6575502325842934193n_assn)) (@ P2 (@ (@ tptp.cons_P2971678138204555879n_assn X3) tptp.nil_Pr5671120429643327159n_assn))) (=> (forall ((X1 tptp.produc6575502325842934193n_assn) (X23 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn)) (=> (@ P2 Xs2) (@ P2 (@ (@ tptp.cons_P2971678138204555879n_assn X1) (@ (@ tptp.cons_P2971678138204555879n_assn X23) Xs2))))) (@ P2 Xs))))))
% 2.52/3.50 (assert (forall ((P2 (-> tptp.list_int Bool)) (Xs tptp.list_int)) (=> (@ P2 tptp.nil_int) (=> (forall ((X3 tptp.int)) (@ P2 (@ (@ tptp.cons_int X3) tptp.nil_int))) (=> (forall ((X1 tptp.int) (X23 tptp.int) (Xs2 tptp.list_int)) (=> (@ P2 Xs2) (@ P2 (@ (@ tptp.cons_int X1) (@ (@ tptp.cons_int X23) Xs2))))) (@ P2 Xs))))))
% 2.52/3.50 (assert (forall ((P2 (-> tptp.list_nat Bool)) (Xs tptp.list_nat)) (=> (@ P2 tptp.nil_nat) (=> (forall ((X3 tptp.nat)) (@ P2 (@ (@ tptp.cons_nat X3) tptp.nil_nat))) (=> (forall ((X1 tptp.nat) (X23 tptp.nat) (Xs2 tptp.list_nat)) (=> (@ P2 Xs2) (@ P2 (@ (@ tptp.cons_nat X1) (@ (@ tptp.cons_nat X23) Xs2))))) (@ P2 Xs))))))
% 2.52/3.50 (assert (forall ((P2 (-> tptp.list_P8527749157015355191n_assn tptp.list_P8527749157015355191n_assn Bool)) (R (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn Bool)) (Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_P8527749157015355191n_assn)) (=> (forall ((Xs2 tptp.list_P8527749157015355191n_assn)) (@ (@ P2 Xs2) tptp.nil_Pr5671120429643327159n_assn)) (=> (forall ((X_1 tptp.list_P8527749157015355191n_assn)) (@ (@ P2 tptp.nil_Pr5671120429643327159n_assn) X_1)) (=> (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn) (Y3 tptp.produc6575502325842934193n_assn) (Ys3 tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ (@ tptp.cons_P2971678138204555879n_assn Y3) Ys3))) (=> (@ (@ R X3) Y3) (=> (@ (@ P2 Xs2) _let_1) (@ (@ P2 (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)) _let_1))))) (=> (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn) (Y3 tptp.produc6575502325842934193n_assn) (Ys3 tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ P2 (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)))) (=> (not (@ (@ R X3) Y3)) (=> (@ _let_1 Ys3) (@ _let_1 (@ (@ tptp.cons_P2971678138204555879n_assn Y3) Ys3)))))) (@ (@ P2 Xs) Ys)))))))
% 2.52/3.50 (assert (forall ((P2 (-> tptp.list_int tptp.list_P8527749157015355191n_assn Bool)) (R (-> tptp.int tptp.produc6575502325842934193n_assn Bool)) (Xs tptp.list_int) (Ys tptp.list_P8527749157015355191n_assn)) (=> (forall ((Xs2 tptp.list_int)) (@ (@ P2 Xs2) tptp.nil_Pr5671120429643327159n_assn)) (=> (forall ((X_1 tptp.list_P8527749157015355191n_assn)) (@ (@ P2 tptp.nil_int) X_1)) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int) (Y3 tptp.produc6575502325842934193n_assn) (Ys3 tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ (@ tptp.cons_P2971678138204555879n_assn Y3) Ys3))) (=> (@ (@ R X3) Y3) (=> (@ (@ P2 Xs2) _let_1) (@ (@ P2 (@ (@ tptp.cons_int X3) Xs2)) _let_1))))) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int) (Y3 tptp.produc6575502325842934193n_assn) (Ys3 tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ P2 (@ (@ tptp.cons_int X3) Xs2)))) (=> (not (@ (@ R X3) Y3)) (=> (@ _let_1 Ys3) (@ _let_1 (@ (@ tptp.cons_P2971678138204555879n_assn Y3) Ys3)))))) (@ (@ P2 Xs) Ys)))))))
% 2.52/3.50 (assert (forall ((P2 (-> tptp.list_nat tptp.list_P8527749157015355191n_assn Bool)) (R (-> tptp.nat tptp.produc6575502325842934193n_assn Bool)) (Xs tptp.list_nat) (Ys tptp.list_P8527749157015355191n_assn)) (=> (forall ((Xs2 tptp.list_nat)) (@ (@ P2 Xs2) tptp.nil_Pr5671120429643327159n_assn)) (=> (forall ((X_1 tptp.list_P8527749157015355191n_assn)) (@ (@ P2 tptp.nil_nat) X_1)) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y3 tptp.produc6575502325842934193n_assn) (Ys3 tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ (@ tptp.cons_P2971678138204555879n_assn Y3) Ys3))) (=> (@ (@ R X3) Y3) (=> (@ (@ P2 Xs2) _let_1) (@ (@ P2 (@ (@ tptp.cons_nat X3) Xs2)) _let_1))))) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y3 tptp.produc6575502325842934193n_assn) (Ys3 tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ P2 (@ (@ tptp.cons_nat X3) Xs2)))) (=> (not (@ (@ R X3) Y3)) (=> (@ _let_1 Ys3) (@ _let_1 (@ (@ tptp.cons_P2971678138204555879n_assn Y3) Ys3)))))) (@ (@ P2 Xs) Ys)))))))
% 2.52/3.50 (assert (forall ((P2 (-> tptp.list_P8527749157015355191n_assn tptp.list_int Bool)) (R (-> tptp.produc6575502325842934193n_assn tptp.int Bool)) (Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_int)) (=> (forall ((Xs2 tptp.list_P8527749157015355191n_assn)) (@ (@ P2 Xs2) tptp.nil_int)) (=> (forall ((X_1 tptp.list_int)) (@ (@ P2 tptp.nil_Pr5671120429643327159n_assn) X_1)) (=> (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn) (Y3 tptp.int) (Ys3 tptp.list_int)) (let ((_let_1 (@ (@ tptp.cons_int Y3) Ys3))) (=> (@ (@ R X3) Y3) (=> (@ (@ P2 Xs2) _let_1) (@ (@ P2 (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)) _let_1))))) (=> (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn) (Y3 tptp.int) (Ys3 tptp.list_int)) (let ((_let_1 (@ P2 (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)))) (=> (not (@ (@ R X3) Y3)) (=> (@ _let_1 Ys3) (@ _let_1 (@ (@ tptp.cons_int Y3) Ys3)))))) (@ (@ P2 Xs) Ys)))))))
% 2.52/3.50 (assert (forall ((P2 (-> tptp.list_int tptp.list_int Bool)) (R (-> tptp.int tptp.int Bool)) (Xs tptp.list_int) (Ys tptp.list_int)) (=> (forall ((Xs2 tptp.list_int)) (@ (@ P2 Xs2) tptp.nil_int)) (=> (forall ((X_1 tptp.list_int)) (@ (@ P2 tptp.nil_int) X_1)) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int) (Y3 tptp.int) (Ys3 tptp.list_int)) (let ((_let_1 (@ (@ tptp.cons_int Y3) Ys3))) (=> (@ (@ R X3) Y3) (=> (@ (@ P2 Xs2) _let_1) (@ (@ P2 (@ (@ tptp.cons_int X3) Xs2)) _let_1))))) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int) (Y3 tptp.int) (Ys3 tptp.list_int)) (let ((_let_1 (@ P2 (@ (@ tptp.cons_int X3) Xs2)))) (=> (not (@ (@ R X3) Y3)) (=> (@ _let_1 Ys3) (@ _let_1 (@ (@ tptp.cons_int Y3) Ys3)))))) (@ (@ P2 Xs) Ys)))))))
% 2.52/3.50 (assert (forall ((P2 (-> tptp.list_nat tptp.list_int Bool)) (R (-> tptp.nat tptp.int Bool)) (Xs tptp.list_nat) (Ys tptp.list_int)) (=> (forall ((Xs2 tptp.list_nat)) (@ (@ P2 Xs2) tptp.nil_int)) (=> (forall ((X_1 tptp.list_int)) (@ (@ P2 tptp.nil_nat) X_1)) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y3 tptp.int) (Ys3 tptp.list_int)) (let ((_let_1 (@ (@ tptp.cons_int Y3) Ys3))) (=> (@ (@ R X3) Y3) (=> (@ (@ P2 Xs2) _let_1) (@ (@ P2 (@ (@ tptp.cons_nat X3) Xs2)) _let_1))))) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y3 tptp.int) (Ys3 tptp.list_int)) (let ((_let_1 (@ P2 (@ (@ tptp.cons_nat X3) Xs2)))) (=> (not (@ (@ R X3) Y3)) (=> (@ _let_1 Ys3) (@ _let_1 (@ (@ tptp.cons_int Y3) Ys3)))))) (@ (@ P2 Xs) Ys)))))))
% 2.52/3.50 (assert (forall ((P2 (-> tptp.list_P8527749157015355191n_assn tptp.list_nat Bool)) (R (-> tptp.produc6575502325842934193n_assn tptp.nat Bool)) (Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_nat)) (=> (forall ((Xs2 tptp.list_P8527749157015355191n_assn)) (@ (@ P2 Xs2) tptp.nil_nat)) (=> (forall ((X_1 tptp.list_nat)) (@ (@ P2 tptp.nil_Pr5671120429643327159n_assn) X_1)) (=> (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn) (Y3 tptp.nat) (Ys3 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat Y3) Ys3))) (=> (@ (@ R X3) Y3) (=> (@ (@ P2 Xs2) _let_1) (@ (@ P2 (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)) _let_1))))) (=> (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn) (Y3 tptp.nat) (Ys3 tptp.list_nat)) (let ((_let_1 (@ P2 (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)))) (=> (not (@ (@ R X3) Y3)) (=> (@ _let_1 Ys3) (@ _let_1 (@ (@ tptp.cons_nat Y3) Ys3)))))) (@ (@ P2 Xs) Ys)))))))
% 2.52/3.50 (assert (forall ((P2 (-> tptp.list_int tptp.list_nat Bool)) (R (-> tptp.int tptp.nat Bool)) (Xs tptp.list_int) (Ys tptp.list_nat)) (=> (forall ((Xs2 tptp.list_int)) (@ (@ P2 Xs2) tptp.nil_nat)) (=> (forall ((X_1 tptp.list_nat)) (@ (@ P2 tptp.nil_int) X_1)) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int) (Y3 tptp.nat) (Ys3 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat Y3) Ys3))) (=> (@ (@ R X3) Y3) (=> (@ (@ P2 Xs2) _let_1) (@ (@ P2 (@ (@ tptp.cons_int X3) Xs2)) _let_1))))) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int) (Y3 tptp.nat) (Ys3 tptp.list_nat)) (let ((_let_1 (@ P2 (@ (@ tptp.cons_int X3) Xs2)))) (=> (not (@ (@ R X3) Y3)) (=> (@ _let_1 Ys3) (@ _let_1 (@ (@ tptp.cons_nat Y3) Ys3)))))) (@ (@ P2 Xs) Ys)))))))
% 2.52/3.50 (assert (forall ((P2 (-> tptp.list_nat tptp.list_nat Bool)) (R (-> tptp.nat tptp.nat Bool)) (Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (forall ((Xs2 tptp.list_nat)) (@ (@ P2 Xs2) tptp.nil_nat)) (=> (forall ((X_1 tptp.list_nat)) (@ (@ P2 tptp.nil_nat) X_1)) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y3 tptp.nat) (Ys3 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat Y3) Ys3))) (=> (@ (@ R X3) Y3) (=> (@ (@ P2 Xs2) _let_1) (@ (@ P2 (@ (@ tptp.cons_nat X3) Xs2)) _let_1))))) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y3 tptp.nat) (Ys3 tptp.list_nat)) (let ((_let_1 (@ P2 (@ (@ tptp.cons_nat X3) Xs2)))) (=> (not (@ (@ R X3) Y3)) (=> (@ _let_1 Ys3) (@ _let_1 (@ (@ tptp.cons_nat Y3) Ys3)))))) (@ (@ P2 Xs) Ys)))))))
% 2.52/3.50 (assert (forall ((X21 tptp.produc6575502325842934193n_assn) (X22 tptp.list_P8527749157015355191n_assn)) (not (= tptp.nil_Pr5671120429643327159n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X21) X22)))))
% 2.52/3.50 (assert (forall ((X21 tptp.int) (X22 tptp.list_int)) (not (= tptp.nil_int (@ (@ tptp.cons_int X21) X22)))))
% 2.52/3.50 (assert (forall ((X21 tptp.nat) (X22 tptp.list_nat)) (not (= tptp.nil_nat (@ (@ tptp.cons_nat X21) X22)))))
% 2.52/3.50 (assert (forall ((List tptp.list_P8527749157015355191n_assn) (X21 tptp.produc6575502325842934193n_assn) (X22 tptp.list_P8527749157015355191n_assn)) (=> (= List (@ (@ tptp.cons_P2971678138204555879n_assn X21) X22)) (not (= List tptp.nil_Pr5671120429643327159n_assn)))))
% 2.52/3.50 (assert (forall ((List tptp.list_int) (X21 tptp.int) (X22 tptp.list_int)) (=> (= List (@ (@ tptp.cons_int X21) X22)) (not (= List tptp.nil_int)))))
% 2.52/3.50 (assert (forall ((List tptp.list_nat) (X21 tptp.nat) (X22 tptp.list_nat)) (=> (= List (@ (@ tptp.cons_nat X21) X22)) (not (= List tptp.nil_nat)))))
% 2.52/3.50 (assert (forall ((Y tptp.list_P8527749157015355191n_assn)) (=> (not (= Y tptp.nil_Pr5671120429643327159n_assn)) (not (forall ((X212 tptp.produc6575502325842934193n_assn) (X222 tptp.list_P8527749157015355191n_assn)) (not (= Y (@ (@ tptp.cons_P2971678138204555879n_assn X212) X222))))))))
% 2.52/3.50 (assert (forall ((Y tptp.list_int)) (=> (not (= Y tptp.nil_int)) (not (forall ((X212 tptp.int) (X222 tptp.list_int)) (not (= Y (@ (@ tptp.cons_int X212) X222))))))))
% 2.52/3.50 (assert (forall ((Y tptp.list_nat)) (=> (not (= Y tptp.nil_nat)) (not (forall ((X212 tptp.nat) (X222 tptp.list_nat)) (not (= Y (@ (@ tptp.cons_nat X212) X222))))))))
% 2.52/3.50 (assert (forall ((X tptp.list_int)) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int)) (not (= X (@ (@ tptp.cons_int X3) Xs2)))) (= X tptp.nil_int))))
% 2.52/3.50 (assert (forall ((X tptp.list_nat)) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat)) (not (= X (@ (@ tptp.cons_nat X3) Xs2)))) (= X tptp.nil_nat))))
% 2.52/3.50 (assert (forall ((X tptp.list_P8527749157015355191n_assn)) (=> (not (= X tptp.nil_Pr5671120429643327159n_assn)) (=> (forall ((X3 tptp.produc6575502325842934193n_assn)) (not (= X (@ (@ tptp.cons_P2971678138204555879n_assn X3) tptp.nil_Pr5671120429643327159n_assn)))) (not (forall ((X3 tptp.produc6575502325842934193n_assn) (Y3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn)) (not (= X (@ (@ tptp.cons_P2971678138204555879n_assn X3) (@ (@ tptp.cons_P2971678138204555879n_assn Y3) Xs2))))))))))
% 2.52/3.50 (assert (forall ((X tptp.list_int)) (=> (not (= X tptp.nil_int)) (=> (forall ((X3 tptp.int)) (not (= X (@ (@ tptp.cons_int X3) tptp.nil_int)))) (not (forall ((X3 tptp.int) (Y3 tptp.int) (Xs2 tptp.list_int)) (not (= X (@ (@ tptp.cons_int X3) (@ (@ tptp.cons_int Y3) Xs2))))))))))
% 2.52/3.50 (assert (forall ((X tptp.list_nat)) (=> (not (= X tptp.nil_nat)) (=> (forall ((X3 tptp.nat)) (not (= X (@ (@ tptp.cons_nat X3) tptp.nil_nat)))) (not (forall ((X3 tptp.nat) (Y3 tptp.nat) (Xs2 tptp.list_nat)) (not (= X (@ (@ tptp.cons_nat X3) (@ (@ tptp.cons_nat Y3) Xs2))))))))))
% 2.52/3.50 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn)) (= (not (= Xs tptp.nil_Pr5671120429643327159n_assn)) (exists ((Y2 tptp.produc6575502325842934193n_assn) (Ys4 tptp.list_P8527749157015355191n_assn)) (= Xs (@ (@ tptp.cons_P2971678138204555879n_assn Y2) Ys4))))))
% 2.52/3.50 (assert (forall ((Xs tptp.list_int)) (= (not (= Xs tptp.nil_int)) (exists ((Y2 tptp.int) (Ys4 tptp.list_int)) (= Xs (@ (@ tptp.cons_int Y2) Ys4))))))
% 2.52/3.50 (assert (forall ((Xs tptp.list_nat)) (= (not (= Xs tptp.nil_nat)) (exists ((Y2 tptp.nat) (Ys4 tptp.list_nat)) (= Xs (@ (@ tptp.cons_nat Y2) Ys4))))))
% 2.52/3.50 (assert (forall ((P2 (-> tptp.list_P8527749157015355191n_assn tptp.list_P8527749157015355191n_assn Bool)) (Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_P8527749157015355191n_assn)) (=> (@ (@ P2 tptp.nil_Pr5671120429643327159n_assn) tptp.nil_Pr5671120429643327159n_assn) (=> (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn)) (@ (@ P2 (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)) tptp.nil_Pr5671120429643327159n_assn)) (=> (forall ((Y3 tptp.produc6575502325842934193n_assn) (Ys3 tptp.list_P8527749157015355191n_assn)) (@ (@ P2 tptp.nil_Pr5671120429643327159n_assn) (@ (@ tptp.cons_P2971678138204555879n_assn Y3) Ys3))) (=> (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn) (Y3 tptp.produc6575502325842934193n_assn) (Ys3 tptp.list_P8527749157015355191n_assn)) (=> (@ (@ P2 Xs2) Ys3) (@ (@ P2 (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)) (@ (@ tptp.cons_P2971678138204555879n_assn Y3) Ys3)))) (@ (@ P2 Xs) Ys)))))))
% 2.52/3.50 (assert (forall ((P2 (-> tptp.list_P8527749157015355191n_assn tptp.list_int Bool)) (Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_int)) (=> (@ (@ P2 tptp.nil_Pr5671120429643327159n_assn) tptp.nil_int) (=> (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn)) (@ (@ P2 (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)) tptp.nil_int)) (=> (forall ((Y3 tptp.int) (Ys3 tptp.list_int)) (@ (@ P2 tptp.nil_Pr5671120429643327159n_assn) (@ (@ tptp.cons_int Y3) Ys3))) (=> (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn) (Y3 tptp.int) (Ys3 tptp.list_int)) (=> (@ (@ P2 Xs2) Ys3) (@ (@ P2 (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)) (@ (@ tptp.cons_int Y3) Ys3)))) (@ (@ P2 Xs) Ys)))))))
% 2.52/3.50 (assert (forall ((P2 (-> tptp.list_P8527749157015355191n_assn tptp.list_nat Bool)) (Xs tptp.list_P8527749157015355191n_assn) (Ys tptp.list_nat)) (=> (@ (@ P2 tptp.nil_Pr5671120429643327159n_assn) tptp.nil_nat) (=> (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn)) (@ (@ P2 (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)) tptp.nil_nat)) (=> (forall ((Y3 tptp.nat) (Ys3 tptp.list_nat)) (@ (@ P2 tptp.nil_Pr5671120429643327159n_assn) (@ (@ tptp.cons_nat Y3) Ys3))) (=> (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn) (Y3 tptp.nat) (Ys3 tptp.list_nat)) (=> (@ (@ P2 Xs2) Ys3) (@ (@ P2 (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)) (@ (@ tptp.cons_nat Y3) Ys3)))) (@ (@ P2 Xs) Ys)))))))
% 2.52/3.50 (assert (forall ((P2 (-> tptp.list_int tptp.list_P8527749157015355191n_assn Bool)) (Xs tptp.list_int) (Ys tptp.list_P8527749157015355191n_assn)) (=> (@ (@ P2 tptp.nil_int) tptp.nil_Pr5671120429643327159n_assn) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int)) (@ (@ P2 (@ (@ tptp.cons_int X3) Xs2)) tptp.nil_Pr5671120429643327159n_assn)) (=> (forall ((Y3 tptp.produc6575502325842934193n_assn) (Ys3 tptp.list_P8527749157015355191n_assn)) (@ (@ P2 tptp.nil_int) (@ (@ tptp.cons_P2971678138204555879n_assn Y3) Ys3))) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int) (Y3 tptp.produc6575502325842934193n_assn) (Ys3 tptp.list_P8527749157015355191n_assn)) (=> (@ (@ P2 Xs2) Ys3) (@ (@ P2 (@ (@ tptp.cons_int X3) Xs2)) (@ (@ tptp.cons_P2971678138204555879n_assn Y3) Ys3)))) (@ (@ P2 Xs) Ys)))))))
% 2.52/3.50 (assert (forall ((P2 (-> tptp.list_int tptp.list_int Bool)) (Xs tptp.list_int) (Ys tptp.list_int)) (=> (@ (@ P2 tptp.nil_int) tptp.nil_int) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int)) (@ (@ P2 (@ (@ tptp.cons_int X3) Xs2)) tptp.nil_int)) (=> (forall ((Y3 tptp.int) (Ys3 tptp.list_int)) (@ (@ P2 tptp.nil_int) (@ (@ tptp.cons_int Y3) Ys3))) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int) (Y3 tptp.int) (Ys3 tptp.list_int)) (=> (@ (@ P2 Xs2) Ys3) (@ (@ P2 (@ (@ tptp.cons_int X3) Xs2)) (@ (@ tptp.cons_int Y3) Ys3)))) (@ (@ P2 Xs) Ys)))))))
% 2.52/3.50 (assert (forall ((P2 (-> tptp.list_int tptp.list_nat Bool)) (Xs tptp.list_int) (Ys tptp.list_nat)) (=> (@ (@ P2 tptp.nil_int) tptp.nil_nat) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int)) (@ (@ P2 (@ (@ tptp.cons_int X3) Xs2)) tptp.nil_nat)) (=> (forall ((Y3 tptp.nat) (Ys3 tptp.list_nat)) (@ (@ P2 tptp.nil_int) (@ (@ tptp.cons_nat Y3) Ys3))) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int) (Y3 tptp.nat) (Ys3 tptp.list_nat)) (=> (@ (@ P2 Xs2) Ys3) (@ (@ P2 (@ (@ tptp.cons_int X3) Xs2)) (@ (@ tptp.cons_nat Y3) Ys3)))) (@ (@ P2 Xs) Ys)))))))
% 2.52/3.50 (assert (forall ((P2 (-> tptp.list_nat tptp.list_P8527749157015355191n_assn Bool)) (Xs tptp.list_nat) (Ys tptp.list_P8527749157015355191n_assn)) (=> (@ (@ P2 tptp.nil_nat) tptp.nil_Pr5671120429643327159n_assn) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat)) (@ (@ P2 (@ (@ tptp.cons_nat X3) Xs2)) tptp.nil_Pr5671120429643327159n_assn)) (=> (forall ((Y3 tptp.produc6575502325842934193n_assn) (Ys3 tptp.list_P8527749157015355191n_assn)) (@ (@ P2 tptp.nil_nat) (@ (@ tptp.cons_P2971678138204555879n_assn Y3) Ys3))) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y3 tptp.produc6575502325842934193n_assn) (Ys3 tptp.list_P8527749157015355191n_assn)) (=> (@ (@ P2 Xs2) Ys3) (@ (@ P2 (@ (@ tptp.cons_nat X3) Xs2)) (@ (@ tptp.cons_P2971678138204555879n_assn Y3) Ys3)))) (@ (@ P2 Xs) Ys)))))))
% 2.52/3.50 (assert (forall ((P2 (-> tptp.list_nat tptp.list_int Bool)) (Xs tptp.list_nat) (Ys tptp.list_int)) (=> (@ (@ P2 tptp.nil_nat) tptp.nil_int) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat)) (@ (@ P2 (@ (@ tptp.cons_nat X3) Xs2)) tptp.nil_int)) (=> (forall ((Y3 tptp.int) (Ys3 tptp.list_int)) (@ (@ P2 tptp.nil_nat) (@ (@ tptp.cons_int Y3) Ys3))) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y3 tptp.int) (Ys3 tptp.list_int)) (=> (@ (@ P2 Xs2) Ys3) (@ (@ P2 (@ (@ tptp.cons_nat X3) Xs2)) (@ (@ tptp.cons_int Y3) Ys3)))) (@ (@ P2 Xs) Ys)))))))
% 2.52/3.50 (assert (forall ((P2 (-> tptp.list_nat tptp.list_nat Bool)) (Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (@ (@ P2 tptp.nil_nat) tptp.nil_nat) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat)) (@ (@ P2 (@ (@ tptp.cons_nat X3) Xs2)) tptp.nil_nat)) (=> (forall ((Y3 tptp.nat) (Ys3 tptp.list_nat)) (@ (@ P2 tptp.nil_nat) (@ (@ tptp.cons_nat Y3) Ys3))) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y3 tptp.nat) (Ys3 tptp.list_nat)) (=> (@ (@ P2 Xs2) Ys3) (@ (@ P2 (@ (@ tptp.cons_nat X3) Xs2)) (@ (@ tptp.cons_nat Y3) Ys3)))) (@ (@ P2 Xs) Ys)))))))
% 2.52/3.50 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn) (P2 (-> tptp.list_P8527749157015355191n_assn Bool))) (=> (not (= Xs tptp.nil_Pr5671120429643327159n_assn)) (=> (forall ((X3 tptp.produc6575502325842934193n_assn)) (@ P2 (@ (@ tptp.cons_P2971678138204555879n_assn X3) tptp.nil_Pr5671120429643327159n_assn))) (=> (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn)) (=> (not (= Xs2 tptp.nil_Pr5671120429643327159n_assn)) (=> (@ P2 Xs2) (@ P2 (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2))))) (@ P2 Xs))))))
% 2.52/3.50 (assert (forall ((Xs tptp.list_int) (P2 (-> tptp.list_int Bool))) (=> (not (= Xs tptp.nil_int)) (=> (forall ((X3 tptp.int)) (@ P2 (@ (@ tptp.cons_int X3) tptp.nil_int))) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int)) (=> (not (= Xs2 tptp.nil_int)) (=> (@ P2 Xs2) (@ P2 (@ (@ tptp.cons_int X3) Xs2))))) (@ P2 Xs))))))
% 2.52/3.50 (assert (forall ((Xs tptp.list_nat) (P2 (-> tptp.list_nat Bool))) (=> (not (= Xs tptp.nil_nat)) (=> (forall ((X3 tptp.nat)) (@ P2 (@ (@ tptp.cons_nat X3) tptp.nil_nat))) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat)) (=> (not (= Xs2 tptp.nil_nat)) (=> (@ P2 Xs2) (@ P2 (@ (@ tptp.cons_nat X3) Xs2))))) (@ P2 Xs))))))
% 2.52/3.50 (assert (forall ((X tptp.produc1186641810826059865st_int)) (=> (forall ((L2 tptp.list_int)) (not (= X (@ (@ tptp.produc364263696895485585st_int tptp.nil_int) L2)))) (=> (forall ((V tptp.int) (Va tptp.list_int)) (not (= X (@ (@ tptp.produc364263696895485585st_int (@ (@ tptp.cons_int V) Va)) tptp.nil_int)))) (not (forall ((X1 tptp.int) (L1 tptp.list_int) (X23 tptp.int) (L2 tptp.list_int)) (not (= X (@ (@ tptp.produc364263696895485585st_int (@ (@ tptp.cons_int X1) L1)) (@ (@ tptp.cons_int X23) L2))))))))))
% 2.52/3.50 (assert (forall ((X tptp.produc1828647624359046049st_nat)) (=> (forall ((L2 tptp.list_nat)) (not (= X (@ (@ tptp.produc2694037385005941721st_nat tptp.nil_nat) L2)))) (=> (forall ((V tptp.nat) (Va tptp.list_nat)) (not (= X (@ (@ tptp.produc2694037385005941721st_nat (@ (@ tptp.cons_nat V) Va)) tptp.nil_nat)))) (not (forall ((X1 tptp.nat) (L1 tptp.list_nat) (X23 tptp.nat) (L2 tptp.list_nat)) (not (= X (@ (@ tptp.produc2694037385005941721st_nat (@ (@ tptp.cons_nat X1) L1)) (@ (@ tptp.cons_nat X23) L2))))))))))
% 2.52/3.50 (assert (forall ((X tptp.produc337509097454979815n_assn)) (=> (forall ((Ys3 tptp.list_P8527749157015355191n_assn)) (not (= X (@ (@ tptp.produc3014731801419794263n_assn tptp.nil_Pr5671120429643327159n_assn) Ys3)))) (=> (forall ((Xs2 tptp.list_P8527749157015355191n_assn)) (not (= X (@ (@ tptp.produc3014731801419794263n_assn Xs2) tptp.nil_Pr5671120429643327159n_assn)))) (not (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn) (Y3 tptp.produc6575502325842934193n_assn) (Ys3 tptp.list_P8527749157015355191n_assn)) (not (= X (@ (@ tptp.produc3014731801419794263n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)) (@ (@ tptp.cons_P2971678138204555879n_assn Y3) Ys3))))))))))
% 2.52/3.50 (assert (forall ((X tptp.produc1186641810826059865st_int)) (=> (forall ((Ys3 tptp.list_int)) (not (= X (@ (@ tptp.produc364263696895485585st_int tptp.nil_int) Ys3)))) (=> (forall ((Xs2 tptp.list_int)) (not (= X (@ (@ tptp.produc364263696895485585st_int Xs2) tptp.nil_int)))) (not (forall ((X3 tptp.int) (Xs2 tptp.list_int) (Y3 tptp.int) (Ys3 tptp.list_int)) (not (= X (@ (@ tptp.produc364263696895485585st_int (@ (@ tptp.cons_int X3) Xs2)) (@ (@ tptp.cons_int Y3) Ys3))))))))))
% 2.52/3.50 (assert (forall ((X tptp.produc1828647624359046049st_nat)) (=> (forall ((Ys3 tptp.list_nat)) (not (= X (@ (@ tptp.produc2694037385005941721st_nat tptp.nil_nat) Ys3)))) (=> (forall ((Xs2 tptp.list_nat)) (not (= X (@ (@ tptp.produc2694037385005941721st_nat Xs2) tptp.nil_nat)))) (not (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y3 tptp.nat) (Ys3 tptp.list_nat)) (not (= X (@ (@ tptp.produc2694037385005941721st_nat (@ (@ tptp.cons_nat X3) Xs2)) (@ (@ tptp.cons_nat Y3) Ys3))))))))))
% 2.52/3.50 (assert (forall ((X tptp.produc4530688714081574576n_assn)) (=> (forall ((P4 (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn Bool))) (not (= X (@ (@ tptp.produc6115016301897879072n_assn P4) tptp.nil_Pr5671120429643327159n_assn)))) (=> (forall ((P4 (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn Bool)) (X3 tptp.produc6575502325842934193n_assn)) (not (= X (@ (@ tptp.produc6115016301897879072n_assn P4) (@ (@ tptp.cons_P2971678138204555879n_assn X3) tptp.nil_Pr5671120429643327159n_assn))))) (not (forall ((P4 (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn Bool)) (X3 tptp.produc6575502325842934193n_assn) (Y3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn)) (not (= X (@ (@ tptp.produc6115016301897879072n_assn P4) (@ (@ tptp.cons_P2971678138204555879n_assn X3) (@ (@ tptp.cons_P2971678138204555879n_assn Y3) Xs2)))))))))))
% 2.52/3.50 (assert (forall ((X tptp.produc5834231552977413017st_int)) (=> (forall ((P4 (-> tptp.int tptp.int Bool))) (not (= X (@ (@ tptp.produc8618682346314911123st_int P4) tptp.nil_int)))) (=> (forall ((P4 (-> tptp.int tptp.int Bool)) (X3 tptp.int)) (not (= X (@ (@ tptp.produc8618682346314911123st_int P4) (@ (@ tptp.cons_int X3) tptp.nil_int))))) (not (forall ((P4 (-> tptp.int tptp.int Bool)) (X3 tptp.int) (Y3 tptp.int) (Xs2 tptp.list_int)) (not (= X (@ (@ tptp.produc8618682346314911123st_int P4) (@ (@ tptp.cons_int X3) (@ (@ tptp.cons_int Y3) Xs2)))))))))))
% 2.52/3.50 (assert (forall ((X tptp.produc254973753779126261st_nat)) (=> (forall ((P4 (-> tptp.nat tptp.nat Bool))) (not (= X (@ (@ tptp.produc4727192421694094319st_nat P4) tptp.nil_nat)))) (=> (forall ((P4 (-> tptp.nat tptp.nat Bool)) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc4727192421694094319st_nat P4) (@ (@ tptp.cons_nat X3) tptp.nil_nat))))) (not (forall ((P4 (-> tptp.nat tptp.nat Bool)) (X3 tptp.nat) (Y3 tptp.nat) (Xs2 tptp.list_nat)) (not (= X (@ (@ tptp.produc4727192421694094319st_nat P4) (@ (@ tptp.cons_nat X3) (@ (@ tptp.cons_nat Y3) Xs2)))))))))))
% 2.52/3.50 (assert (forall ((X tptp.produc4530688714081574576n_assn)) (=> (forall ((P4 (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn Bool))) (not (= X (@ (@ tptp.produc6115016301897879072n_assn P4) tptp.nil_Pr5671120429643327159n_assn)))) (not (forall ((P4 (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn Bool)) (X3 tptp.produc6575502325842934193n_assn) (Ys3 tptp.list_P8527749157015355191n_assn)) (not (= X (@ (@ tptp.produc6115016301897879072n_assn P4) (@ (@ tptp.cons_P2971678138204555879n_assn X3) Ys3)))))))))
% 2.52/3.50 (assert (forall ((X tptp.produc5834231552977413017st_int)) (=> (forall ((P4 (-> tptp.int tptp.int Bool))) (not (= X (@ (@ tptp.produc8618682346314911123st_int P4) tptp.nil_int)))) (not (forall ((P4 (-> tptp.int tptp.int Bool)) (X3 tptp.int) (Ys3 tptp.list_int)) (not (= X (@ (@ tptp.produc8618682346314911123st_int P4) (@ (@ tptp.cons_int X3) Ys3)))))))))
% 2.52/3.50 (assert (forall ((X tptp.produc254973753779126261st_nat)) (=> (forall ((P4 (-> tptp.nat tptp.nat Bool))) (not (= X (@ (@ tptp.produc4727192421694094319st_nat P4) tptp.nil_nat)))) (not (forall ((P4 (-> tptp.nat tptp.nat Bool)) (X3 tptp.nat) (Ys3 tptp.list_nat)) (not (= X (@ (@ tptp.produc4727192421694094319st_nat P4) (@ (@ tptp.cons_nat X3) Ys3)))))))))
% 2.52/3.50 (assert (forall ((X tptp.produc858023921370090807n_assn)) (=> (forall ((Xs1 tptp.list_P8527749157015355191n_assn) (Xs22 tptp.list_P8527749157015355191n_assn)) (not (= X (@ (@ tptp.produc7497315745449715623n_assn (@ (@ tptp.produc3014731801419794263n_assn Xs1) Xs22)) tptp.nil_Pr5671120429643327159n_assn)))) (=> (forall ((Xs1 tptp.list_P8527749157015355191n_assn) (Xs22 tptp.list_P8527749157015355191n_assn) (X3 tptp.produc6575502325842934193n_assn)) (not (= X (@ (@ tptp.produc7497315745449715623n_assn (@ (@ tptp.produc3014731801419794263n_assn Xs1) Xs22)) (@ (@ tptp.cons_P2971678138204555879n_assn X3) tptp.nil_Pr5671120429643327159n_assn))))) (not (forall ((Xs1 tptp.list_P8527749157015355191n_assn) (Xs22 tptp.list_P8527749157015355191n_assn) (X1 tptp.produc6575502325842934193n_assn) (X23 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn)) (not (= X (@ (@ tptp.produc7497315745449715623n_assn (@ (@ tptp.produc3014731801419794263n_assn Xs1) Xs22)) (@ (@ tptp.cons_P2971678138204555879n_assn X1) (@ (@ tptp.cons_P2971678138204555879n_assn X23) Xs2)))))))))))
% 2.52/3.50 (assert (forall ((X tptp.produc5625914783551145028st_int)) (=> (forall ((Xs1 tptp.list_int) (Xs22 tptp.list_int)) (not (= X (@ (@ tptp.produc6571967182415643454st_int (@ (@ tptp.produc364263696895485585st_int Xs1) Xs22)) tptp.nil_int)))) (=> (forall ((Xs1 tptp.list_int) (Xs22 tptp.list_int) (X3 tptp.int)) (not (= X (@ (@ tptp.produc6571967182415643454st_int (@ (@ tptp.produc364263696895485585st_int Xs1) Xs22)) (@ (@ tptp.cons_int X3) tptp.nil_int))))) (not (forall ((Xs1 tptp.list_int) (Xs22 tptp.list_int) (X1 tptp.int) (X23 tptp.int) (Xs2 tptp.list_int)) (not (= X (@ (@ tptp.produc6571967182415643454st_int (@ (@ tptp.produc364263696895485585st_int Xs1) Xs22)) (@ (@ tptp.cons_int X1) (@ (@ tptp.cons_int X23) Xs2)))))))))))
% 2.52/3.50 (assert (forall ((X tptp.produc8368264342088597808st_nat)) (=> (forall ((Xs1 tptp.list_nat) (Xs22 tptp.list_nat)) (not (= X (@ (@ tptp.produc1778712578675790378st_nat (@ (@ tptp.produc2694037385005941721st_nat Xs1) Xs22)) tptp.nil_nat)))) (=> (forall ((Xs1 tptp.list_nat) (Xs22 tptp.list_nat) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc1778712578675790378st_nat (@ (@ tptp.produc2694037385005941721st_nat Xs1) Xs22)) (@ (@ tptp.cons_nat X3) tptp.nil_nat))))) (not (forall ((Xs1 tptp.list_nat) (Xs22 tptp.list_nat) (X1 tptp.nat) (X23 tptp.nat) (Xs2 tptp.list_nat)) (not (= X (@ (@ tptp.produc1778712578675790378st_nat (@ (@ tptp.produc2694037385005941721st_nat Xs1) Xs22)) (@ (@ tptp.cons_nat X1) (@ (@ tptp.cons_nat X23) Xs2)))))))))))
% 2.52/3.50 (assert (forall ((X tptp.produc6691681559177096800n_assn)) (=> (forall ((R3 (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn Bool)) (X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn) (Y3 tptp.produc6575502325842934193n_assn) (Ys3 tptp.list_P8527749157015355191n_assn)) (not (= X (@ (@ tptp.produc218933061472242640n_assn R3) (@ (@ tptp.produc3014731801419794263n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)) (@ (@ tptp.cons_P2971678138204555879n_assn Y3) Ys3)))))) (=> (forall ((R3 (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn Bool)) (Xs2 tptp.list_P8527749157015355191n_assn)) (not (= X (@ (@ tptp.produc218933061472242640n_assn R3) (@ (@ tptp.produc3014731801419794263n_assn Xs2) tptp.nil_Pr5671120429643327159n_assn))))) (not (forall ((R3 (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn Bool)) (V tptp.produc6575502325842934193n_assn) (Va tptp.list_P8527749157015355191n_assn)) (not (= X (@ (@ tptp.produc218933061472242640n_assn R3) (@ (@ tptp.produc3014731801419794263n_assn tptp.nil_Pr5671120429643327159n_assn) (@ (@ tptp.cons_P2971678138204555879n_assn V) Va)))))))))))
% 2.52/3.50 (assert (forall ((X tptp.produc6134427711877206866st_int)) (=> (forall ((R3 (-> tptp.int tptp.int Bool)) (X3 tptp.int) (Xs2 tptp.list_int) (Y3 tptp.int) (Ys3 tptp.list_int)) (not (= X (@ (@ tptp.produc6519019827157805250st_int R3) (@ (@ tptp.produc364263696895485585st_int (@ (@ tptp.cons_int X3) Xs2)) (@ (@ tptp.cons_int Y3) Ys3)))))) (=> (forall ((R3 (-> tptp.int tptp.int Bool)) (Xs2 tptp.list_int)) (not (= X (@ (@ tptp.produc6519019827157805250st_int R3) (@ (@ tptp.produc364263696895485585st_int Xs2) tptp.nil_int))))) (not (forall ((R3 (-> tptp.int tptp.int Bool)) (V tptp.int) (Va tptp.list_int)) (not (= X (@ (@ tptp.produc6519019827157805250st_int R3) (@ (@ tptp.produc364263696895485585st_int tptp.nil_int) (@ (@ tptp.cons_int V) Va)))))))))))
% 2.52/3.50 (assert (forall ((X tptp.produc4787317212837456354st_nat)) (=> (forall ((R3 (-> tptp.nat tptp.nat Bool)) (X3 tptp.nat) (Xs2 tptp.list_nat) (Y3 tptp.nat) (Ys3 tptp.list_nat)) (not (= X (@ (@ tptp.produc3127733452865184594st_nat R3) (@ (@ tptp.produc2694037385005941721st_nat (@ (@ tptp.cons_nat X3) Xs2)) (@ (@ tptp.cons_nat Y3) Ys3)))))) (=> (forall ((R3 (-> tptp.nat tptp.nat Bool)) (Xs2 tptp.list_nat)) (not (= X (@ (@ tptp.produc3127733452865184594st_nat R3) (@ (@ tptp.produc2694037385005941721st_nat Xs2) tptp.nil_nat))))) (not (forall ((R3 (-> tptp.nat tptp.nat Bool)) (V tptp.nat) (Va tptp.list_nat)) (not (= X (@ (@ tptp.produc3127733452865184594st_nat R3) (@ (@ tptp.produc2694037385005941721st_nat tptp.nil_nat) (@ (@ tptp.cons_nat V) Va)))))))))))
% 2.52/3.50 (assert (forall ((X tptp.produc6691681559177096800n_assn)) (=> (forall ((R3 (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn Bool)) (Sl tptp.list_P8527749157015355191n_assn)) (not (= X (@ (@ tptp.produc218933061472242640n_assn R3) (@ (@ tptp.produc3014731801419794263n_assn Sl) tptp.nil_Pr5671120429643327159n_assn))))) (not (forall ((R3 (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn Bool)) (Sl tptp.list_P8527749157015355191n_assn) (X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn)) (not (= X (@ (@ tptp.produc218933061472242640n_assn R3) (@ (@ tptp.produc3014731801419794263n_assn Sl) (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2))))))))))
% 2.52/3.50 (assert (forall ((X tptp.produc6134427711877206866st_int)) (=> (forall ((R3 (-> tptp.int tptp.int Bool)) (Sl tptp.list_int)) (not (= X (@ (@ tptp.produc6519019827157805250st_int R3) (@ (@ tptp.produc364263696895485585st_int Sl) tptp.nil_int))))) (not (forall ((R3 (-> tptp.int tptp.int Bool)) (Sl tptp.list_int) (X3 tptp.int) (Xs2 tptp.list_int)) (not (= X (@ (@ tptp.produc6519019827157805250st_int R3) (@ (@ tptp.produc364263696895485585st_int Sl) (@ (@ tptp.cons_int X3) Xs2))))))))))
% 2.52/3.50 (assert (forall ((X tptp.produc4787317212837456354st_nat)) (=> (forall ((R3 (-> tptp.nat tptp.nat Bool)) (Sl tptp.list_nat)) (not (= X (@ (@ tptp.produc3127733452865184594st_nat R3) (@ (@ tptp.produc2694037385005941721st_nat Sl) tptp.nil_nat))))) (not (forall ((R3 (-> tptp.nat tptp.nat Bool)) (Sl tptp.list_nat) (X3 tptp.nat) (Xs2 tptp.list_nat)) (not (= X (@ (@ tptp.produc3127733452865184594st_nat R3) (@ (@ tptp.produc2694037385005941721st_nat Sl) (@ (@ tptp.cons_nat X3) Xs2))))))))))
% 2.52/3.50 (assert (forall ((X tptp.produc3251403909973641504n_assn)) (=> (forall ((P4 (-> tptp.produc6575502325842934193n_assn Bool)) (Yes tptp.list_P8527749157015355191n_assn) (No tptp.list_P8527749157015355191n_assn)) (not (= X (@ (@ tptp.produc7995034776595945426n_assn P4) (@ (@ tptp.produc7497315745449715623n_assn (@ (@ tptp.produc3014731801419794263n_assn Yes) No)) tptp.nil_Pr5671120429643327159n_assn))))) (not (forall ((P4 (-> tptp.produc6575502325842934193n_assn Bool)) (Yes tptp.list_P8527749157015355191n_assn) (No tptp.list_P8527749157015355191n_assn) (X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn)) (not (= X (@ (@ tptp.produc7995034776595945426n_assn P4) (@ (@ tptp.produc7497315745449715623n_assn (@ (@ tptp.produc3014731801419794263n_assn Yes) No)) (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2))))))))))
% 2.52/3.50 (assert (forall ((X tptp.produc141556263843406102st_int)) (=> (forall ((P4 (-> tptp.int Bool)) (Yes tptp.list_int) (No tptp.list_int)) (not (= X (@ (@ tptp.produc3116401902672145424st_int P4) (@ (@ tptp.produc6571967182415643454st_int (@ (@ tptp.produc364263696895485585st_int Yes) No)) tptp.nil_int))))) (not (forall ((P4 (-> tptp.int Bool)) (Yes tptp.list_int) (No tptp.list_int) (X3 tptp.int) (Xs2 tptp.list_int)) (not (= X (@ (@ tptp.produc3116401902672145424st_int P4) (@ (@ tptp.produc6571967182415643454st_int (@ (@ tptp.produc364263696895485585st_int Yes) No)) (@ (@ tptp.cons_int X3) Xs2))))))))))
% 2.52/3.50 (assert (forall ((X tptp.produc6155704871766690142st_nat)) (=> (forall ((P4 (-> tptp.nat Bool)) (Yes tptp.list_nat) (No tptp.list_nat)) (not (= X (@ (@ tptp.produc2404789219858123352st_nat P4) (@ (@ tptp.produc1778712578675790378st_nat (@ (@ tptp.produc2694037385005941721st_nat Yes) No)) tptp.nil_nat))))) (not (forall ((P4 (-> tptp.nat Bool)) (Yes tptp.list_nat) (No tptp.list_nat) (X3 tptp.nat) (Xs2 tptp.list_nat)) (not (= X (@ (@ tptp.produc2404789219858123352st_nat P4) (@ (@ tptp.produc1778712578675790378st_nat (@ (@ tptp.produc2694037385005941721st_nat Yes) No)) (@ (@ tptp.cons_nat X3) Xs2))))))))))
% 2.52/3.50 (assert (forall ((X tptp.produc6691681559177096800n_assn)) (=> (forall ((P4 (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn Bool))) (not (= X (@ (@ tptp.produc218933061472242640n_assn P4) (@ (@ tptp.produc3014731801419794263n_assn tptp.nil_Pr5671120429643327159n_assn) tptp.nil_Pr5671120429643327159n_assn))))) (=> (forall ((P4 (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn Bool)) (A6 tptp.produc6575502325842934193n_assn) (As tptp.list_P8527749157015355191n_assn) (B5 tptp.produc6575502325842934193n_assn) (Bs2 tptp.list_P8527749157015355191n_assn)) (not (= X (@ (@ tptp.produc218933061472242640n_assn P4) (@ (@ tptp.produc3014731801419794263n_assn (@ (@ tptp.cons_P2971678138204555879n_assn A6) As)) (@ (@ tptp.cons_P2971678138204555879n_assn B5) Bs2)))))) (=> (forall ((P4 (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn Bool)) (V tptp.produc6575502325842934193n_assn) (Va tptp.list_P8527749157015355191n_assn)) (not (= X (@ (@ tptp.produc218933061472242640n_assn P4) (@ (@ tptp.produc3014731801419794263n_assn (@ (@ tptp.cons_P2971678138204555879n_assn V) Va)) tptp.nil_Pr5671120429643327159n_assn))))) (not (forall ((P4 (-> tptp.produc6575502325842934193n_assn tptp.produc6575502325842934193n_assn Bool)) (V tptp.produc6575502325842934193n_assn) (Va tptp.list_P8527749157015355191n_assn)) (not (= X (@ (@ tptp.produc218933061472242640n_assn P4) (@ (@ tptp.produc3014731801419794263n_assn tptp.nil_Pr5671120429643327159n_assn) (@ (@ tptp.cons_P2971678138204555879n_assn V) Va))))))))))))
% 2.52/3.50 (assert (forall ((X tptp.produc4920635200459206554st_int)) (=> (forall ((P4 (-> tptp.produc6575502325842934193n_assn tptp.int Bool))) (not (= X (@ (@ tptp.produc7143791561355829714st_int P4) (@ (@ tptp.produc1996262876970182428st_int tptp.nil_Pr5671120429643327159n_assn) tptp.nil_int))))) (=> (forall ((P4 (-> tptp.produc6575502325842934193n_assn tptp.int Bool)) (A6 tptp.produc6575502325842934193n_assn) (As tptp.list_P8527749157015355191n_assn) (B5 tptp.int) (Bs2 tptp.list_int)) (not (= X (@ (@ tptp.produc7143791561355829714st_int P4) (@ (@ tptp.produc1996262876970182428st_int (@ (@ tptp.cons_P2971678138204555879n_assn A6) As)) (@ (@ tptp.cons_int B5) Bs2)))))) (=> (forall ((P4 (-> tptp.produc6575502325842934193n_assn tptp.int Bool)) (V tptp.produc6575502325842934193n_assn) (Va tptp.list_P8527749157015355191n_assn)) (not (= X (@ (@ tptp.produc7143791561355829714st_int P4) (@ (@ tptp.produc1996262876970182428st_int (@ (@ tptp.cons_P2971678138204555879n_assn V) Va)) tptp.nil_int))))) (not (forall ((P4 (-> tptp.produc6575502325842934193n_assn tptp.int Bool)) (V tptp.int) (Va tptp.list_int)) (not (= X (@ (@ tptp.produc7143791561355829714st_int P4) (@ (@ tptp.produc1996262876970182428st_int tptp.nil_Pr5671120429643327159n_assn) (@ (@ tptp.cons_int V) Va))))))))))))
% 2.52/3.50 (assert (forall ((X tptp.produc6280221377895650458st_nat)) (=> (forall ((P4 (-> tptp.produc6575502325842934193n_assn tptp.nat Bool))) (not (= X (@ (@ tptp.produc6179912464936081618st_nat P4) (@ (@ tptp.produc6174113896479379136st_nat tptp.nil_Pr5671120429643327159n_assn) tptp.nil_nat))))) (=> (forall ((P4 (-> tptp.produc6575502325842934193n_assn tptp.nat Bool)) (A6 tptp.produc6575502325842934193n_assn) (As tptp.list_P8527749157015355191n_assn) (B5 tptp.nat) (Bs2 tptp.list_nat)) (not (= X (@ (@ tptp.produc6179912464936081618st_nat P4) (@ (@ tptp.produc6174113896479379136st_nat (@ (@ tptp.cons_P2971678138204555879n_assn A6) As)) (@ (@ tptp.cons_nat B5) Bs2)))))) (=> (forall ((P4 (-> tptp.produc6575502325842934193n_assn tptp.nat Bool)) (V tptp.produc6575502325842934193n_assn) (Va tptp.list_P8527749157015355191n_assn)) (not (= X (@ (@ tptp.produc6179912464936081618st_nat P4) (@ (@ tptp.produc6174113896479379136st_nat (@ (@ tptp.cons_P2971678138204555879n_assn V) Va)) tptp.nil_nat))))) (not (forall ((P4 (-> tptp.produc6575502325842934193n_assn tptp.nat Bool)) (V tptp.nat) (Va tptp.list_nat)) (not (= X (@ (@ tptp.produc6179912464936081618st_nat P4) (@ (@ tptp.produc6174113896479379136st_nat tptp.nil_Pr5671120429643327159n_assn) (@ (@ tptp.cons_nat V) Va))))))))))))
% 2.52/3.50 (assert (forall ((X tptp.produc4944321512348556200n_assn)) (=> (forall ((P4 (-> tptp.int tptp.produc6575502325842934193n_assn Bool))) (not (= X (@ (@ tptp.produc3092413063583913184n_assn P4) (@ (@ tptp.produc4510294837168919970n_assn tptp.nil_int) tptp.nil_Pr5671120429643327159n_assn))))) (=> (forall ((P4 (-> tptp.int tptp.produc6575502325842934193n_assn Bool)) (A6 tptp.int) (As tptp.list_int) (B5 tptp.produc6575502325842934193n_assn) (Bs2 tptp.list_P8527749157015355191n_assn)) (not (= X (@ (@ tptp.produc3092413063583913184n_assn P4) (@ (@ tptp.produc4510294837168919970n_assn (@ (@ tptp.cons_int A6) As)) (@ (@ tptp.cons_P2971678138204555879n_assn B5) Bs2)))))) (=> (forall ((P4 (-> tptp.int tptp.produc6575502325842934193n_assn Bool)) (V tptp.int) (Va tptp.list_int)) (not (= X (@ (@ tptp.produc3092413063583913184n_assn P4) (@ (@ tptp.produc4510294837168919970n_assn (@ (@ tptp.cons_int V) Va)) tptp.nil_Pr5671120429643327159n_assn))))) (not (forall ((P4 (-> tptp.int tptp.produc6575502325842934193n_assn Bool)) (V tptp.produc6575502325842934193n_assn) (Va tptp.list_P8527749157015355191n_assn)) (not (= X (@ (@ tptp.produc3092413063583913184n_assn P4) (@ (@ tptp.produc4510294837168919970n_assn tptp.nil_int) (@ (@ tptp.cons_P2971678138204555879n_assn V) Va))))))))))))
% 2.52/3.50 (assert (forall ((X tptp.produc6134427711877206866st_int)) (=> (forall ((P4 (-> tptp.int tptp.int Bool))) (not (= X (@ (@ tptp.produc6519019827157805250st_int P4) (@ (@ tptp.produc364263696895485585st_int tptp.nil_int) tptp.nil_int))))) (=> (forall ((P4 (-> tptp.int tptp.int Bool)) (A6 tptp.int) (As tptp.list_int) (B5 tptp.int) (Bs2 tptp.list_int)) (not (= X (@ (@ tptp.produc6519019827157805250st_int P4) (@ (@ tptp.produc364263696895485585st_int (@ (@ tptp.cons_int A6) As)) (@ (@ tptp.cons_int B5) Bs2)))))) (=> (forall ((P4 (-> tptp.int tptp.int Bool)) (V tptp.int) (Va tptp.list_int)) (not (= X (@ (@ tptp.produc6519019827157805250st_int P4) (@ (@ tptp.produc364263696895485585st_int (@ (@ tptp.cons_int V) Va)) tptp.nil_int))))) (not (forall ((P4 (-> tptp.int tptp.int Bool)) (V tptp.int) (Va tptp.list_int)) (not (= X (@ (@ tptp.produc6519019827157805250st_int P4) (@ (@ tptp.produc364263696895485585st_int tptp.nil_int) (@ (@ tptp.cons_int V) Va))))))))))))
% 2.52/3.50 (assert (forall ((X tptp.produc5074578776457504922st_nat)) (=> (forall ((P4 (-> tptp.int tptp.nat Bool))) (not (= X (@ (@ tptp.produc3135705617881911306st_nat P4) (@ (@ tptp.produc4542114716404682293st_nat tptp.nil_int) tptp.nil_nat))))) (=> (forall ((P4 (-> tptp.int tptp.nat Bool)) (A6 tptp.int) (As tptp.list_int) (B5 tptp.nat) (Bs2 tptp.list_nat)) (not (= X (@ (@ tptp.produc3135705617881911306st_nat P4) (@ (@ tptp.produc4542114716404682293st_nat (@ (@ tptp.cons_int A6) As)) (@ (@ tptp.cons_nat B5) Bs2)))))) (=> (forall ((P4 (-> tptp.int tptp.nat Bool)) (V tptp.int) (Va tptp.list_int)) (not (= X (@ (@ tptp.produc3135705617881911306st_nat P4) (@ (@ tptp.produc4542114716404682293st_nat (@ (@ tptp.cons_int V) Va)) tptp.nil_nat))))) (not (forall ((P4 (-> tptp.int tptp.nat Bool)) (V tptp.nat) (Va tptp.list_nat)) (not (= X (@ (@ tptp.produc3135705617881911306st_nat P4) (@ (@ tptp.produc4542114716404682293st_nat tptp.nil_int) (@ (@ tptp.cons_nat V) Va))))))))))))
% 2.52/3.50 (assert (forall ((X tptp.produc3272579373640082088n_assn)) (=> (forall ((P4 (-> tptp.nat tptp.produc6575502325842934193n_assn Bool))) (not (= X (@ (@ tptp.produc1692222275734866400n_assn P4) (@ (@ tptp.produc7706768604797473534n_assn tptp.nil_nat) tptp.nil_Pr5671120429643327159n_assn))))) (=> (forall ((P4 (-> tptp.nat tptp.produc6575502325842934193n_assn Bool)) (A6 tptp.nat) (As tptp.list_nat) (B5 tptp.produc6575502325842934193n_assn) (Bs2 tptp.list_P8527749157015355191n_assn)) (not (= X (@ (@ tptp.produc1692222275734866400n_assn P4) (@ (@ tptp.produc7706768604797473534n_assn (@ (@ tptp.cons_nat A6) As)) (@ (@ tptp.cons_P2971678138204555879n_assn B5) Bs2)))))) (=> (forall ((P4 (-> tptp.nat tptp.produc6575502325842934193n_assn Bool)) (V tptp.nat) (Va tptp.list_nat)) (not (= X (@ (@ tptp.produc1692222275734866400n_assn P4) (@ (@ tptp.produc7706768604797473534n_assn (@ (@ tptp.cons_nat V) Va)) tptp.nil_Pr5671120429643327159n_assn))))) (not (forall ((P4 (-> tptp.nat tptp.produc6575502325842934193n_assn Bool)) (V tptp.produc6575502325842934193n_assn) (Va tptp.list_P8527749157015355191n_assn)) (not (= X (@ (@ tptp.produc1692222275734866400n_assn P4) (@ (@ tptp.produc7706768604797473534n_assn tptp.nil_nat) (@ (@ tptp.cons_P2971678138204555879n_assn V) Va))))))))))))
% 2.52/3.50 (assert (forall ((X tptp.produc5847166148257158298st_int)) (=> (forall ((P4 (-> tptp.nat tptp.int Bool))) (not (= X (@ (@ tptp.produc6511047662141078538st_int P4) (@ (@ tptp.produc7739558402351520821st_int tptp.nil_nat) tptp.nil_int))))) (=> (forall ((P4 (-> tptp.nat tptp.int Bool)) (A6 tptp.nat) (As tptp.list_nat) (B5 tptp.int) (Bs2 tptp.list_int)) (not (= X (@ (@ tptp.produc6511047662141078538st_int P4) (@ (@ tptp.produc7739558402351520821st_int (@ (@ tptp.cons_nat A6) As)) (@ (@ tptp.cons_int B5) Bs2)))))) (=> (forall ((P4 (-> tptp.nat tptp.int Bool)) (V tptp.nat) (Va tptp.list_nat)) (not (= X (@ (@ tptp.produc6511047662141078538st_int P4) (@ (@ tptp.produc7739558402351520821st_int (@ (@ tptp.cons_nat V) Va)) tptp.nil_int))))) (not (forall ((P4 (-> tptp.nat tptp.int Bool)) (V tptp.int) (Va tptp.list_int)) (not (= X (@ (@ tptp.produc6511047662141078538st_int P4) (@ (@ tptp.produc7739558402351520821st_int tptp.nil_nat) (@ (@ tptp.cons_int V) Va))))))))))))
% 2.52/3.50 (assert (forall ((X tptp.produc4787317212837456354st_nat)) (=> (forall ((P4 (-> tptp.nat tptp.nat Bool))) (not (= X (@ (@ tptp.produc3127733452865184594st_nat P4) (@ (@ tptp.produc2694037385005941721st_nat tptp.nil_nat) tptp.nil_nat))))) (=> (forall ((P4 (-> tptp.nat tptp.nat Bool)) (A6 tptp.nat) (As tptp.list_nat) (B5 tptp.nat) (Bs2 tptp.list_nat)) (not (= X (@ (@ tptp.produc3127733452865184594st_nat P4) (@ (@ tptp.produc2694037385005941721st_nat (@ (@ tptp.cons_nat A6) As)) (@ (@ tptp.cons_nat B5) Bs2)))))) (=> (forall ((P4 (-> tptp.nat tptp.nat Bool)) (V tptp.nat) (Va tptp.list_nat)) (not (= X (@ (@ tptp.produc3127733452865184594st_nat P4) (@ (@ tptp.produc2694037385005941721st_nat (@ (@ tptp.cons_nat V) Va)) tptp.nil_nat))))) (not (forall ((P4 (-> tptp.nat tptp.nat Bool)) (V tptp.nat) (Va tptp.list_nat)) (not (= X (@ (@ tptp.produc3127733452865184594st_nat P4) (@ (@ tptp.produc2694037385005941721st_nat tptp.nil_nat) (@ (@ tptp.cons_nat V) Va))))))))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B)) A))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) A))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) A))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.ord_less_int B) (@ tptp.uminus_uminus_int A)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.ord_less_rat B) (@ tptp.uminus_uminus_rat A)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le6747313008572928689nteger B) (@ tptp.uminus1351360451143612070nteger A)))))
% 2.52/3.50 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (X tptp.nat) (Y tptp.nat) (Fs tptp.list_nat_nat)) (=> (@ (@ tptp.ord_less_nat (@ F2 X)) (@ F2 Y)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ tptp.measures_nat (@ (@ tptp.cons_nat_nat F2) Fs))))))
% 2.52/3.50 (assert (forall ((F2 (-> tptp.int tptp.nat)) (X tptp.int) (Y tptp.int) (Fs tptp.list_int_nat)) (=> (@ (@ tptp.ord_less_nat (@ F2 X)) (@ F2 Y)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) (@ tptp.measures_int (@ (@ tptp.cons_int_nat F2) Fs))))))
% 2.52/3.50 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat A) X) (@ (@ tptp.ord_le7866589430770878221at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) X))))
% 2.52/3.50 (assert (forall ((A tptp.set_nat) (X tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A) X) (@ (@ tptp.ord_less_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) X))))
% 2.52/3.50 (assert (forall ((A (-> tptp.product_prod_int_int Bool)) (X (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le8213806771718485336_int_o A) X) (@ (@ tptp.ord_le8213806771718485336_int_o (@ (@ tptp.inf_in3604695632404883862_int_o A) B)) X))))
% 2.52/3.50 (assert (forall ((A tptp.assn) (X tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.ord_less_assn A) X) (@ (@ tptp.ord_less_assn (@ (@ tptp.inf_inf_assn A) B)) X))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (X tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) X) (@ (@ tptp.ord_less_rat (@ (@ tptp.inf_inf_rat A) B)) X))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (X tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) X) (@ (@ tptp.ord_less_nat (@ (@ tptp.inf_inf_nat A) B)) X))))
% 2.52/3.50 (assert (forall ((A tptp.int) (X tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) X) (@ (@ tptp.ord_less_int (@ (@ tptp.inf_inf_int A) B)) X))))
% 2.52/3.50 (assert (forall ((B tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat B) X) (@ (@ tptp.ord_le7866589430770878221at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) X))))
% 2.52/3.50 (assert (forall ((B tptp.set_nat) (X tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B) X) (@ (@ tptp.ord_less_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) X))))
% 2.52/3.50 (assert (forall ((B (-> tptp.product_prod_int_int Bool)) (X (-> tptp.product_prod_int_int Bool)) (A (-> tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le8213806771718485336_int_o B) X) (@ (@ tptp.ord_le8213806771718485336_int_o (@ (@ tptp.inf_in3604695632404883862_int_o A) B)) X))))
% 2.52/3.50 (assert (forall ((B tptp.assn) (X tptp.assn) (A tptp.assn)) (=> (@ (@ tptp.ord_less_assn B) X) (@ (@ tptp.ord_less_assn (@ (@ tptp.inf_inf_assn A) B)) X))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (X tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) X) (@ (@ tptp.ord_less_rat (@ (@ tptp.inf_inf_rat A) B)) X))))
% 2.52/3.50 (assert (forall ((B tptp.nat) (X tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) X) (@ (@ tptp.ord_less_nat (@ (@ tptp.inf_inf_nat A) B)) X))))
% 2.52/3.50 (assert (forall ((B tptp.int) (X tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) X) (@ (@ tptp.ord_less_int (@ (@ tptp.inf_inf_int A) B)) X))))
% 2.52/3.50 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat A) B) (= (@ (@ tptp.inf_in2572325071724192079at_nat A) B) A))))
% 2.52/3.50 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A) B) (= (@ (@ tptp.inf_inf_set_nat A) B) A))))
% 2.52/3.50 (assert (forall ((A (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le8213806771718485336_int_o A) B) (= (@ (@ tptp.inf_in3604695632404883862_int_o A) B) A))))
% 2.52/3.50 (assert (forall ((A tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.ord_less_assn A) B) (= (@ (@ tptp.inf_inf_assn A) B) A))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (= (@ (@ tptp.inf_inf_rat A) B) A))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.inf_inf_nat A) B) A))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (= (@ (@ tptp.inf_inf_int A) B) A))))
% 2.52/3.50 (assert (forall ((B tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat B) A) (= (@ (@ tptp.inf_in2572325071724192079at_nat A) B) B))))
% 2.52/3.50 (assert (forall ((B tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B) A) (= (@ (@ tptp.inf_inf_set_nat A) B) B))))
% 2.52/3.50 (assert (forall ((B (-> tptp.product_prod_int_int Bool)) (A (-> tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le8213806771718485336_int_o B) A) (= (@ (@ tptp.inf_in3604695632404883862_int_o A) B) B))))
% 2.52/3.50 (assert (forall ((B tptp.assn) (A tptp.assn)) (=> (@ (@ tptp.ord_less_assn B) A) (= (@ (@ tptp.inf_inf_assn A) B) B))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (= (@ (@ tptp.inf_inf_rat A) B) B))))
% 2.52/3.50 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (= (@ (@ tptp.inf_inf_nat A) B) B))))
% 2.52/3.50 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (= (@ (@ tptp.inf_inf_int A) B) B))))
% 2.52/3.50 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le7866589430770878221at_nat A))) (=> (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))))
% 2.52/3.50 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))))
% 2.52/3.50 (assert (forall ((A (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool)) (C (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.ord_le8213806771718485336_int_o A))) (=> (@ _let_1 (@ (@ tptp.inf_in3604695632404883862_int_o B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))))
% 2.52/3.50 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_assn B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_rat B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_nat B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_int B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))))
% 2.52/3.50 (assert (= tptp.ord_le7866589430770878221at_nat (lambda ((A2 tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (and (= A2 (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2)) (not (= A2 B2))))))
% 2.52/3.50 (assert (= tptp.ord_less_set_nat (lambda ((A2 tptp.set_nat) (B2 tptp.set_nat)) (and (= A2 (@ (@ tptp.inf_inf_set_nat A2) B2)) (not (= A2 B2))))))
% 2.52/3.50 (assert (= tptp.ord_le8213806771718485336_int_o (lambda ((A2 (-> tptp.product_prod_int_int Bool)) (B2 (-> tptp.product_prod_int_int Bool))) (and (= A2 (@ (@ tptp.inf_in3604695632404883862_int_o A2) B2)) (not (= A2 B2))))))
% 2.52/3.50 (assert (= tptp.ord_less_assn (lambda ((A2 tptp.assn) (B2 tptp.assn)) (and (= A2 (@ (@ tptp.inf_inf_assn A2) B2)) (not (= A2 B2))))))
% 2.52/3.50 (assert (= tptp.ord_less_rat (lambda ((A2 tptp.rat) (B2 tptp.rat)) (and (= A2 (@ (@ tptp.inf_inf_rat A2) B2)) (not (= A2 B2))))))
% 2.52/3.50 (assert (= tptp.ord_less_nat (lambda ((A2 tptp.nat) (B2 tptp.nat)) (and (= A2 (@ (@ tptp.inf_inf_nat A2) B2)) (not (= A2 B2))))))
% 2.52/3.50 (assert (= tptp.ord_less_int (lambda ((A2 tptp.int) (B2 tptp.int)) (and (= A2 (@ (@ tptp.inf_inf_int A2) B2)) (not (= A2 B2))))))
% 2.52/3.50 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat A) C) (@ (@ tptp.ord_le7866589430770878221at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) C))))
% 2.52/3.50 (assert (forall ((A tptp.set_nat) (C tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A) C) (@ (@ tptp.ord_less_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) C))))
% 2.52/3.50 (assert (forall ((A (-> tptp.product_prod_int_int Bool)) (C (-> tptp.product_prod_int_int Bool)) (B (-> tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le8213806771718485336_int_o A) C) (@ (@ tptp.ord_le8213806771718485336_int_o (@ (@ tptp.inf_in3604695632404883862_int_o A) B)) C))))
% 2.52/3.50 (assert (forall ((A tptp.assn) (C tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.ord_less_assn A) C) (@ (@ tptp.ord_less_assn (@ (@ tptp.inf_inf_assn A) B)) C))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.inf_inf_rat A) B)) C))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.inf_inf_nat A) B)) C))))
% 2.52/3.50 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) C) (@ (@ tptp.ord_less_int (@ (@ tptp.inf_inf_int A) B)) C))))
% 2.52/3.50 (assert (forall ((B tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat B) C) (@ (@ tptp.ord_le7866589430770878221at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) C))))
% 2.52/3.50 (assert (forall ((B tptp.set_nat) (C tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B) C) (@ (@ tptp.ord_less_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) C))))
% 2.52/3.50 (assert (forall ((B (-> tptp.product_prod_int_int Bool)) (C (-> tptp.product_prod_int_int Bool)) (A (-> tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le8213806771718485336_int_o B) C) (@ (@ tptp.ord_le8213806771718485336_int_o (@ (@ tptp.inf_in3604695632404883862_int_o A) B)) C))))
% 2.52/3.50 (assert (forall ((B tptp.assn) (C tptp.assn) (A tptp.assn)) (=> (@ (@ tptp.ord_less_assn B) C) (@ (@ tptp.ord_less_assn (@ (@ tptp.inf_inf_assn A) B)) C))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.inf_inf_rat A) B)) C))))
% 2.52/3.50 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.inf_inf_nat A) B)) C))))
% 2.52/3.50 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) C) (@ (@ tptp.ord_less_int (@ (@ tptp.inf_inf_int A) B)) C))))
% 2.52/3.50 (assert (forall ((C tptp.set_nat) (B tptp.set_nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B))))))
% 2.52/3.50 (assert (forall ((C tptp.assn) (B tptp.assn) (A tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_assn A) B))))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_rat A) B))))))
% 2.52/3.50 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_nat A) B))))))
% 2.52/3.50 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_int A) B))))))
% 2.52/3.50 (assert (forall ((C tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B))))))
% 2.52/3.50 (assert (forall ((C tptp.assn) (A tptp.assn) (B tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_assn A) B))))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_rat A) B))))))
% 2.52/3.50 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_nat A) B))))))
% 2.52/3.50 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_int A) B))))))
% 2.52/3.50 (assert (= tptp.ord_less_set_nat (lambda ((B2 tptp.set_nat) (A2 tptp.set_nat)) (and (= A2 (@ (@ tptp.sup_sup_set_nat A2) B2)) (not (= A2 B2))))))
% 2.52/3.50 (assert (= tptp.ord_less_assn (lambda ((B2 tptp.assn) (A2 tptp.assn)) (and (= A2 (@ (@ tptp.sup_sup_assn A2) B2)) (not (= A2 B2))))))
% 2.52/3.50 (assert (= tptp.ord_less_rat (lambda ((B2 tptp.rat) (A2 tptp.rat)) (and (= A2 (@ (@ tptp.sup_sup_rat A2) B2)) (not (= A2 B2))))))
% 2.52/3.50 (assert (= tptp.ord_less_nat (lambda ((B2 tptp.nat) (A2 tptp.nat)) (and (= A2 (@ (@ tptp.sup_sup_nat A2) B2)) (not (= A2 B2))))))
% 2.52/3.50 (assert (= tptp.ord_less_int (lambda ((B2 tptp.int) (A2 tptp.int)) (and (= A2 (@ (@ tptp.sup_sup_int A2) B2)) (not (= A2 B2))))))
% 2.52/3.50 (assert (forall ((B tptp.set_nat) (C tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat (@ (@ tptp.sup_sup_set_nat B) C)) A) (not (=> (@ (@ tptp.ord_less_set_nat B) A) (not (@ (@ tptp.ord_less_set_nat C) A)))))))
% 2.52/3.50 (assert (forall ((B tptp.assn) (C tptp.assn) (A tptp.assn)) (=> (@ (@ tptp.ord_less_assn (@ (@ tptp.sup_sup_assn B) C)) A) (not (=> (@ (@ tptp.ord_less_assn B) A) (not (@ (@ tptp.ord_less_assn C) A)))))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.sup_sup_rat B) C)) A) (not (=> (@ (@ tptp.ord_less_rat B) A) (not (@ (@ tptp.ord_less_rat C) A)))))))
% 2.52/3.50 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.sup_sup_nat B) C)) A) (not (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat C) A)))))))
% 2.52/3.50 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.sup_sup_int B) C)) A) (not (=> (@ (@ tptp.ord_less_int B) A) (not (@ (@ tptp.ord_less_int C) A)))))))
% 2.52/3.50 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A) B) (= (@ (@ tptp.sup_sup_set_nat A) B) B))))
% 2.52/3.50 (assert (forall ((A tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.ord_less_assn A) B) (= (@ (@ tptp.sup_sup_assn A) B) B))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (= (@ (@ tptp.sup_sup_rat A) B) B))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.sup_sup_nat A) B) B))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (= (@ (@ tptp.sup_sup_int A) B) B))))
% 2.52/3.50 (assert (forall ((B tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B) A) (= (@ (@ tptp.sup_sup_set_nat A) B) A))))
% 2.52/3.50 (assert (forall ((B tptp.assn) (A tptp.assn)) (=> (@ (@ tptp.ord_less_assn B) A) (= (@ (@ tptp.sup_sup_assn A) B) A))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (= (@ (@ tptp.sup_sup_rat A) B) A))))
% 2.52/3.50 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (= (@ (@ tptp.sup_sup_nat A) B) A))))
% 2.52/3.50 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (= (@ (@ tptp.sup_sup_int A) B) A))))
% 2.52/3.50 (assert (forall ((X tptp.set_nat) (B tptp.set_nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat X))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B))))))
% 2.52/3.50 (assert (forall ((X tptp.assn) (B tptp.assn) (A tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn X))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_assn A) B))))))
% 2.52/3.50 (assert (forall ((X tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_rat A) B))))))
% 2.52/3.50 (assert (forall ((X tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_nat A) B))))))
% 2.52/3.50 (assert (forall ((X tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_int A) B))))))
% 2.52/3.50 (assert (forall ((X tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat X))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B))))))
% 2.52/3.50 (assert (forall ((X tptp.assn) (A tptp.assn) (B tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn X))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_assn A) B))))))
% 2.52/3.50 (assert (forall ((X tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_rat A) B))))))
% 2.52/3.50 (assert (forall ((X tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_nat A) B))))))
% 2.52/3.50 (assert (forall ((X tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_int A) B))))))
% 2.52/3.50 (assert (forall ((F2 (-> tptp.produc6575502325842934193n_assn tptp.assn)) (Xs tptp.list_P8527749157015355191n_assn) (Y tptp.assn) (Ys tptp.list_assn)) (= (= (@ (@ tptp.map_Pr8991440229025900053n_assn F2) Xs) (@ (@ tptp.cons_assn Y) Ys)) (exists ((Z3 tptp.produc6575502325842934193n_assn) (Zs2 tptp.list_P8527749157015355191n_assn)) (and (= Xs (@ (@ tptp.cons_P2971678138204555879n_assn Z3) Zs2)) (= (@ F2 Z3) Y) (= (@ (@ tptp.map_Pr8991440229025900053n_assn F2) Zs2) Ys))))))
% 2.52/3.50 (assert (forall ((F2 (-> tptp.int tptp.int)) (Xs tptp.list_int) (Y tptp.int) (Ys tptp.list_int)) (= (= (@ (@ tptp.map_int_int F2) Xs) (@ (@ tptp.cons_int Y) Ys)) (exists ((Z3 tptp.int) (Zs2 tptp.list_int)) (and (= Xs (@ (@ tptp.cons_int Z3) Zs2)) (= (@ F2 Z3) Y) (= (@ (@ tptp.map_int_int F2) Zs2) Ys))))))
% 2.52/3.50 (assert (forall ((F2 (-> tptp.nat tptp.int)) (Xs tptp.list_nat) (Y tptp.int) (Ys tptp.list_int)) (= (= (@ (@ tptp.map_nat_int F2) Xs) (@ (@ tptp.cons_int Y) Ys)) (exists ((Z3 tptp.nat) (Zs2 tptp.list_nat)) (and (= Xs (@ (@ tptp.cons_nat Z3) Zs2)) (= (@ F2 Z3) Y) (= (@ (@ tptp.map_nat_int F2) Zs2) Ys))))))
% 2.52/3.50 (assert (forall ((F2 (-> tptp.int tptp.nat)) (Xs tptp.list_int) (Y tptp.nat) (Ys tptp.list_nat)) (= (= (@ (@ tptp.map_int_nat F2) Xs) (@ (@ tptp.cons_nat Y) Ys)) (exists ((Z3 tptp.int) (Zs2 tptp.list_int)) (and (= Xs (@ (@ tptp.cons_int Z3) Zs2)) (= (@ F2 Z3) Y) (= (@ (@ tptp.map_int_nat F2) Zs2) Ys))))))
% 2.52/3.50 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (Xs tptp.list_nat) (Y tptp.nat) (Ys tptp.list_nat)) (= (= (@ (@ tptp.map_nat_nat F2) Xs) (@ (@ tptp.cons_nat Y) Ys)) (exists ((Z3 tptp.nat) (Zs2 tptp.list_nat)) (and (= Xs (@ (@ tptp.cons_nat Z3) Zs2)) (= (@ F2 Z3) Y) (= (@ (@ tptp.map_nat_nat F2) Zs2) Ys))))))
% 2.52/3.50 (assert (forall ((X tptp.assn) (Xs tptp.list_assn) (F2 (-> tptp.produc6575502325842934193n_assn tptp.assn)) (Ys tptp.list_P8527749157015355191n_assn)) (= (= (@ (@ tptp.cons_assn X) Xs) (@ (@ tptp.map_Pr8991440229025900053n_assn F2) Ys)) (exists ((Z3 tptp.produc6575502325842934193n_assn) (Zs2 tptp.list_P8527749157015355191n_assn)) (and (= Ys (@ (@ tptp.cons_P2971678138204555879n_assn Z3) Zs2)) (= X (@ F2 Z3)) (= Xs (@ (@ tptp.map_Pr8991440229025900053n_assn F2) Zs2)))))))
% 2.52/3.50 (assert (forall ((X tptp.int) (Xs tptp.list_int) (F2 (-> tptp.int tptp.int)) (Ys tptp.list_int)) (= (= (@ (@ tptp.cons_int X) Xs) (@ (@ tptp.map_int_int F2) Ys)) (exists ((Z3 tptp.int) (Zs2 tptp.list_int)) (and (= Ys (@ (@ tptp.cons_int Z3) Zs2)) (= X (@ F2 Z3)) (= Xs (@ (@ tptp.map_int_int F2) Zs2)))))))
% 2.52/3.50 (assert (forall ((X tptp.int) (Xs tptp.list_int) (F2 (-> tptp.nat tptp.int)) (Ys tptp.list_nat)) (= (= (@ (@ tptp.cons_int X) Xs) (@ (@ tptp.map_nat_int F2) Ys)) (exists ((Z3 tptp.nat) (Zs2 tptp.list_nat)) (and (= Ys (@ (@ tptp.cons_nat Z3) Zs2)) (= X (@ F2 Z3)) (= Xs (@ (@ tptp.map_nat_int F2) Zs2)))))))
% 2.52/3.50 (assert (forall ((X tptp.nat) (Xs tptp.list_nat) (F2 (-> tptp.int tptp.nat)) (Ys tptp.list_int)) (= (= (@ (@ tptp.cons_nat X) Xs) (@ (@ tptp.map_int_nat F2) Ys)) (exists ((Z3 tptp.int) (Zs2 tptp.list_int)) (and (= Ys (@ (@ tptp.cons_int Z3) Zs2)) (= X (@ F2 Z3)) (= Xs (@ (@ tptp.map_int_nat F2) Zs2)))))))
% 2.52/3.50 (assert (forall ((X tptp.nat) (Xs tptp.list_nat) (F2 (-> tptp.nat tptp.nat)) (Ys tptp.list_nat)) (= (= (@ (@ tptp.cons_nat X) Xs) (@ (@ tptp.map_nat_nat F2) Ys)) (exists ((Z3 tptp.nat) (Zs2 tptp.list_nat)) (and (= Ys (@ (@ tptp.cons_nat Z3) Zs2)) (= X (@ F2 Z3)) (= Xs (@ (@ tptp.map_nat_nat F2) Zs2)))))))
% 2.52/3.50 (assert (forall ((F2 (-> tptp.produc6575502325842934193n_assn tptp.assn)) (Xs tptp.list_P8527749157015355191n_assn) (Y tptp.assn) (Ys tptp.list_assn)) (=> (= (@ (@ tptp.map_Pr8991440229025900053n_assn F2) Xs) (@ (@ tptp.cons_assn Y) Ys)) (exists ((Z2 tptp.produc6575502325842934193n_assn) (Zs3 tptp.list_P8527749157015355191n_assn)) (and (= Xs (@ (@ tptp.cons_P2971678138204555879n_assn Z2) Zs3)) (= (@ F2 Z2) Y) (= (@ (@ tptp.map_Pr8991440229025900053n_assn F2) Zs3) Ys))))))
% 2.52/3.50 (assert (forall ((F2 (-> tptp.int tptp.int)) (Xs tptp.list_int) (Y tptp.int) (Ys tptp.list_int)) (=> (= (@ (@ tptp.map_int_int F2) Xs) (@ (@ tptp.cons_int Y) Ys)) (exists ((Z2 tptp.int) (Zs3 tptp.list_int)) (and (= Xs (@ (@ tptp.cons_int Z2) Zs3)) (= (@ F2 Z2) Y) (= (@ (@ tptp.map_int_int F2) Zs3) Ys))))))
% 2.52/3.50 (assert (forall ((F2 (-> tptp.nat tptp.int)) (Xs tptp.list_nat) (Y tptp.int) (Ys tptp.list_int)) (=> (= (@ (@ tptp.map_nat_int F2) Xs) (@ (@ tptp.cons_int Y) Ys)) (exists ((Z2 tptp.nat) (Zs3 tptp.list_nat)) (and (= Xs (@ (@ tptp.cons_nat Z2) Zs3)) (= (@ F2 Z2) Y) (= (@ (@ tptp.map_nat_int F2) Zs3) Ys))))))
% 2.52/3.50 (assert (forall ((F2 (-> tptp.int tptp.nat)) (Xs tptp.list_int) (Y tptp.nat) (Ys tptp.list_nat)) (=> (= (@ (@ tptp.map_int_nat F2) Xs) (@ (@ tptp.cons_nat Y) Ys)) (exists ((Z2 tptp.int) (Zs3 tptp.list_int)) (and (= Xs (@ (@ tptp.cons_int Z2) Zs3)) (= (@ F2 Z2) Y) (= (@ (@ tptp.map_int_nat F2) Zs3) Ys))))))
% 2.52/3.50 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (Xs tptp.list_nat) (Y tptp.nat) (Ys tptp.list_nat)) (=> (= (@ (@ tptp.map_nat_nat F2) Xs) (@ (@ tptp.cons_nat Y) Ys)) (exists ((Z2 tptp.nat) (Zs3 tptp.list_nat)) (and (= Xs (@ (@ tptp.cons_nat Z2) Zs3)) (= (@ F2 Z2) Y) (= (@ (@ tptp.map_nat_nat F2) Zs3) Ys))))))
% 2.52/3.50 (assert (forall ((X tptp.assn) (Xs tptp.list_assn) (F2 (-> tptp.produc6575502325842934193n_assn tptp.assn)) (Ys tptp.list_P8527749157015355191n_assn)) (=> (= (@ (@ tptp.cons_assn X) Xs) (@ (@ tptp.map_Pr8991440229025900053n_assn F2) Ys)) (exists ((Z2 tptp.produc6575502325842934193n_assn) (Zs3 tptp.list_P8527749157015355191n_assn)) (and (= Ys (@ (@ tptp.cons_P2971678138204555879n_assn Z2) Zs3)) (= X (@ F2 Z2)) (= Xs (@ (@ tptp.map_Pr8991440229025900053n_assn F2) Zs3)))))))
% 2.52/3.50 (assert (forall ((X tptp.int) (Xs tptp.list_int) (F2 (-> tptp.int tptp.int)) (Ys tptp.list_int)) (=> (= (@ (@ tptp.cons_int X) Xs) (@ (@ tptp.map_int_int F2) Ys)) (exists ((Z2 tptp.int) (Zs3 tptp.list_int)) (and (= Ys (@ (@ tptp.cons_int Z2) Zs3)) (= X (@ F2 Z2)) (= Xs (@ (@ tptp.map_int_int F2) Zs3)))))))
% 2.52/3.50 (assert (forall ((X tptp.int) (Xs tptp.list_int) (F2 (-> tptp.nat tptp.int)) (Ys tptp.list_nat)) (=> (= (@ (@ tptp.cons_int X) Xs) (@ (@ tptp.map_nat_int F2) Ys)) (exists ((Z2 tptp.nat) (Zs3 tptp.list_nat)) (and (= Ys (@ (@ tptp.cons_nat Z2) Zs3)) (= X (@ F2 Z2)) (= Xs (@ (@ tptp.map_nat_int F2) Zs3)))))))
% 2.52/3.50 (assert (forall ((X tptp.nat) (Xs tptp.list_nat) (F2 (-> tptp.int tptp.nat)) (Ys tptp.list_int)) (=> (= (@ (@ tptp.cons_nat X) Xs) (@ (@ tptp.map_int_nat F2) Ys)) (exists ((Z2 tptp.int) (Zs3 tptp.list_int)) (and (= Ys (@ (@ tptp.cons_int Z2) Zs3)) (= X (@ F2 Z2)) (= Xs (@ (@ tptp.map_int_nat F2) Zs3)))))))
% 2.52/3.50 (assert (forall ((X tptp.nat) (Xs tptp.list_nat) (F2 (-> tptp.nat tptp.nat)) (Ys tptp.list_nat)) (=> (= (@ (@ tptp.cons_nat X) Xs) (@ (@ tptp.map_nat_nat F2) Ys)) (exists ((Z2 tptp.nat) (Zs3 tptp.list_nat)) (and (= Ys (@ (@ tptp.cons_nat Z2) Zs3)) (= X (@ F2 Z2)) (= Xs (@ (@ tptp.map_nat_nat F2) Zs3)))))))
% 2.52/3.50 (assert (forall ((F2 (-> tptp.produc6575502325842934193n_assn tptp.assn)) (X21 tptp.produc6575502325842934193n_assn) (X22 tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ tptp.map_Pr8991440229025900053n_assn F2))) (= (@ _let_1 (@ (@ tptp.cons_P2971678138204555879n_assn X21) X22)) (@ (@ tptp.cons_assn (@ F2 X21)) (@ _let_1 X22))))))
% 2.52/3.50 (assert (forall ((F2 (-> tptp.int tptp.int)) (X21 tptp.int) (X22 tptp.list_int)) (let ((_let_1 (@ tptp.map_int_int F2))) (= (@ _let_1 (@ (@ tptp.cons_int X21) X22)) (@ (@ tptp.cons_int (@ F2 X21)) (@ _let_1 X22))))))
% 2.52/3.50 (assert (forall ((F2 (-> tptp.int tptp.nat)) (X21 tptp.int) (X22 tptp.list_int)) (let ((_let_1 (@ tptp.map_int_nat F2))) (= (@ _let_1 (@ (@ tptp.cons_int X21) X22)) (@ (@ tptp.cons_nat (@ F2 X21)) (@ _let_1 X22))))))
% 2.52/3.50 (assert (forall ((F2 (-> tptp.nat tptp.int)) (X21 tptp.nat) (X22 tptp.list_nat)) (let ((_let_1 (@ tptp.map_nat_int F2))) (= (@ _let_1 (@ (@ tptp.cons_nat X21) X22)) (@ (@ tptp.cons_int (@ F2 X21)) (@ _let_1 X22))))))
% 2.52/3.50 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (X21 tptp.nat) (X22 tptp.list_nat)) (let ((_let_1 (@ tptp.map_nat_nat F2))) (= (@ _let_1 (@ (@ tptp.cons_nat X21) X22)) (@ (@ tptp.cons_nat (@ F2 X21)) (@ _let_1 X22))))))
% 2.52/3.50 (assert (forall ((X tptp.int) (Xs tptp.list_int) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.cons_int X))) (= (@ (@ tptp.splice_int (@ _let_1 Xs)) Ys) (@ _let_1 (@ (@ tptp.splice_int Ys) Xs))))))
% 2.52/3.50 (assert (forall ((X tptp.nat) (Xs tptp.list_nat) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.cons_nat X))) (= (@ (@ tptp.splice_nat (@ _let_1 Xs)) Ys) (@ _let_1 (@ (@ tptp.splice_nat Ys) Xs))))))
% 2.52/3.50 (assert (forall ((X tptp.int) (Xs tptp.list_int)) (not (@ tptp.null_int (@ (@ tptp.cons_int X) Xs)))))
% 2.52/3.50 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (not (@ tptp.null_nat (@ (@ tptp.cons_nat X) Xs)))))
% 2.52/3.50 (assert (forall ((X tptp.int) (Xs tptp.list_int) (Y tptp.int)) (= (@ (@ tptp.member_int (@ (@ tptp.cons_int X) Xs)) Y) (or (= X Y) (@ (@ tptp.member_int Xs) Y)))))
% 2.52/3.50 (assert (forall ((X tptp.nat) (Xs tptp.list_nat) (Y tptp.nat)) (= (@ (@ tptp.member_nat (@ (@ tptp.cons_nat X) Xs)) Y) (or (= X Y) (@ (@ tptp.member_nat Xs) Y)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.times_3573771949741848930nteger A) B))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) B))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) A)) tptp.zero_z3403309356797280102nteger))))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) A)) tptp.zero_zero_rat))))
% 2.52/3.50 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) A)) tptp.zero_zero_int))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.zero_z3403309356797280102nteger) (or (and (@ _let_1 A) (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.zero_z3403309356797280102nteger)) (and (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (@ _let_1 B)))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ _let_1 B)))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_int B) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (@ _let_1 B)))))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (@ (@ tptp.ord_le5570908160329646204atural A) tptp.zero_z2226904508553997617atural) (=> (@ (@ tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural) B) (@ (@ tptp.ord_le5570908160329646204atural (@ (@ tptp.times_2397367101498566445atural A) B)) tptp.zero_z2226904508553997617atural)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.zero_z3403309356797280102nteger)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (@ (@ tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural) A) (=> (@ (@ tptp.ord_le5570908160329646204atural B) tptp.zero_z2226904508553997617atural) (@ (@ tptp.ord_le5570908160329646204atural (@ (@ tptp.times_2397367101498566445atural A) B)) tptp.zero_z2226904508553997617atural)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.zero_z3403309356797280102nteger)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (@ tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_2397367101498566445atural A) B)))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A) B)))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_rat A) B)))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_nat A) B)))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_int A) B)))))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (@ (@ tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural) A) (=> (@ (@ tptp.ord_le5570908160329646204atural B) tptp.zero_z2226904508553997617atural) (@ (@ tptp.ord_le5570908160329646204atural (@ (@ tptp.times_2397367101498566445atural B) A)) tptp.zero_z2226904508553997617atural)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger B) A)) tptp.zero_z3403309356797280102nteger)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat B) A)) tptp.zero_zero_rat)))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat B) A)) tptp.zero_zero_nat)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int B) A)) tptp.zero_zero_int)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.zero_z3403309356797280102nteger)))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.times_times_rat A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat)))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.times_times_int A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) tptp.zero_zero_int)))))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (@ tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural))) (=> (@ _let_1 (@ (@ tptp.times_2397367101498566445atural A) B)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A) B)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.times_times_rat A) B)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat A) B)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.times_times_int A) B)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 2.52/3.50 (assert (forall ((B tptp.code_natural) (A tptp.code_natural)) (let ((_let_1 (@ tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural))) (=> (@ _let_1 (@ (@ tptp.times_2397367101498566445atural B) A)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 2.52/3.50 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) A)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.times_times_rat B) A)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 2.52/3.50 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat B) A)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 2.52/3.50 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.times_times_int B) A)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 2.52/3.50 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_le6747313008572928689nteger B) A))))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat B) A))))))
% 2.52/3.50 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int B) A))))))
% 2.52/3.50 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_le6747313008572928689nteger A) B))))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat A) B))))))
% 2.52/3.50 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int A) B))))))
% 2.52/3.50 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A)) (@ _let_1 B)))))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 2.52/3.50 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)))))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural C))) (=> (@ (@ tptp.ord_le5570908160329646204atural A) B) (=> (@ (@ tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural) C) (@ (@ tptp.ord_le5570908160329646204atural (@ _let_1 A)) (@ _let_1 B)))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A)) (@ _let_1 B)))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)))))))
% 2.52/3.50 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A) B)) (and (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B) A)))))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (and (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)))))))
% 2.52/3.50 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)) (and (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A)))))))
% 2.52/3.50 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 2.52/3.50 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (=> (@ (@ tptp.ord_le5570908160329646204atural A) B) (=> (@ (@ tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural) C) (@ (@ tptp.ord_le5570908160329646204atural (@ (@ tptp.times_2397367101498566445atural A) C)) (@ (@ tptp.times_2397367101498566445atural B) C))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (or (and (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A) B)) (and (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B) A))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (and (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)) (and (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A))))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural C))) (=> (@ (@ tptp.ord_le5570908160329646204atural A) B) (=> (@ (@ tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural) C) (@ (@ tptp.ord_le5570908160329646204atural (@ _let_1 A)) (@ _let_1 B)))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A)) (@ _let_1 B)))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)))))))
% 2.52/3.50 (assert (@ (@ tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural) tptp.one_one_Code_natural))
% 2.52/3.50 (assert (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer))
% 2.52/3.50 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 2.52/3.50 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 2.52/3.50 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 2.52/3.50 (assert (@ (@ tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural) tptp.one_one_Code_natural))
% 2.52/3.50 (assert (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer))
% 2.52/3.50 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 2.52/3.50 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 2.52/3.50 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 2.52/3.50 (assert (not (@ (@ tptp.ord_le5570908160329646204atural tptp.one_one_Code_natural) tptp.zero_z2226904508553997617atural)))
% 2.52/3.50 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 2.52/3.50 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 2.52/3.50 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 2.52/3.50 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.zero_zero_int)))
% 2.52/3.50 (assert (forall ((M2 tptp.code_natural) (N tptp.code_natural)) (let ((_let_1 (@ tptp.ord_le5570908160329646204atural tptp.one_one_Code_natural))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_2397367101498566445atural M2) N)))))))
% 2.52/3.50 (assert (forall ((M2 tptp.code_integer) (N tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger M2) N)))))))
% 2.52/3.50 (assert (forall ((M2 tptp.rat) (N tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_rat M2) N)))))))
% 2.52/3.50 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_nat M2) N)))))))
% 2.52/3.50 (assert (forall ((M2 tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_int M2) N)))))))
% 2.52/3.50 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 2.52/3.50 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 2.52/3.50 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 2.52/3.50 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 2.52/3.50 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 2.52/3.50 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 2.52/3.50 (assert (forall ((X tptp.list_P8527749157015355191n_assn) (Xa tptp.list_P8527749157015355191n_assn) (Y tptp.list_P8527749157015355191n_assn)) (=> (= (@ (@ tptp.splice4588524007259616650n_assn X) Xa) Y) (=> (=> (= X tptp.nil_Pr5671120429643327159n_assn) (not (= Y Xa))) (not (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn)) (let ((_let_1 (@ tptp.cons_P2971678138204555879n_assn X3))) (=> (= X (@ _let_1 Xs2)) (not (= Y (@ _let_1 (@ (@ tptp.splice4588524007259616650n_assn Xa) Xs2))))))))))))
% 2.52/3.50 (assert (forall ((X tptp.list_int) (Xa tptp.list_int) (Y tptp.list_int)) (=> (= (@ (@ tptp.splice_int X) Xa) Y) (=> (=> (= X tptp.nil_int) (not (= Y Xa))) (not (forall ((X3 tptp.int) (Xs2 tptp.list_int)) (let ((_let_1 (@ tptp.cons_int X3))) (=> (= X (@ _let_1 Xs2)) (not (= Y (@ _let_1 (@ (@ tptp.splice_int Xa) Xs2))))))))))))
% 2.52/3.50 (assert (forall ((X tptp.list_nat) (Xa tptp.list_nat) (Y tptp.list_nat)) (=> (= (@ (@ tptp.splice_nat X) Xa) Y) (=> (=> (= X tptp.nil_nat) (not (= Y Xa))) (not (forall ((X3 tptp.nat) (Xs2 tptp.list_nat)) (let ((_let_1 (@ tptp.cons_nat X3))) (=> (= X (@ _let_1 Xs2)) (not (= Y (@ _let_1 (@ (@ tptp.splice_nat Xa) Xs2))))))))))))
% 2.52/3.50 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (X tptp.nat) (Y tptp.nat) (Fs tptp.list_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)))) (=> (@ (@ tptp.ord_less_eq_nat (@ F2 X)) (@ F2 Y)) (=> (@ _let_1 (@ tptp.measures_nat Fs)) (@ _let_1 (@ tptp.measures_nat (@ (@ tptp.cons_nat_nat F2) Fs))))))))
% 2.52/3.50 (assert (forall ((F2 (-> tptp.int tptp.nat)) (X tptp.int) (Y tptp.int) (Fs tptp.list_int_nat)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)))) (=> (@ (@ tptp.ord_less_eq_nat (@ F2 X)) (@ F2 Y)) (=> (@ _let_1 (@ tptp.measures_int Fs)) (@ _let_1 (@ tptp.measures_int (@ (@ tptp.cons_int_nat F2) Fs))))))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural) (D2 tptp.code_natural)) (=> (@ (@ tptp.ord_le5570908160329646204atural A) B) (=> (@ (@ tptp.ord_le1926595141338095240atural C) D2) (=> (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) A) (=> (@ (@ tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural) C) (@ (@ tptp.ord_le5570908160329646204atural (@ (@ tptp.times_2397367101498566445atural A) C)) (@ (@ tptp.times_2397367101498566445atural B) D2))))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) D2) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D2))))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D2))))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D2))))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D2))))))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural) (D2 tptp.code_natural)) (=> (@ (@ tptp.ord_le1926595141338095240atural A) B) (=> (@ (@ tptp.ord_le5570908160329646204atural C) D2) (=> (@ (@ tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural) A) (=> (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) C) (@ (@ tptp.ord_le5570908160329646204atural (@ (@ tptp.times_2397367101498566445atural A) C)) (@ (@ tptp.times_2397367101498566445atural B) D2))))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) D2) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D2))))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D2))))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D2))))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int C) D2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D2))))))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (C tptp.code_natural) (B tptp.code_natural)) (=> (@ (@ tptp.ord_le1926595141338095240atural (@ (@ tptp.times_2397367101498566445atural A) C)) (@ (@ tptp.times_2397367101498566445atural B) C)) (=> (@ (@ tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural) C) (@ (@ tptp.ord_le1926595141338095240atural A) B)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger A) B)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat A) B)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B)))))
% 2.52/3.50 (assert (forall ((C tptp.code_natural) (A tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural C))) (=> (@ (@ tptp.ord_le1926595141338095240atural (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural) C) (@ (@ tptp.ord_le1926595141338095240atural A) B))))))
% 2.52/3.50 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger A) B))))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B))))))
% 2.52/3.50 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat A) B))))))
% 2.52/3.50 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B))))))
% 2.52/3.50 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_le3102999989581377725nteger A) B))))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A) B))))))
% 2.52/3.50 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int A) B))))))
% 2.52/3.50 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_le3102999989581377725nteger B) A))))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 2.52/3.50 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int B) A))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A) B)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B) A))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A))))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural) (D2 tptp.code_natural)) (let ((_let_1 (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural))) (=> (@ (@ tptp.ord_le5570908160329646204atural A) B) (=> (@ (@ tptp.ord_le5570908160329646204atural C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_le5570908160329646204atural (@ (@ tptp.times_2397367101498566445atural A) C)) (@ (@ tptp.times_2397367101498566445atural B) D2)))))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D2)))))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D2)))))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D2)))))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D2)))))))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (C tptp.code_natural) (B tptp.code_natural)) (=> (@ (@ tptp.ord_le5570908160329646204atural (@ (@ tptp.times_2397367101498566445atural A) C)) (@ (@ tptp.times_2397367101498566445atural B) C)) (=> (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) C) (@ (@ tptp.ord_le5570908160329646204atural A) B)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A) B)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat A) B)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)))))
% 2.52/3.50 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A) B)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B) A)))))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)))))))
% 2.52/3.50 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A)))))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural) (D2 tptp.code_natural)) (=> (@ (@ tptp.ord_le5570908160329646204atural A) B) (=> (@ (@ tptp.ord_le5570908160329646204atural C) D2) (=> (@ (@ tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural) B) (=> (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) C) (@ (@ tptp.ord_le5570908160329646204atural (@ (@ tptp.times_2397367101498566445atural A) C)) (@ (@ tptp.times_2397367101498566445atural B) D2))))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) D2) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D2))))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D2))))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D2))))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D2))))))))
% 2.52/3.50 (assert (forall ((C tptp.code_natural) (A tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural C))) (=> (@ (@ tptp.ord_le5570908160329646204atural (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) C) (@ (@ tptp.ord_le5570908160329646204atural A) B))))))
% 2.52/3.50 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A) B))))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B))))))
% 2.52/3.50 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat A) B))))))
% 2.52/3.50 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger A) B)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B) A))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) A))))))
% 2.52/3.50 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger A) B)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B) A)))))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A)))))))
% 2.52/3.50 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) A)))))))
% 2.52/3.50 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 2.52/3.50 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 2.52/3.50 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 2.52/3.50 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 2.52/3.50 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 2.52/3.50 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) C) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.one_one_Code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) C) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) A))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) C) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) A))))))
% 2.52/3.50 (assert (forall ((C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger C) (@ (@ tptp.times_3573771949741848930nteger B) C)) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) B)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.one_one_Code_integer))))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat C) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.one_one_rat))))))
% 2.52/3.50 (assert (forall ((C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int C) (@ (@ tptp.times_times_int B) C)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) tptp.one_one_int))))))
% 2.52/3.50 (assert (forall ((C tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger C) A)) C) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.one_one_Code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A))))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat C) A)) C) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) A))))))
% 2.52/3.50 (assert (forall ((C tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int C) A)) C) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) A))))))
% 2.52/3.50 (assert (forall ((C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger C) (@ (@ tptp.times_3573771949741848930nteger C) B)) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) B)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.one_one_Code_integer))))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat C) (@ (@ tptp.times_times_rat C) B)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.one_one_rat))))))
% 2.52/3.50 (assert (forall ((C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int C) (@ (@ tptp.times_times_int C) B)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) tptp.one_one_int))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) C) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.one_one_Code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) A))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) C) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) C) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A))))))
% 2.52/3.50 (assert (forall ((C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger C) (@ (@ tptp.times_3573771949741848930nteger B) C)) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) B)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.one_one_Code_integer))))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.one_one_rat))))))
% 2.52/3.50 (assert (forall ((C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.times_times_int B) C)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.one_one_int))))))
% 2.52/3.50 (assert (forall ((C tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger C) A)) C) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.one_one_Code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) A))))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat C) A)) C) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A))))))
% 2.52/3.50 (assert (forall ((C tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int C) A)) C) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A))))))
% 2.52/3.50 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (forall ((Z2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z2) (=> (@ (@ tptp.ord_less_rat Z2) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z2) X)) Y)))) (@ (@ tptp.ord_less_eq_rat X) Y))))
% 2.52/3.50 (assert (forall ((Z tptp.code_integer) (X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) Z) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger X) Z)) (@ (@ tptp.times_3573771949741848930nteger Y) Z)) (@ (@ tptp.ord_le3102999989581377725nteger X) Y)))))
% 2.52/3.50 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat Y) Z)) (@ (@ tptp.ord_less_eq_rat X) Y)))))
% 2.52/3.50 (assert (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X) Z)) (@ (@ tptp.times_times_int Y) Z)) (@ (@ tptp.ord_less_eq_int X) Y)))))
% 2.52/3.50 (assert (forall ((Z tptp.code_integer) (X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger Z))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) Z) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_le3102999989581377725nteger X) Y))))))
% 2.52/3.50 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat Z))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_rat X) Y))))))
% 2.52/3.50 (assert (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.times_times_int Z))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_int X) Y))))))
% 2.52/3.50 (assert (forall ((Z tptp.code_integer) (X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) Z) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger X) Z)) (@ (@ tptp.times_3573771949741848930nteger Y) Z)) (@ (@ tptp.ord_le6747313008572928689nteger X) Y)))))
% 2.52/3.50 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat Y) Z)) (@ (@ tptp.ord_less_rat X) Y)))))
% 2.52/3.50 (assert (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int X) Z)) (@ (@ tptp.times_times_int Y) Z)) (@ (@ tptp.ord_less_int X) Y)))))
% 2.52/3.50 (assert (forall ((X tptp.list_int)) (=> (not (= X tptp.nil_int)) (not (forall ((X3 tptp.int) (Xs2 tptp.list_int)) (not (= X (@ (@ tptp.cons_int X3) Xs2))))))))
% 2.52/3.50 (assert (forall ((X tptp.list_nat)) (=> (not (= X tptp.nil_nat)) (not (forall ((X3 tptp.nat) (Xs2 tptp.list_nat)) (not (= X (@ (@ tptp.cons_nat X3) Xs2))))))))
% 2.52/3.50 (assert (forall ((X tptp.produc337509097454979815n_assn)) (=> (forall ((Ys3 tptp.list_P8527749157015355191n_assn)) (not (= X (@ (@ tptp.produc3014731801419794263n_assn tptp.nil_Pr5671120429643327159n_assn) Ys3)))) (not (forall ((X3 tptp.produc6575502325842934193n_assn) (Xs2 tptp.list_P8527749157015355191n_assn) (Ys3 tptp.list_P8527749157015355191n_assn)) (not (= X (@ (@ tptp.produc3014731801419794263n_assn (@ (@ tptp.cons_P2971678138204555879n_assn X3) Xs2)) Ys3))))))))
% 2.52/3.50 (assert (forall ((X tptp.produc1186641810826059865st_int)) (=> (forall ((Ys3 tptp.list_int)) (not (= X (@ (@ tptp.produc364263696895485585st_int tptp.nil_int) Ys3)))) (not (forall ((X3 tptp.int) (Xs2 tptp.list_int) (Ys3 tptp.list_int)) (not (= X (@ (@ tptp.produc364263696895485585st_int (@ (@ tptp.cons_int X3) Xs2)) Ys3))))))))
% 2.52/3.50 (assert (forall ((X tptp.produc1828647624359046049st_nat)) (=> (forall ((Ys3 tptp.list_nat)) (not (= X (@ (@ tptp.produc2694037385005941721st_nat tptp.nil_nat) Ys3)))) (not (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Ys3 tptp.list_nat)) (not (= X (@ (@ tptp.produc2694037385005941721st_nat (@ (@ tptp.cons_nat X3) Xs2)) Ys3))))))))
% 2.52/3.50 (assert (@ (@ (@ (@ tptp.semila4918476307565957903at_nat tptp.inf_in2572325071724192079at_nat) tptp.top_to4669805908274784177at_nat) tptp.ord_le3146513528884898305at_nat) tptp.ord_le7866589430770878221at_nat))
% 2.52/3.50 (assert (@ (@ (@ (@ tptp.semila8052717425514686422_int_o tptp.inf_in3604695632404883862_int_o) tptp.top_to1578927101902068148_int_o) tptp.ord_le8369615600986905444_int_o) tptp.ord_le8213806771718485336_int_o))
% 2.52/3.50 (assert (@ (@ (@ (@ tptp.semila4423693302617054363t_unit tptp.inf_in4660618365625256667t_unit) tptp.top_to1996260823553986621t_unit) tptp.ord_le3507040750410214029t_unit) tptp.ord_le8056459307392131481t_unit))
% 2.52/3.50 (assert (@ (@ (@ (@ tptp.semila8603258263270017530r_assn tptp.inf_inf_assn) tptp.top_top_assn) tptp.ord_less_eq_assn) tptp.ord_less_assn))
% 2.52/3.50 (assert (@ (@ (@ (@ tptp.semila1667268886620078168et_nat tptp.inf_inf_set_nat) tptp.top_top_set_nat) tptp.ord_less_eq_set_nat) tptp.ord_less_set_nat))
% 2.52/3.50 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (= (@ tptp.sgn_sgn_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ tptp.sgn_sgn_rat A) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.sgn_sgn_Code_integer A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 2.52/3.50 (assert (forall ((X tptp.produc6575502325842934193n_assn)) (= (@ (@ tptp.insert3246601298802261197n_assn X) tptp.nil_Pr5671120429643327159n_assn) (@ (@ tptp.cons_P2971678138204555879n_assn X) tptp.nil_Pr5671120429643327159n_assn))))
% 2.52/3.50 (assert (forall ((X tptp.int)) (= (@ (@ tptp.insert_int X) tptp.nil_int) (@ (@ tptp.cons_int X) tptp.nil_int))))
% 2.52/3.50 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.insert_nat X) tptp.nil_nat) (@ (@ tptp.cons_nat X) tptp.nil_nat))))
% 2.52/3.50 (assert (forall ((X tptp.code_integer) (A tptp.code_integer) (Y tptp.code_integer) (U tptp.code_integer) (V2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V2) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger U) V2) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger U) X)) (@ (@ tptp.times_3573771949741848930nteger V2) Y))) A)))))))))
% 2.52/3.50 (assert (forall ((X tptp.rat) (A tptp.rat) (Y tptp.rat) (U tptp.rat) (V2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat X) A) (=> (@ (@ tptp.ord_less_rat Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V2) (=> (= (@ (@ tptp.plus_plus_rat U) V2) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat U) X)) (@ (@ tptp.times_times_rat V2) Y))) A)))))))))
% 2.52/3.50 (assert (forall ((X tptp.int) (A tptp.int) (Y tptp.int) (U tptp.int) (V2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int X) A) (=> (@ (@ tptp.ord_less_int Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V2) (=> (= (@ (@ tptp.plus_plus_int U) V2) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X)) (@ (@ tptp.times_times_int V2) Y))) A)))))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 2.52/3.50 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger B) A) (@ (@ tptp.plus_p5714425477246183910nteger C) A)) (= B C))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) (@ (@ tptp.plus_plus_rat C) A)) (= B C))))
% 2.52/3.50 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) (@ (@ tptp.plus_plus_nat C) A)) (= B C))))
% 2.52/3.50 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) (@ (@ tptp.plus_plus_int C) A)) (= B C))))
% 2.52/3.50 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger C))) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_le3102999989581377725nteger A) B)))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 2.52/3.50 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_nat A) B)))))
% 2.52/3.50 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int A) B)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A) C)) (@ (@ tptp.plus_p5714425477246183910nteger B) C)) (@ (@ tptp.ord_le3102999989581377725nteger A) B))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_eq_rat A) B))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_eq_nat A) B))))
% 2.52/3.50 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.ord_less_eq_int A) B))))
% 2.52/3.50 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 2.52/3.50 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 2.52/3.50 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) tptp.zero_z3403309356797280102nteger) A)))
% 2.52/3.50 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.plus_p4538020629002901425atural A) tptp.zero_z2226904508553997617atural) A)))
% 2.52/3.50 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ (@ tptp.plus_plus_int A) A)) (= A tptp.zero_zero_int))))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.plus_plus_rat A) A)) (= A tptp.zero_zero_rat))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ (@ tptp.plus_p5714425477246183910nteger A) A)) (= A tptp.zero_z3403309356797280102nteger))))
% 2.52/3.50 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) A) (= B tptp.zero_zero_nat))))
% 2.52/3.50 (assert (forall ((B tptp.int) (A tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) A) (= B tptp.zero_zero_int))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) A) (= B tptp.zero_zero_rat))))
% 2.52/3.50 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger B) A) A) (= B tptp.zero_z3403309356797280102nteger))))
% 2.52/3.50 (assert (forall ((B tptp.code_natural) (A tptp.code_natural)) (= (= (@ (@ tptp.plus_p4538020629002901425atural B) A) A) (= B tptp.zero_z2226904508553997617atural))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat A) B) A) (= B tptp.zero_zero_nat))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) A) (= B tptp.zero_zero_int))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) A) (= B tptp.zero_zero_rat))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) A) (= B tptp.zero_z3403309356797280102nteger))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (= (@ (@ tptp.plus_p4538020629002901425atural A) B) A) (= B tptp.zero_z2226904508553997617atural))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat B) A)) (= B tptp.zero_zero_nat))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int B) A)) (= B tptp.zero_zero_int))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat B) A)) (= B tptp.zero_zero_rat))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ (@ tptp.plus_p5714425477246183910nteger B) A)) (= B tptp.zero_z3403309356797280102nteger))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (= A (@ (@ tptp.plus_p4538020629002901425atural B) A)) (= B tptp.zero_z2226904508553997617atural))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat A) B)) (= B tptp.zero_zero_nat))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int A) B)) (= B tptp.zero_zero_int))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat A) B)) (= B tptp.zero_zero_rat))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (= B tptp.zero_z3403309356797280102nteger))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (= A (@ (@ tptp.plus_p4538020629002901425atural A) B)) (= B tptp.zero_z2226904508553997617atural))))
% 2.52/3.50 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))
% 2.52/3.50 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.plus_plus_nat X) Y)) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))
% 2.52/3.50 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 2.52/3.50 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 2.52/3.50 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.zero_z3403309356797280102nteger) A) A)))
% 2.52/3.50 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.plus_p4538020629002901425atural tptp.zero_z2226904508553997617atural) A) A)))
% 2.52/3.50 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger C))) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_le6747313008572928689nteger A) B)))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat A) B)))))
% 2.52/3.50 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_nat A) B)))))
% 2.52/3.50 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int A) B)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A) C)) (@ (@ tptp.plus_p5714425477246183910nteger B) C)) (@ (@ tptp.ord_le6747313008572928689nteger A) B))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_rat A) B))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_nat A) B))))
% 2.52/3.50 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.ord_less_int A) B))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B)) B)))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B)) B)))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B)) B)))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) (@ (@ tptp.plus_plus_int A) B)) B)))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.plus_plus_rat A) B)) B)))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B)))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)))))
% 2.52/3.50 (assert (= (@ tptp.sgn_sgn_int tptp.one_one_int) tptp.one_one_int))
% 2.52/3.50 (assert (= (@ tptp.sgn_sgn_rat tptp.one_one_rat) tptp.one_one_rat))
% 2.52/3.50 (assert (= (@ tptp.sgn_sgn_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 2.52/3.50 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger B) A)) B) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger))))
% 2.52/3.50 (assert (forall ((B tptp.code_natural) (A tptp.code_natural)) (= (@ (@ tptp.ord_le1926595141338095240atural (@ (@ tptp.plus_p4538020629002901425atural B) A)) B) (@ (@ tptp.ord_le1926595141338095240atural A) tptp.zero_z2226904508553997617atural))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat B) A)) B) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 2.52/3.50 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat B) A)) B) (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat))))
% 2.52/3.50 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int B) A)) B) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.ord_le1926595141338095240atural (@ (@ tptp.plus_p4538020629002901425atural A) B)) B) (@ (@ tptp.ord_le1926595141338095240atural A) tptp.zero_z2226904508553997617atural))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) B)) B) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) B)) B) (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) B)) B) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger A) (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.ord_le1926595141338095240atural A) (@ (@ tptp.plus_p4538020629002901425atural A) B)) (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) B))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.plus_plus_nat A) B)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger A) (@ (@ tptp.plus_p5714425477246183910nteger B) A)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.ord_le1926595141338095240atural A) (@ (@ tptp.plus_p4538020629002901425atural B) A)) (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) B))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.plus_plus_rat B) A)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.plus_plus_nat B) A)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.plus_plus_int B) A)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A) A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger))))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 2.52/3.50 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) A)) (@ _let_1 A)))))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat A) A)) (@ _let_1 A)))))
% 2.52/3.50 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) A)) (@ _let_1 A)))))
% 2.52/3.50 (assert (forall ((B tptp.code_natural) (A tptp.code_natural)) (= (@ (@ tptp.ord_le5570908160329646204atural (@ (@ tptp.plus_p4538020629002901425atural B) A)) B) (@ (@ tptp.ord_le5570908160329646204atural A) tptp.zero_z2226904508553997617atural))))
% 2.52/3.50 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger B) A)) B) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat B) A)) B) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 2.52/3.50 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat B) A)) B) (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 2.52/3.50 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int B) A)) B) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.ord_le5570908160329646204atural (@ (@ tptp.plus_p4538020629002901425atural A) B)) B) (@ (@ tptp.ord_le5570908160329646204atural A) tptp.zero_z2226904508553997617atural))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) B) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B)) B) (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) B) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.ord_le5570908160329646204atural A) (@ (@ tptp.plus_p4538020629002901425atural A) B)) (@ (@ tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural) B))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger A) (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat A) B)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) B))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.ord_le5570908160329646204atural A) (@ (@ tptp.plus_p4538020629002901425atural B) A)) (@ (@ tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural) B))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger A) (@ (@ tptp.plus_p5714425477246183910nteger B) A)) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat B) A)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat B) A)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int B) A)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) B))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A) A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 2.52/3.50 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) A)) (@ _let_1 A)))))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat A) A)) (@ _let_1 A)))))
% 2.52/3.50 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) A)) (@ _let_1 A)))))
% 2.52/3.50 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int)))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ tptp.uminus_uminus_rat A)) tptp.zero_zero_rat)))
% 2.52/3.50 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger)))
% 2.52/3.50 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)))
% 2.52/3.50 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)))
% 2.52/3.50 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 2.52/3.50 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 2.52/3.50 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 2.52/3.50 (assert (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int) tptp.zero_zero_int))
% 2.52/3.50 (assert (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat) tptp.zero_zero_rat))
% 2.52/3.50 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))
% 2.52/3.50 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.sgn_sgn_Code_integer A) tptp.one_one_Code_integer))))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ tptp.sgn_sgn_rat A) tptp.one_one_rat))))
% 2.52/3.50 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (= (@ tptp.sgn_sgn_int A) tptp.one_one_int))))
% 2.52/3.50 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) X) (not (= X tptp.zero_zero_nat)))))
% 2.52/3.50 (assert (forall ((I2 tptp.code_integer) (J tptp.code_integer) (K tptp.code_integer) (L tptp.code_integer)) (=> (and (= I2 J) (= K L)) (= (@ (@ tptp.plus_p5714425477246183910nteger I2) K) (@ (@ tptp.plus_p5714425477246183910nteger J) L)))))
% 2.52/3.50 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (= I2 J) (= K L)) (= (@ (@ tptp.plus_plus_rat I2) K) (@ (@ tptp.plus_plus_rat J) L)))))
% 2.52/3.50 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I2 J) (= K L)) (= (@ (@ tptp.plus_plus_nat I2) K) (@ (@ tptp.plus_plus_nat J) L)))))
% 2.52/3.50 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I2 J) (= K L)) (= (@ (@ tptp.plus_plus_int I2) K) (@ (@ tptp.plus_plus_int J) L)))))
% 2.52/3.50 (assert (forall ((A3 tptp.code_integer) (K tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.plus_p5714425477246183910nteger A3) B) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B)))))))
% 2.52/3.50 (assert (forall ((A3 tptp.rat) (K tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_rat A3) B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 2.52/3.50 (assert (forall ((A3 tptp.nat) (K tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_nat A3) B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 2.52/3.50 (assert (forall ((A3 tptp.int) (K tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_int A3) B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 2.52/3.50 (assert (forall ((B3 tptp.code_integer) (K tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger A))) (let ((_let_2 (@ tptp.plus_p5714425477246183910nteger K))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B))))))))
% 2.52/3.50 (assert (forall ((B3 tptp.rat) (K tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (let ((_let_2 (@ tptp.plus_plus_rat K))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B))))))))
% 2.52/3.50 (assert (forall ((B3 tptp.nat) (K tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (let ((_let_2 (@ tptp.plus_plus_nat K))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B))))))))
% 2.52/3.50 (assert (forall ((B3 tptp.int) (K tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (let ((_let_2 (@ tptp.plus_plus_int K))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B))))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger A))) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B) C))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger A))) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 C)) B)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B)) C) (@ (@ tptp.plus_plus_rat (@ _let_1 C)) B)))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B)) C) (@ (@ tptp.plus_plus_nat (@ _let_1 C)) B)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B)) C) (@ (@ tptp.plus_plus_int (@ _let_1 C)) B)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger A))) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B) C))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 2.52/3.50 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger B) A) (@ (@ tptp.plus_p5714425477246183910nteger C) A)) (= B C))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) (@ (@ tptp.plus_plus_rat C) A)) (= B C))))
% 2.52/3.50 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) (@ (@ tptp.plus_plus_int C) A)) (= B C))))
% 2.52/3.50 (assert (= tptp.plus_p5714425477246183910nteger (lambda ((A2 tptp.code_integer) (B2 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger B2) A2))))
% 2.52/3.50 (assert (= tptp.plus_plus_rat (lambda ((A2 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.plus_plus_rat B2) A2))))
% 2.52/3.50 (assert (= tptp.plus_plus_nat (lambda ((A2 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.plus_plus_nat B2) A2))))
% 2.52/3.50 (assert (= tptp.plus_plus_int (lambda ((A2 tptp.int) (B2 tptp.int)) (@ (@ tptp.plus_plus_int B2) A2))))
% 2.52/3.50 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger B))) (let ((_let_2 (@ tptp.plus_p5714425477246183910nteger A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat B))) (let ((_let_2 (@ tptp.plus_plus_rat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 2.52/3.50 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat B))) (let ((_let_2 (@ tptp.plus_plus_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 2.52/3.50 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int B))) (let ((_let_2 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 2.52/3.50 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger B) A) (@ (@ tptp.plus_p5714425477246183910nteger C) A)) (= B C))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat B) A) (@ (@ tptp.plus_plus_rat C) A)) (= B C))))
% 2.52/3.50 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat B) A) (@ (@ tptp.plus_plus_nat C) A)) (= B C))))
% 2.52/3.50 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (= (@ (@ tptp.plus_plus_int B) A) (@ (@ tptp.plus_plus_int C) A)) (= B C))))
% 2.52/3.50 (assert (forall ((I2 tptp.code_integer) (J tptp.code_integer) (K tptp.code_integer) (L tptp.code_integer)) (=> (and (@ (@ tptp.ord_le3102999989581377725nteger I2) J) (= K L)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger I2) K)) (@ (@ tptp.plus_p5714425477246183910nteger J) L)))))
% 2.52/3.50 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I2) J) (= K L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 2.52/3.50 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J) (= K L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 2.52/3.50 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J) (= K L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 2.52/3.50 (assert (forall ((I2 tptp.code_integer) (J tptp.code_integer) (K tptp.code_integer) (L tptp.code_integer)) (=> (and (= I2 J) (@ (@ tptp.ord_le3102999989581377725nteger K) L)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger I2) K)) (@ (@ tptp.plus_p5714425477246183910nteger J) L)))))
% 2.52/3.50 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (= I2 J) (@ (@ tptp.ord_less_eq_rat K) L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 2.52/3.50 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I2 J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 2.52/3.50 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I2 J) (@ (@ tptp.ord_less_eq_int K) L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 2.52/3.50 (assert (forall ((I2 tptp.code_integer) (J tptp.code_integer) (K tptp.code_integer) (L tptp.code_integer)) (=> (and (@ (@ tptp.ord_le3102999989581377725nteger I2) J) (@ (@ tptp.ord_le3102999989581377725nteger K) L)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger I2) K)) (@ (@ tptp.plus_p5714425477246183910nteger J) L)))))
% 2.52/3.50 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I2) J) (@ (@ tptp.ord_less_eq_rat K) L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 2.52/3.50 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 2.52/3.50 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J) (@ (@ tptp.ord_less_eq_int K) L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) D2) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A) C)) (@ (@ tptp.plus_p5714425477246183910nteger B) D2))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D2))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D2))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D2))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger C))) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A)) (@ _let_1 B))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (not (forall ((C3 tptp.nat)) (not (= B (@ (@ tptp.plus_plus_nat A) C3))))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A) C)) (@ (@ tptp.plus_p5714425477246183910nteger B) C)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)))))
% 2.52/3.50 (assert (= tptp.ord_less_eq_nat (lambda ((A2 tptp.nat) (B2 tptp.nat)) (exists ((C4 tptp.nat)) (= B2 (@ (@ tptp.plus_plus_nat A2) C4))))))
% 2.52/3.50 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger C))) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_le3102999989581377725nteger A) B)))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 2.52/3.50 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_nat A) B)))))
% 2.52/3.50 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int A) B)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A) C)) (@ (@ tptp.plus_p5714425477246183910nteger B) C)) (@ (@ tptp.ord_le3102999989581377725nteger A) B))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_eq_rat A) B))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_eq_nat A) B))))
% 2.52/3.50 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.ord_less_eq_int A) B))))
% 2.52/3.50 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 2.52/3.50 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 2.52/3.50 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.zero_z3403309356797280102nteger) A) A)))
% 2.52/3.50 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.plus_p4538020629002901425atural tptp.zero_z2226904508553997617atural) A) A)))
% 2.52/3.50 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 2.52/3.50 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 2.52/3.50 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) tptp.zero_z3403309356797280102nteger) A)))
% 2.52/3.50 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.plus_p4538020629002901425atural A) tptp.zero_z2226904508553997617atural) A)))
% 2.52/3.50 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 2.52/3.50 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.zero_z3403309356797280102nteger) A) A)))
% 2.52/3.50 (assert (forall ((I2 tptp.code_integer) (J tptp.code_integer) (K tptp.code_integer) (L tptp.code_integer)) (=> (and (@ (@ tptp.ord_le6747313008572928689nteger I2) J) (@ (@ tptp.ord_le6747313008572928689nteger K) L)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger I2) K)) (@ (@ tptp.plus_p5714425477246183910nteger J) L)))))
% 2.52/3.50 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I2) J) (@ (@ tptp.ord_less_rat K) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 2.52/3.50 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 2.52/3.50 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J) (@ (@ tptp.ord_less_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 2.52/3.50 (assert (forall ((I2 tptp.code_integer) (J tptp.code_integer) (K tptp.code_integer) (L tptp.code_integer)) (=> (and (= I2 J) (@ (@ tptp.ord_le6747313008572928689nteger K) L)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger I2) K)) (@ (@ tptp.plus_p5714425477246183910nteger J) L)))))
% 2.52/3.50 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (= I2 J) (@ (@ tptp.ord_less_rat K) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 2.52/3.50 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I2 J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 2.52/3.50 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I2 J) (@ (@ tptp.ord_less_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 2.52/3.50 (assert (forall ((I2 tptp.code_integer) (J tptp.code_integer) (K tptp.code_integer) (L tptp.code_integer)) (=> (and (@ (@ tptp.ord_le6747313008572928689nteger I2) J) (= K L)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger I2) K)) (@ (@ tptp.plus_p5714425477246183910nteger J) L)))))
% 2.52/3.50 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I2) J) (= K L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 2.52/3.50 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J) (= K L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 2.52/3.50 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J) (= K L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) D2) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A) C)) (@ (@ tptp.plus_p5714425477246183910nteger B) D2))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D2) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D2))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D2))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D2))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A)) (@ _let_1 B))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A) C)) (@ (@ tptp.plus_p5714425477246183910nteger B) C)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)))))
% 2.52/3.50 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_le6747313008572928689nteger A) B)))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat A) B)))))
% 2.52/3.50 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_nat A) B)))))
% 2.52/3.50 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int A) B)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A) C)) (@ (@ tptp.plus_p5714425477246183910nteger B) C)) (@ (@ tptp.ord_le6747313008572928689nteger A) B))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_rat A) B))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_nat A) B))))
% 2.52/3.50 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.ord_less_int A) B))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (E2 tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) E2)) C))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (E2 tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) E2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) E2)) C)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) E2)) C))))
% 2.52/3.50 (assert (forall ((A tptp.int) (E2 tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) E2)) C))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (E2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A) E2)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) E2)) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) E2)) C))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (E2 tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (= (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural A) E2)) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural B) E2)) C)) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.plus_p4538020629002901425atural A) B)) E2)) C))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (= (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.plus_p4538020629002901425atural A) B)) C) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural A) C)) (@ (@ tptp.times_2397367101498566445atural B) C)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.plus_plus_nat (@ _let_1 B)) (@ _let_1 C))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 B)) (@ _let_1 C))))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural A))) (= (@ _let_1 (@ (@ tptp.plus_p4538020629002901425atural B) C)) (@ (@ tptp.plus_p4538020629002901425atural (@ _let_1 B)) (@ _let_1 C))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (= (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.plus_p4538020629002901425atural A) B)) C) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural A) C)) (@ (@ tptp.times_2397367101498566445atural B) C)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 B)) (@ _let_1 C))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)))))
% 2.52/3.50 (assert (forall ((A3 tptp.int) (K tptp.int) (A tptp.int)) (=> (= A3 (@ (@ tptp.plus_plus_int K) A)) (= (@ tptp.uminus_uminus_int A3) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K)) (@ tptp.uminus_uminus_int A))))))
% 2.52/3.50 (assert (forall ((A3 tptp.rat) (K tptp.rat) (A tptp.rat)) (=> (= A3 (@ (@ tptp.plus_plus_rat K) A)) (= (@ tptp.uminus_uminus_rat A3) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat K)) (@ tptp.uminus_uminus_rat A))))))
% 2.52/3.50 (assert (forall ((A3 tptp.code_integer) (K tptp.code_integer) (A tptp.code_integer)) (=> (= A3 (@ (@ tptp.plus_p5714425477246183910nteger K) A)) (= (@ tptp.uminus1351360451143612070nteger A3) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger K)) (@ tptp.uminus1351360451143612070nteger A))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.sgn_sgn_rat (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.times_times_rat (@ tptp.sgn_sgn_rat A)) (@ tptp.sgn_sgn_rat B)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.sgn_sgn_int (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A)) (@ tptp.sgn_sgn_int B)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.sgn_sgn_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.sgn_sgn_Code_integer A)) (@ tptp.sgn_sgn_Code_integer B)))))
% 2.52/3.50 (assert (@ tptp.abel_s8772020223019846471nteger tptp.plus_p5714425477246183910nteger))
% 2.52/3.50 (assert (@ tptp.abel_semigroup_rat tptp.plus_plus_rat))
% 2.52/3.50 (assert (@ tptp.abel_semigroup_nat tptp.plus_plus_nat))
% 2.52/3.50 (assert (@ tptp.abel_semigroup_int tptp.plus_plus_int))
% 2.52/3.50 (assert (@ tptp.semigr7036097719740861967nteger tptp.plus_p5714425477246183910nteger))
% 2.52/3.50 (assert (@ tptp.semigroup_rat tptp.plus_plus_rat))
% 2.52/3.50 (assert (@ tptp.semigroup_nat tptp.plus_plus_nat))
% 2.52/3.50 (assert (@ tptp.semigroup_int tptp.plus_plus_int))
% 2.52/3.50 (assert (@ tptp.syntax414191934074104506nteger tptp.plus_p5714425477246183910nteger))
% 2.52/3.50 (assert (@ tptp.syntax8165409007564224565or_rat tptp.plus_plus_rat))
% 2.52/3.50 (assert (@ tptp.syntax8800539067650720301or_nat tptp.plus_plus_nat))
% 2.52/3.50 (assert (@ tptp.syntax8798048597141670025or_int tptp.plus_plus_int))
% 2.52/3.50 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.syntax380677951125133566nteger (@ (@ tptp.plus_p5714425477246183910nteger X) Y)) A) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) (@ (@ tptp.plus_p5714425477246183910nteger B) A)))))
% 2.52/3.50 (assert (forall ((X tptp.rat) (Y tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.syntax3730441303064801268at_rat (@ (@ tptp.plus_plus_rat X) Y)) A) (= (@ (@ tptp.plus_plus_rat A) B) (@ (@ tptp.plus_plus_rat B) A)))))
% 2.52/3.50 (assert (forall ((X tptp.nat) (Y tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.syntax4682126007086162916at_nat (@ (@ tptp.plus_plus_nat X) Y)) A) (= (@ (@ tptp.plus_plus_nat A) B) (@ (@ tptp.plus_plus_nat B) A)))))
% 2.52/3.50 (assert (forall ((X tptp.int) (Y tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.syntax5678989248478167196nt_int (@ (@ tptp.plus_plus_int X) Y)) A) (= (@ (@ tptp.plus_plus_int A) B) (@ (@ tptp.plus_plus_int B) A)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A) C)) B)))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (C tptp.code_natural) (B tptp.code_natural)) (=> (@ (@ tptp.ord_le1926595141338095240atural A) tptp.zero_z2226904508553997617atural) (=> (@ (@ tptp.ord_le1926595141338095240atural C) B) (@ (@ tptp.ord_le1926595141338095240atural (@ (@ tptp.plus_p4538020629002901425atural A) C)) B)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat C) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) B)))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat C) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) B)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int C) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) B)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger B))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) C)))))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (let ((_let_1 (@ tptp.ord_le1926595141338095240atural B))) (=> (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_p4538020629002901425atural A) C)))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat B))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 2.52/3.50 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A) C)) B)))))
% 2.52/3.50 (assert (forall ((C tptp.code_natural) (A tptp.code_natural) (B tptp.code_natural)) (=> (@ (@ tptp.ord_le1926595141338095240atural C) tptp.zero_z2226904508553997617atural) (=> (@ (@ tptp.ord_le1926595141338095240atural A) B) (@ (@ tptp.ord_le1926595141338095240atural (@ (@ tptp.plus_p4538020629002901425atural A) C)) B)))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) B)))))
% 2.52/3.50 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) B)))))
% 2.52/3.50 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) B)))))
% 2.52/3.50 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger B))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) C)))))))
% 2.52/3.50 (assert (forall ((C tptp.code_natural) (B tptp.code_natural) (A tptp.code_natural)) (let ((_let_1 (@ tptp.ord_le1926595141338095240atural B))) (=> (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_p4538020629002901425atural A) C)))))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat B))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))))
% 2.52/3.50 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 2.52/3.50 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B)))))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_p4538020629002901425atural A) B)))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) tptp.zero_z3403309356797280102nteger)))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (@ (@ tptp.ord_le1926595141338095240atural A) tptp.zero_z2226904508553997617atural) (=> (@ (@ tptp.ord_le1926595141338095240atural B) tptp.zero_z2226904508553997617atural) (@ (@ tptp.ord_le1926595141338095240atural (@ (@ tptp.plus_p4538020629002901425atural A) B)) tptp.zero_z2226904508553997617atural)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.zero_zero_rat)))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) B)) tptp.zero_zero_int)))))
% 2.52/3.50 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_p5714425477246183910nteger X) Y) tptp.zero_z3403309356797280102nteger) (and (= X tptp.zero_z3403309356797280102nteger) (= Y tptp.zero_z3403309356797280102nteger))))))))
% 2.52/3.50 (assert (forall ((X tptp.code_natural) (Y tptp.code_natural)) (let ((_let_1 (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_p4538020629002901425atural X) Y) tptp.zero_z2226904508553997617atural) (and (= X tptp.zero_z2226904508553997617atural) (= Y tptp.zero_z2226904508553997617atural))))))))
% 2.52/3.50 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_rat X) Y) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))))))
% 2.52/3.50 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat))))))))
% 2.52/3.50 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_int X) Y) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))))
% 2.52/3.50 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger X) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le3102999989581377725nteger Y) tptp.zero_z3403309356797280102nteger) (= (= (@ (@ tptp.plus_p5714425477246183910nteger X) Y) tptp.zero_z3403309356797280102nteger) (and (= X tptp.zero_z3403309356797280102nteger) (= Y tptp.zero_z3403309356797280102nteger)))))))
% 2.52/3.50 (assert (forall ((X tptp.code_natural) (Y tptp.code_natural)) (=> (@ (@ tptp.ord_le1926595141338095240atural X) tptp.zero_z2226904508553997617atural) (=> (@ (@ tptp.ord_le1926595141338095240atural Y) tptp.zero_z2226904508553997617atural) (= (= (@ (@ tptp.plus_p4538020629002901425atural X) Y) tptp.zero_z2226904508553997617atural) (and (= X tptp.zero_z2226904508553997617atural) (= Y tptp.zero_z2226904508553997617atural)))))))
% 2.52/3.50 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.zero_zero_rat) (= (= (@ (@ tptp.plus_plus_rat X) Y) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))))
% 2.52/3.50 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat Y) tptp.zero_zero_nat) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))))
% 2.52/3.50 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.zero_zero_int) (= (= (@ (@ tptp.plus_plus_int X) Y) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))))
% 2.52/3.50 (assert (forall ((I2 tptp.code_integer) (J tptp.code_integer) (K tptp.code_integer) (L tptp.code_integer)) (=> (and (@ (@ tptp.ord_le3102999989581377725nteger I2) J) (@ (@ tptp.ord_le6747313008572928689nteger K) L)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger I2) K)) (@ (@ tptp.plus_p5714425477246183910nteger J) L)))))
% 2.52/3.50 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I2) J) (@ (@ tptp.ord_less_rat K) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 2.52/3.50 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 2.52/3.50 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J) (@ (@ tptp.ord_less_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 2.52/3.50 (assert (forall ((I2 tptp.code_integer) (J tptp.code_integer) (K tptp.code_integer) (L tptp.code_integer)) (=> (and (@ (@ tptp.ord_le6747313008572928689nteger I2) J) (@ (@ tptp.ord_le3102999989581377725nteger K) L)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger I2) K)) (@ (@ tptp.plus_p5714425477246183910nteger J) L)))))
% 2.52/3.50 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I2) J) (@ (@ tptp.ord_less_eq_rat K) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 2.52/3.50 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 2.52/3.50 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J) (@ (@ tptp.ord_less_eq_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) D2) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A) C)) (@ (@ tptp.plus_p5714425477246183910nteger B) D2))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D2) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D2))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D2))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int C) D2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D2))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) D2) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A) C)) (@ (@ tptp.plus_p5714425477246183910nteger B) D2))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D2) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D2))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D2))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D2))))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (@ (@ tptp.ord_le5570908160329646204atural A) tptp.zero_z2226904508553997617atural) (=> (@ (@ tptp.ord_le5570908160329646204atural B) tptp.zero_z2226904508553997617atural) (@ (@ tptp.ord_le5570908160329646204atural (@ (@ tptp.plus_p4538020629002901425atural A) B)) tptp.zero_z2226904508553997617atural)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) tptp.zero_z3403309356797280102nteger)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.zero_zero_rat)))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) tptp.zero_zero_int)))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (@ tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_p4538020629002901425atural A) B)))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B)))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (forall ((C3 tptp.nat)) (=> (= B (@ (@ tptp.plus_plus_nat A) C3)) (= C3 tptp.zero_zero_nat)))))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (let ((_let_1 (@ tptp.ord_le5570908160329646204atural B))) (=> (@ (@ tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_p4538020629002901425atural A) C)))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger B))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) C)))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger B) tptp.one_one_Code_integer)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat)) (@ (@ tptp.plus_plus_rat B) tptp.one_one_rat)))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat B) tptp.one_one_nat)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) (@ (@ tptp.plus_plus_int B) tptp.one_one_int)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le6747313008572928689nteger A) (@ (@ tptp.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer))))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))))
% 2.52/3.50 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat))))
% 2.52/3.50 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int A) tptp.one_one_int))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= B (@ tptp.uminus_uminus_int A)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= B (@ tptp.uminus_uminus_rat A)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= B (@ tptp.uminus1351360451143612070nteger A)))))
% 2.52/3.50 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)))
% 2.52/3.50 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= (@ tptp.uminus_uminus_int A) B))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= (@ tptp.uminus_uminus_rat A) B))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= (@ tptp.uminus1351360451143612070nteger A) B))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B)) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger B)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) B) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 2.52/3.50 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ tptp.sgn_sgn_int _let_1) _let_1)))
% 2.52/3.50 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ tptp.sgn_sgn_rat _let_1) _let_1)))
% 2.52/3.50 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ tptp.sgn_sgn_Code_integer _let_1) _let_1)))
% 2.52/3.50 (assert (@ (@ tptp.comm_monoid_nat tptp.plus_plus_nat) tptp.zero_zero_nat))
% 2.52/3.50 (assert (@ (@ tptp.comm_monoid_int tptp.plus_plus_int) tptp.zero_zero_int))
% 2.52/3.50 (assert (@ (@ tptp.comm_monoid_rat tptp.plus_plus_rat) tptp.zero_zero_rat))
% 2.52/3.50 (assert (@ (@ tptp.comm_m1654649897431166824nteger tptp.plus_p5714425477246183910nteger) tptp.zero_z3403309356797280102nteger))
% 2.52/3.50 (assert (@ (@ tptp.comm_m478245049187884339atural tptp.plus_p4538020629002901425atural) tptp.zero_z2226904508553997617atural))
% 2.52/3.50 (assert (@ (@ tptp.monoid_nat tptp.plus_plus_nat) tptp.zero_zero_nat))
% 2.52/3.50 (assert (@ (@ tptp.monoid_int tptp.plus_plus_int) tptp.zero_zero_int))
% 2.52/3.50 (assert (@ (@ tptp.monoid_rat tptp.plus_plus_rat) tptp.zero_zero_rat))
% 2.52/3.50 (assert (@ (@ tptp.monoid_Code_integer tptp.plus_p5714425477246183910nteger) tptp.zero_z3403309356797280102nteger))
% 2.52/3.50 (assert (@ (@ tptp.monoid_Code_natural tptp.plus_p4538020629002901425atural) tptp.zero_z2226904508553997617atural))
% 2.52/3.50 (assert (= tptp.neg_nu5831290666863070958nteger (lambda ((X2 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger X2) X2)) tptp.one_one_Code_integer))))
% 2.52/3.50 (assert (= tptp.neg_nu5219082963157363817nc_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat X2) X2)) tptp.one_one_rat))))
% 2.52/3.50 (assert (= tptp.neg_nu5851722552734809277nc_int (lambda ((X2 tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int X2) X2)) tptp.one_one_int))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (@ (@ tptp.ord_le5570908160329646204atural A) tptp.zero_z2226904508553997617atural) (=> (@ (@ tptp.ord_le1926595141338095240atural B) tptp.zero_z2226904508553997617atural) (@ (@ tptp.ord_le5570908160329646204atural (@ (@ tptp.plus_p4538020629002901425atural A) B)) tptp.zero_z2226904508553997617atural)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) tptp.zero_z3403309356797280102nteger)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.zero_zero_rat)))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) tptp.zero_zero_int)))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (@ tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural))) (=> (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_p4538020629002901425atural A) B)))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B)))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (@ (@ tptp.ord_le1926595141338095240atural A) tptp.zero_z2226904508553997617atural) (=> (@ (@ tptp.ord_le5570908160329646204atural B) tptp.zero_z2226904508553997617atural) (@ (@ tptp.ord_le5570908160329646204atural (@ (@ tptp.plus_p4538020629002901425atural A) B)) tptp.zero_z2226904508553997617atural)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) tptp.zero_z3403309356797280102nteger)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.zero_zero_rat)))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) tptp.zero_zero_int)))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (@ tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) B) (@ _let_1 (@ (@ tptp.plus_p4538020629002901425atural A) B)))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B)))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (=> (@ (@ tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural) A) (=> (@ (@ tptp.ord_le1926595141338095240atural B) C) (@ (@ tptp.ord_le5570908160329646204atural B) (@ (@ tptp.plus_p4538020629002901425atural A) C))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) C) (@ (@ tptp.ord_le6747313008572928689nteger B) (@ (@ tptp.plus_p5714425477246183910nteger A) C))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.plus_plus_rat A) C))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ (@ tptp.ord_less_nat B) (@ (@ tptp.plus_plus_nat A) C))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int B) C) (@ (@ tptp.ord_less_int B) (@ (@ tptp.plus_plus_int A) C))))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (let ((_let_1 (@ tptp.ord_le5570908160329646204atural B))) (=> (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_p4538020629002901425atural A) C)))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger B))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) C)))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 2.52/3.50 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger X) X)) (@ (@ tptp.times_3573771949741848930nteger Y) Y)))))
% 2.52/3.50 (assert (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y)))))
% 2.52/3.50 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)))))
% 2.52/3.50 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger X) X)) (@ (@ tptp.times_3573771949741848930nteger Y) Y))) tptp.zero_z3403309356797280102nteger))))
% 2.52/3.50 (assert (forall ((X tptp.rat) (Y tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y))) tptp.zero_zero_rat))))
% 2.52/3.50 (assert (forall ((X tptp.int) (Y tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y))) tptp.zero_zero_int))))
% 2.52/3.50 (assert (@ (@ tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural) (@ (@ tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural) tptp.one_one_Code_natural)))
% 2.52/3.50 (assert (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) tptp.one_one_Code_integer)))
% 2.52/3.50 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat)))
% 2.52/3.50 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)))
% 2.52/3.50 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int)))
% 2.52/3.50 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.sgn_sgn_Code_integer A) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (= (= (@ tptp.sgn_sgn_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))))
% 2.52/3.50 (assert (forall ((A tptp.int)) (= (= (@ tptp.sgn_sgn_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 2.52/3.50 (assert (forall ((X tptp.code_integer) (A tptp.code_integer) (Y tptp.code_integer) (U tptp.code_integer) (V2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_le3102999989581377725nteger X) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V2) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger U) V2) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger U) X)) (@ (@ tptp.times_3573771949741848930nteger V2) Y))) A)))))))))
% 2.52/3.50 (assert (forall ((X tptp.rat) (A tptp.rat) (Y tptp.rat) (U tptp.rat) (V2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat X) A) (=> (@ (@ tptp.ord_less_eq_rat Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V2) (=> (= (@ (@ tptp.plus_plus_rat U) V2) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat U) X)) (@ (@ tptp.times_times_rat V2) Y))) A)))))))))
% 2.52/3.50 (assert (forall ((X tptp.int) (A tptp.int) (Y tptp.int) (U tptp.int) (V2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int X) A) (=> (@ (@ tptp.ord_less_eq_int Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V2) (=> (= (@ (@ tptp.plus_plus_int U) V2) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X)) (@ (@ tptp.times_times_int V2) Y))) A)))))))))
% 2.52/3.50 (assert (= tptp.sgn_sgn_int (lambda ((X2 tptp.int)) (@ (@ (@ tptp.if_int (= X2 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) X2)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 2.52/3.50 (assert (= tptp.sgn_sgn_rat (lambda ((X2 tptp.rat)) (@ (@ (@ tptp.if_rat (= X2 tptp.zero_zero_rat)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X2)) tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 2.52/3.50 (assert (= tptp.sgn_sgn_Code_integer (lambda ((X2 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (= X2 tptp.zero_z3403309356797280102nteger)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) X2)) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))))
% 2.52/3.50 (assert (forall ((A tptp.int)) (= (= (@ tptp.sgn_sgn_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (= (= (@ tptp.sgn_sgn_rat A) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.sgn_sgn_Code_integer A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))
% 2.52/3.50 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) tptp.one_one_nat) (= N tptp.zero_zero_nat))))
% 2.52/3.50 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((A2 tptp.code_integer) (__flatten_var_0 tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) tptp.one_one_Code_integer)) __flatten_var_0))))
% 2.52/3.50 (assert (= tptp.ord_less_nat (lambda ((A2 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) tptp.one_one_nat)) __flatten_var_0))))
% 2.52/3.50 (assert (= tptp.ord_less_int (lambda ((A2 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) tptp.one_one_int)) __flatten_var_0))))
% 2.52/3.50 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger X) X)) (@ (@ tptp.times_3573771949741848930nteger Y) Y))) (or (not (= X tptp.zero_z3403309356797280102nteger)) (not (= Y tptp.zero_z3403309356797280102nteger))))))
% 2.52/3.50 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y))) (or (not (= X tptp.zero_zero_rat)) (not (= Y tptp.zero_zero_rat))))))
% 2.52/3.50 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y))) (or (not (= X tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int))))))
% 2.52/3.50 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger X) X)) (@ (@ tptp.times_3573771949741848930nteger Y) Y))) tptp.zero_z3403309356797280102nteger) (and (= X tptp.zero_z3403309356797280102nteger) (= Y tptp.zero_z3403309356797280102nteger)))))
% 2.52/3.50 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y))) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))
% 2.52/3.50 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y))) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))
% 2.52/3.50 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.n_list679713369942834879n_assn N) tptp.nil_Pr5671120429643327159n_assn))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 (@ (@ tptp.cons_l2423627976422276333n_assn tptp.nil_Pr5671120429643327159n_assn) tptp.nil_li5476096274760905021n_assn))) (=> (not _let_2) (= _let_1 tptp.nil_li5476096274760905021n_assn)))))))
% 2.52/3.50 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.n_lists_int N) tptp.nil_int))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 (@ (@ tptp.cons_list_int tptp.nil_int) tptp.nil_list_int))) (=> (not _let_2) (= _let_1 tptp.nil_list_int)))))))
% 2.52/3.50 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.n_lists_nat N) tptp.nil_nat))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 (@ (@ tptp.cons_list_nat tptp.nil_nat) tptp.nil_list_nat))) (=> (not _let_2) (= _let_1 tptp.nil_list_nat)))))))
% 2.52/3.50 (assert (forall ((R2 tptp.rat) (A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat R2))) (=> (not (= R2 tptp.zero_zero_rat)) (=> (and (= A B) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_rat A) (@ _let_1 C)) (@ (@ tptp.plus_plus_rat B) (@ _let_1 D2)))))))))
% 2.52/3.50 (assert (forall ((R2 tptp.nat) (A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat R2))) (=> (not (= R2 tptp.zero_zero_nat)) (=> (and (= A B) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_nat A) (@ _let_1 C)) (@ (@ tptp.plus_plus_nat B) (@ _let_1 D2)))))))))
% 2.52/3.50 (assert (forall ((R2 tptp.int) (A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int R2))) (=> (not (= R2 tptp.zero_zero_int)) (=> (and (= A B) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_int A) (@ _let_1 C)) (@ (@ tptp.plus_plus_int B) (@ _let_1 D2)))))))))
% 2.52/3.50 (assert (forall ((R2 tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger R2))) (=> (not (= R2 tptp.zero_z3403309356797280102nteger)) (=> (and (= A B) (not (= C D2))) (not (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ _let_1 C)) (@ (@ tptp.plus_p5714425477246183910nteger B) (@ _let_1 D2)))))))))
% 2.52/3.50 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y)) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))
% 2.52/3.50 (assert (forall ((X tptp.int) (Y tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))
% 2.52/3.50 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger X) X)) (@ (@ tptp.times_3573771949741848930nteger Y) Y)) tptp.zero_z3403309356797280102nteger) (and (= X tptp.zero_z3403309356797280102nteger) (= Y tptp.zero_z3403309356797280102nteger)))))
% 2.52/3.50 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn)) (= (@ (@ tptp.n_list679713369942834879n_assn tptp.zero_zero_nat) Xs) (@ (@ tptp.cons_l2423627976422276333n_assn tptp.nil_Pr5671120429643327159n_assn) tptp.nil_li5476096274760905021n_assn))))
% 2.52/3.50 (assert (forall ((Xs tptp.list_int)) (= (@ (@ tptp.n_lists_int tptp.zero_zero_nat) Xs) (@ (@ tptp.cons_list_int tptp.nil_int) tptp.nil_list_int))))
% 2.52/3.50 (assert (forall ((Xs tptp.list_nat)) (= (@ (@ tptp.n_lists_nat tptp.zero_zero_nat) Xs) (@ (@ tptp.cons_list_nat tptp.nil_nat) tptp.nil_list_nat))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat B))) (let ((_let_2 (@ tptp.times_times_rat A))) (= (and (not (= A B)) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_rat (@ _let_2 C)) (@ _let_1 D2)) (@ (@ tptp.plus_plus_rat (@ _let_2 D2)) (@ _let_1 C)))))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B))) (let ((_let_2 (@ tptp.times_times_nat A))) (= (and (not (= A B)) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_nat (@ _let_2 C)) (@ _let_1 D2)) (@ (@ tptp.plus_plus_nat (@ _let_2 D2)) (@ _let_1 C)))))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (let ((_let_2 (@ tptp.times_times_int A))) (= (and (not (= A B)) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_int (@ _let_2 C)) (@ _let_1 D2)) (@ (@ tptp.plus_plus_int (@ _let_2 D2)) (@ _let_1 C)))))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger B))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger A))) (= (and (not (= A B)) (not (= C D2))) (not (= (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 C)) (@ _let_1 D2)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 D2)) (@ _let_1 C)))))))))
% 2.52/3.50 (assert (forall ((W tptp.rat) (Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X))) (let ((_let_2 (@ tptp.times_times_rat W))) (= (= (@ (@ tptp.plus_plus_rat (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_rat (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X) (= Y Z)))))))
% 2.52/3.50 (assert (forall ((W tptp.nat) (Y tptp.nat) (X tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat X))) (let ((_let_2 (@ tptp.times_times_nat W))) (= (= (@ (@ tptp.plus_plus_nat (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_nat (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X) (= Y Z)))))))
% 2.52/3.50 (assert (forall ((W tptp.int) (Y tptp.int) (X tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.times_times_int X))) (let ((_let_2 (@ tptp.times_times_int W))) (= (= (@ (@ tptp.plus_plus_int (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_int (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X) (= Y Z)))))))
% 2.52/3.50 (assert (forall ((W tptp.code_integer) (Y tptp.code_integer) (X tptp.code_integer) (Z tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger X))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger W))) (= (= (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X) (= Y Z)))))))
% 2.52/3.50 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (= tptp.one_one_nat (@ (@ tptp.times_times_nat M2) N)) (and (= M2 tptp.one_one_nat) (= N tptp.one_one_nat)))))
% 2.52/3.50 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M2) N) tptp.one_one_nat) (and (= M2 tptp.one_one_nat) (= N tptp.one_one_nat)))))
% 2.52/3.50 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) N) N)))
% 2.52/3.50 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat N) tptp.one_one_nat) N)))
% 2.52/3.50 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (= M2 (@ (@ tptp.times_times_nat M2) N)) (or (= N tptp.one_one_nat) (= M2 tptp.zero_zero_nat)))))
% 2.52/3.50 (assert (= (@ tptp.produc1566369527784499744n_assn tptp.nil_li5476096274760905021n_assn) (@ (@ tptp.cons_l2423627976422276333n_assn tptp.nil_Pr5671120429643327159n_assn) tptp.nil_li5476096274760905021n_assn)))
% 2.52/3.50 (assert (= (@ tptp.product_lists_int tptp.nil_list_int) (@ (@ tptp.cons_list_int tptp.nil_int) tptp.nil_list_int)))
% 2.52/3.50 (assert (= (@ tptp.product_lists_nat tptp.nil_list_nat) (@ (@ tptp.cons_list_nat tptp.nil_nat) tptp.nil_list_nat)))
% 2.52/3.50 (assert (forall ((B tptp.code_natural) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_7079662738309270450atural B))) (=> (@ (@ tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural) B) (=> (@ (@ tptp.ord_le5570908160329646204atural B) tptp.one_one_Code_natural) (= (@ (@ tptp.ord_le1926595141338095240atural (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M2)))))))
% 2.52/3.50 (assert (forall ((B tptp.code_integer) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger B))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.one_one_Code_integer) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M2)))))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_rat B) tptp.one_one_rat) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M2)))))))
% 2.52/3.50 (assert (forall ((B tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat B) tptp.one_one_nat) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M2)))))))
% 2.52/3.50 (assert (forall ((B tptp.int) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int B) tptp.one_one_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M2)))))))
% 2.52/3.50 (assert (= (@ tptp.subseq184808802919281286n_assn tptp.nil_Pr5671120429643327159n_assn) (@ (@ tptp.cons_l2423627976422276333n_assn tptp.nil_Pr5671120429643327159n_assn) tptp.nil_li5476096274760905021n_assn)))
% 2.52/3.50 (assert (= (@ tptp.subseqs_int tptp.nil_int) (@ (@ tptp.cons_list_int tptp.nil_int) tptp.nil_list_int)))
% 2.52/3.50 (assert (= (@ tptp.subseqs_nat tptp.nil_nat) (@ (@ tptp.cons_list_nat tptp.nil_nat) tptp.nil_list_nat)))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ tptp.uminus_uminus_rat B))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat)))))))))))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.uminus_uminus_rat B))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat _let_2) _let_3)) (=> (not _let_4) (and (=> _let_1 (@ (@ tptp.ord_less_eq_rat _let_3) _let_2)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A))))))))))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.divide_divide_rat (@ _let_1 B)) C)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) C)) B))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (= (@ (@ tptp.divide_divide_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat B) A)) C))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) tptp.one_one_Code_integer) A)))
% 2.52/3.50 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)))
% 2.52/3.50 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.one_one_rat) A)))
% 2.52/3.50 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.divide5121882707175180666atural A) tptp.one_one_Code_natural) A)))
% 2.52/3.50 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger tptp.one_one_Code_integer) N) tptp.one_one_Code_integer)))
% 2.52/3.50 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_assn tptp.one_one_assn) N) tptp.one_one_assn)))
% 2.52/3.50 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.one_one_rat) N) tptp.one_one_rat)))
% 2.52/3.50 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int tptp.one_one_int) N) tptp.one_one_int)))
% 2.52/3.50 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.one_one_nat) N) tptp.one_one_nat)))
% 2.52/3.50 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.one_one_nat) A)))
% 2.52/3.50 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.one_one_nat) A)))
% 2.52/3.50 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat C) B)) (@ (@ tptp.divide_divide_rat A) B)))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (@ (@ tptp.divide_divide_rat A) B)))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat C) A)) (@ (@ tptp.times_times_rat B) C)) (@ (@ tptp.divide_divide_rat A) B)))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_rat A) B))))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (let ((_let_2 (@ (@ tptp.divide_divide_rat (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_rat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_rat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_rat A) B)))))))))
% 2.52/3.50 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) B) A))))
% 2.52/3.50 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) B)) B) A))))
% 2.52/3.50 (assert (forall ((B tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) B)) B) A))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) B)) B) A))))
% 2.52/3.50 (assert (forall ((B tptp.code_natural) (A tptp.code_natural)) (=> (not (= B tptp.zero_z2226904508553997617atural)) (= (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.times_2397367101498566445atural A) B)) B) A))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) A) B))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) B)) A) B))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) B)) A) B))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) B)) A) B))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (not (= A tptp.zero_z2226904508553997617atural)) (= (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.times_2397367101498566445atural A) B)) A) B))))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) (= A tptp.zero_zero_rat))))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= tptp.one_one_rat (@ (@ tptp.divide_divide_rat B) A)) (and (not (= A tptp.zero_zero_rat)) (= A B)))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat B) A) tptp.one_one_rat) (and (not (= A tptp.zero_zero_rat)) (= A B)))))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ (@ tptp.divide_divide_rat A) A))) (let ((_let_2 (= A tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_rat)) (=> (not _let_2) (= _let_1 tptp.one_one_rat)))))))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= tptp.one_one_rat (@ (@ tptp.divide_divide_rat A) B)) (and (not (= B tptp.zero_zero_rat)) (= A B)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) B) tptp.one_one_rat) (and (not (= B tptp.zero_zero_rat)) (= A B)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger A) A) tptp.one_one_Code_integer))))
% 2.52/3.50 (assert (forall ((A tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat A) A) tptp.one_one_nat))))
% 2.52/3.50 (assert (forall ((A tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int A) A) tptp.one_one_int))))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural)) (=> (not (= A tptp.zero_z2226904508553997617atural)) (= (@ (@ tptp.divide5121882707175180666atural A) A) tptp.one_one_Code_natural))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A) (= (= (@ _let_1 M2) (@ _let_1 N)) (= M2 N))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (= (= (@ _let_1 M2) (@ _let_1 N)) (= M2 N))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (= (= (@ _let_1 M2) (@ _let_1 N)) (= M2 N))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (= (= (@ _let_1 M2) (@ _let_1 N)) (= M2 N))))))
% 2.52/3.50 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.divide_divide_rat X) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat X))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat B))) (= (@ (@ tptp.divide_divide_rat A) _let_1) (@ (@ tptp.times_times_rat A) _let_1)))))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) (@ _let_1 A)))))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) (@ _let_1 A)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (@ (@ tptp.ord_less_rat A) B)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (@ (@ tptp.ord_less_rat B) A)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (@ (@ tptp.ord_less_rat B) A)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (@ _let_1 B))))))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat B) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) B)))))
% 2.52/3.50 (assert (forall ((B tptp.code_integer) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger B))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) B) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) B) (= (@ (@ tptp.ord_less_rat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 2.52/3.50 (assert (forall ((B tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B) (= (@ (@ tptp.ord_less_nat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 2.52/3.50 (assert (forall ((B tptp.int) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B) (= (@ (@ tptp.ord_less_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 2.52/3.50 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 2.52/3.50 (assert (forall ((N tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 2.52/3.50 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 2.52/3.50 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N))) (= (@ (@ tptp.times_times_int _let_1) _let_1) tptp.one_one_int))))
% 2.52/3.50 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) tptp.one_one_rat))))
% 2.52/3.50 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) tptp.one_one_Code_integer))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (@ (@ tptp.ord_less_eq_rat B) A)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat B) A)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 2.52/3.50 (assert (forall ((B tptp.code_natural) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_7079662738309270450atural B))) (=> (@ (@ tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural) B) (=> (@ (@ tptp.ord_le5570908160329646204atural B) tptp.one_one_Code_natural) (= (@ (@ tptp.ord_le5570908160329646204atural (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M2)))))))
% 2.52/3.50 (assert (forall ((B tptp.code_integer) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger B))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.one_one_Code_integer) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M2)))))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_rat B) tptp.one_one_rat) (= (@ (@ tptp.ord_less_rat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M2)))))))
% 2.52/3.50 (assert (forall ((B tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat B) tptp.one_one_nat) (= (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M2)))))))
% 2.52/3.50 (assert (forall ((B tptp.int) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int B) tptp.one_one_int) (= (@ (@ tptp.ord_less_int (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M2)))))))
% 2.52/3.50 (assert (forall ((B tptp.code_integer) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger B))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) B) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) B) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 2.52/3.50 (assert (forall ((B tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 2.52/3.50 (assert (forall ((B tptp.int) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_rat tptp.one_one_rat))) (= (@ (@ tptp.power_power_rat (@ _let_1 A)) N) (@ _let_1 (@ (@ tptp.power_power_rat A) N))))))
% 2.52/3.50 (assert (forall ((A tptp.assn) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_assn A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.times_times_assn (@ _let_1 M2)) (@ _let_1 N))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.times_times_nat (@ _let_1 M2)) (@ _let_1 N))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.times_times_int (@ _let_1 M2)) (@ _let_1 N))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 M2)) (@ _let_1 N))))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_7079662738309270450atural A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M2) N)) (@ (@ tptp.times_2397367101498566445atural (@ _let_1 M2)) (@ _let_1 N))))))
% 2.52/3.50 (assert (forall ((X tptp.assn) (Y tptp.assn) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_assn X) N))) (let ((_let_2 (@ tptp.times_times_assn Y))) (=> (= (@ (@ tptp.times_times_assn X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_times_assn _let_1) Y) (@ _let_2 _let_1)))))))
% 2.52/3.50 (assert (forall ((X tptp.nat) (Y tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat X) N))) (let ((_let_2 (@ tptp.times_times_nat Y))) (=> (= (@ (@ tptp.times_times_nat X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_times_nat _let_1) Y) (@ _let_2 _let_1)))))))
% 2.52/3.50 (assert (forall ((X tptp.int) (Y tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int X) N))) (let ((_let_2 (@ tptp.times_times_int Y))) (=> (= (@ (@ tptp.times_times_int X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_times_int _let_1) Y) (@ _let_2 _let_1)))))))
% 2.52/3.50 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger X) N))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger Y))) (=> (= (@ (@ tptp.times_3573771949741848930nteger X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) Y) (@ _let_2 _let_1)))))))
% 2.52/3.50 (assert (forall ((X tptp.code_natural) (Y tptp.code_natural) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_7079662738309270450atural X) N))) (let ((_let_2 (@ tptp.times_2397367101498566445atural Y))) (=> (= (@ (@ tptp.times_2397367101498566445atural X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_2397367101498566445atural _let_1) Y) (@ _let_2 _let_1)))))))
% 2.52/3.50 (assert (forall ((A tptp.assn) (B tptp.assn) (N tptp.nat)) (= (@ (@ tptp.power_power_assn (@ (@ tptp.times_times_assn A) B)) N) (@ (@ tptp.times_times_assn (@ (@ tptp.power_power_assn A) N)) (@ (@ tptp.power_power_assn B) N)))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.times_times_nat A) B)) N) (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.times_times_int A) B)) N) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) N) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger A) N)) (@ (@ tptp.power_8256067586552552935nteger B) N)))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (N tptp.nat)) (= (@ (@ tptp.power_7079662738309270450atural (@ (@ tptp.times_2397367101498566445atural A) B)) N) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.power_7079662738309270450atural A) N)) (@ (@ tptp.power_7079662738309270450atural B) N)))))
% 2.52/3.50 (assert (forall ((A tptp.assn) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_assn A) N))) (= (@ (@ tptp.times_times_assn _let_1) A) (@ (@ tptp.times_times_assn A) _let_1)))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N))) (= (@ (@ tptp.times_times_nat _let_1) A) (@ (@ tptp.times_times_nat A) _let_1)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N))) (= (@ (@ tptp.times_times_int _let_1) A) (@ (@ tptp.times_times_int A) _let_1)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger A) N))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) A) (@ (@ tptp.times_3573771949741848930nteger A) _let_1)))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_7079662738309270450atural A) N))) (= (@ (@ tptp.times_2397367101498566445atural _let_1) A) (@ (@ tptp.times_2397367101498566445atural A) _let_1)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (= (@ (@ tptp.divide_divide_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_rat C) B))))))
% 2.52/3.50 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat) (W tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat Z) W)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat X) W)) (@ (@ tptp.times_times_rat Y) Z)))))
% 2.52/3.50 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat) (W tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat Z) W)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat Y) W)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A) N))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.one_one_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N))))))
% 2.52/3.50 (assert (forall ((X tptp.rat) (Y tptp.rat) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_rat X) Y) tptp.one_one_rat) (= (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X) N)) (@ (@ tptp.power_power_rat Y) N)) tptp.one_one_rat))))
% 2.52/3.50 (assert (forall ((X tptp.assn) (Y tptp.assn) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_assn X) Y) tptp.one_one_assn) (= (@ (@ tptp.times_times_assn (@ (@ tptp.power_power_assn X) N)) (@ (@ tptp.power_power_assn Y) N)) tptp.one_one_assn))))
% 2.52/3.50 (assert (forall ((X tptp.nat) (Y tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_nat X) Y) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat X) N)) (@ (@ tptp.power_power_nat Y) N)) tptp.one_one_nat))))
% 2.52/3.50 (assert (forall ((X tptp.int) (Y tptp.int) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_int X) Y) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X) N)) (@ (@ tptp.power_power_int Y) N)) tptp.one_one_int))))
% 2.52/3.50 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (N tptp.nat)) (=> (= (@ (@ tptp.times_3573771949741848930nteger X) Y) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger X) N)) (@ (@ tptp.power_8256067586552552935nteger Y) N)) tptp.one_one_Code_integer))))
% 2.52/3.50 (assert (forall ((X tptp.code_natural) (Y tptp.code_natural) (N tptp.nat)) (=> (= (@ (@ tptp.times_2397367101498566445atural X) Y) tptp.one_one_Code_natural) (= (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.power_7079662738309270450atural X) N)) (@ (@ tptp.power_7079662738309270450atural Y) N)) tptp.one_one_Code_natural))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= A (@ (@ tptp.divide_divide_rat B) C)) (= (@ (@ tptp.times_times_rat A) C) B)))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat B) C) A) (= B (@ (@ tptp.times_times_rat A) C))))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (=> (= (@ (@ tptp.times_times_rat A) C) B) (= A (@ (@ tptp.divide_divide_rat B) C))))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (=> (= B (@ (@ tptp.times_times_rat A) C)) (= (@ (@ tptp.divide_divide_rat B) C) A)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= A (@ (@ tptp.divide_divide_rat B) C)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_rat A) C) B)) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) C) A) (and (=> (not _let_1) (= B (@ (@ tptp.times_times_rat A) C))) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 2.52/3.50 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat X) Y) (@ (@ tptp.divide_divide_rat W) Z)) (= (@ (@ tptp.times_times_rat X) Z) (@ (@ tptp.times_times_rat W) Y)))))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat A) B) tptp.one_one_rat) (= A B)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.power_8256067586552552935nteger A) tptp.zero_zero_nat) tptp.one_one_Code_integer)))
% 2.52/3.50 (assert (forall ((A tptp.assn)) (= (@ (@ tptp.power_power_assn A) tptp.zero_zero_nat) tptp.one_one_assn)))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 2.52/3.50 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 2.52/3.50 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A) N)) tptp.one_one_Code_integer)))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (N tptp.nat)) (=> (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) A) (=> (@ (@ tptp.ord_le1926595141338095240atural A) tptp.one_one_Code_natural) (@ (@ tptp.ord_le1926595141338095240atural (@ (@ tptp.power_7079662738309270450atural A) N)) tptp.one_one_Code_natural)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) tptp.one_one_rat)))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N)) tptp.one_one_nat)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) tptp.one_one_int)))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_7079662738309270450atural A) N))) (=> (@ (@ tptp.ord_le5570908160329646204atural tptp.one_one_Code_natural) A) (@ (@ tptp.ord_le5570908160329646204atural _let_1) (@ (@ tptp.times_2397367101498566445atural A) _let_1))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger A) N))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A) (@ (@ tptp.ord_le6747313008572928689nteger _let_1) (@ (@ tptp.times_3573771949741848930nteger A) _let_1))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_rat _let_1) (@ (@ tptp.times_times_rat A) _let_1))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_nat _let_1) (@ (@ tptp.times_times_nat A) _let_1))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (@ (@ tptp.ord_less_int _let_1) (@ (@ tptp.times_times_int A) _let_1))))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_le5570908160329646204atural tptp.one_one_Code_natural))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_2397367101498566445atural A) (@ (@ tptp.power_7079662738309270450atural A) N)))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A) (@ (@ tptp.power_8256067586552552935nteger A) N)))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_rat A) (@ (@ tptp.power_power_rat A) N)))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_nat A) (@ (@ tptp.power_power_nat A) N)))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_int A) (@ (@ tptp.power_power_int A) N)))))))
% 2.52/3.50 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C))))))
% 2.52/3.50 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C))))))
% 2.52/3.50 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ _let_2 C) (=> (@ _let_2 (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))))
% 2.52/3.50 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat Z) Y)) X) (@ (@ tptp.ord_less_rat Z) (@ (@ tptp.divide_divide_rat X) Y))))))
% 2.52/3.50 (assert (forall ((Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_rat X) (@ (@ tptp.times_times_rat Z) Y)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y)) Z)))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) B)))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) C))))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) C))))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) B)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_4 (@ (@ tptp.ord_less_rat _let_3) B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_rat B) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat))))))))))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ _let_1 C))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) A) (and (=> _let_4 (@ (@ tptp.ord_less_rat B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_3) B)) (=> (not _let_2) (@ _let_1 A))))))))))))
% 2.52/3.50 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat tptp.zero_zero_rat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))))
% 2.52/3.50 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger tptp.zero_z3403309356797280102nteger) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_Code_integer)) (=> (not _let_2) (= _let_1 tptp.zero_z3403309356797280102nteger)))))))
% 2.52/3.50 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_7079662738309270450atural tptp.zero_z2226904508553997617atural) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_Code_natural)) (=> (not _let_2) (= _let_1 tptp.zero_z2226904508553997617atural)))))))
% 2.52/3.50 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int tptp.zero_zero_int) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))))
% 2.52/3.50 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat tptp.zero_zero_nat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ _let_1 B)) (and (@ _let_1 tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)))))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_rat B) A)) (and (@ _let_1 tptp.zero_zero_rat) (@ _let_1 B)) (= A tptp.zero_zero_rat))))))
% 2.52/3.50 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X) Z)) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.times_times_rat Y) Z))) Z)))))
% 2.52/3.50 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.divide_divide_rat Y) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) Z)) Y)) Z)))))
% 2.52/3.50 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.times_times_rat Z) Y))) Y)))))
% 2.52/3.50 (assert (forall ((Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X) Y)) Z) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.times_times_rat Z) Y))) Y)))))
% 2.52/3.50 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z)))))))
% 2.52/3.50 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.divide_divide_rat B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) Z)) B)) Z))))))))
% 2.52/3.50 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 2.52/3.50 (assert (forall ((N tptp.nat) (N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_less_nat N) N2) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 N)) (@ _let_1 N2)))))))
% 2.52/3.50 (assert (forall ((N tptp.nat) (N2 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N) N2) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_rat (@ _let_1 N)) (@ _let_1 N2)))))))
% 2.52/3.50 (assert (forall ((N tptp.nat) (N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N) N2) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 N2)))))))
% 2.52/3.50 (assert (forall ((N tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N) N2) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (@ (@ tptp.ord_less_int (@ _let_1 N)) (@ _let_1 N2)))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M2) N))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (=> (@ (@ tptp.ord_less_rat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M2) N))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M2) N))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_int (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M2) N))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N)) (@ (@ tptp.power_power_int A) N)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N)) (@ (@ tptp.power_power_rat A) N)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N)) (@ (@ tptp.power_8256067586552552935nteger A) N)))))
% 2.52/3.50 (assert (forall ((N tptp.nat) (N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_less_eq_nat N) N2) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) A) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 N)) (@ _let_1 N2)))))))
% 2.52/3.50 (assert (forall ((N tptp.nat) (N2 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N2) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N)) (@ _let_1 N2)))))))
% 2.52/3.50 (assert (forall ((N tptp.nat) (N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N2) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 N2)))))))
% 2.52/3.50 (assert (forall ((N tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N) N2) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 N)) (@ _let_1 N2)))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat)))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat))) B))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= C (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B))) (= (@ (@ tptp.times_times_rat C) B) (@ tptp.uminus_uminus_rat A))))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B)) C) (= (@ tptp.uminus_uminus_rat A) (@ (@ tptp.times_times_rat C) B))))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C)) A) (and (=> (not _let_1) (= (@ tptp.uminus_uminus_rat B) (@ (@ tptp.times_times_rat A) C))) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= A (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_rat A) C) (@ tptp.uminus_uminus_rat B))) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) B) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (and (not (= B tptp.zero_zero_rat)) (= A (@ tptp.uminus_uminus_rat B))))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_7079662738309270450atural A) N))) (=> (@ (@ tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural) A) (=> (@ (@ tptp.ord_le5570908160329646204atural A) tptp.one_one_Code_natural) (@ (@ tptp.ord_le5570908160329646204atural (@ (@ tptp.times_2397367101498566445atural A) _let_1)) _let_1))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger A) N))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) _let_1)) _let_1))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) _let_1)) _let_1))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) _let_1)) _let_1))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) _let_1)) _let_1))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))))
% 2.52/3.50 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z) Y)) X) (@ (@ tptp.ord_less_eq_rat Z) (@ (@ tptp.divide_divide_rat X) Y))))))
% 2.52/3.50 (assert (forall ((Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.times_times_rat Z) Y)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y)) Z)))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) B)))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) C))))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) C))))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) B)))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat _let_3) B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat B) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat))))))))))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.times_times_rat A) C))) (let ((_let_3 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) A) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B) _let_2)) (=> (not _let_3) (and (=> _let_1 (@ (@ tptp.ord_less_eq_rat _let_2) B)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A)))))))))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat B) A)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) B)) (= A tptp.zero_zero_rat)))))
% 2.52/3.50 (assert (forall ((N tptp.nat) (N2 tptp.nat) (A tptp.code_natural)) (let ((_let_1 (@ tptp.power_7079662738309270450atural A))) (=> (@ (@ tptp.ord_less_nat N) N2) (=> (@ (@ tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural) A) (=> (@ (@ tptp.ord_le5570908160329646204atural A) tptp.one_one_Code_natural) (@ (@ tptp.ord_le5570908160329646204atural (@ _let_1 N2)) (@ _let_1 N))))))))
% 2.52/3.50 (assert (forall ((N tptp.nat) (N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_less_nat N) N2) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 N2)) (@ _let_1 N))))))))
% 2.52/3.50 (assert (forall ((N tptp.nat) (N2 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N) N2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ _let_1 N2)) (@ _let_1 N))))))))
% 2.52/3.50 (assert (forall ((N tptp.nat) (N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N) N2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ _let_1 N2)) (@ _let_1 N))))))))
% 2.52/3.50 (assert (forall ((N tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N) N2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ _let_1 N2)) (@ _let_1 N))))))))
% 2.52/3.50 (assert (forall ((N tptp.nat) (N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_less_eq_nat N) N2) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 N2)) (@ _let_1 N))))))))
% 2.52/3.50 (assert (forall ((N tptp.nat) (N2 tptp.nat) (A tptp.code_natural)) (let ((_let_1 (@ tptp.power_7079662738309270450atural A))) (=> (@ (@ tptp.ord_less_eq_nat N) N2) (=> (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) A) (=> (@ (@ tptp.ord_le1926595141338095240atural A) tptp.one_one_Code_natural) (@ (@ tptp.ord_le1926595141338095240atural (@ _let_1 N2)) (@ _let_1 N))))))))
% 2.52/3.50 (assert (forall ((N tptp.nat) (N2 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N2)) (@ _let_1 N))))))))
% 2.52/3.50 (assert (forall ((N tptp.nat) (N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) (@ _let_1 N))))))))
% 2.52/3.50 (assert (forall ((N tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N) N2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 N2)) (@ _let_1 N))))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_le3102999989581377725nteger A) (@ (@ tptp.power_8256067586552552935nteger A) N))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.power_power_rat A) N))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.power_power_nat A) N))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int A) N))))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ tptp.uminus_uminus_rat B))) (let ((_let_4 (@ (@ tptp.times_times_rat A) C))) (let ((_let_5 (@ _let_1 C))) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 A)))))))))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ tptp.uminus_uminus_rat B))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat)))))))))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A) N)))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_rat A) N)))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_nat A) N)))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_int A) N)))))))
% 2.52/3.50 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X) Z))) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat X)) (@ (@ tptp.times_times_rat Y) Z))) Z)))))
% 2.52/3.50 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))))
% 2.52/3.50 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) C)) A)) B) (@ (@ tptp.plus_p5714425477246183910nteger C) (@ (@ tptp.divide6298287555418463151nteger A) B))))))
% 2.52/3.50 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) C)) A)) B) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B))))))
% 2.52/3.50 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) C)) A)) B) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B))))))
% 2.52/3.50 (assert (forall ((B tptp.code_natural) (C tptp.code_natural) (A tptp.code_natural)) (=> (not (= B tptp.zero_z2226904508553997617atural)) (= (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural B) C)) A)) B) (@ (@ tptp.plus_p4538020629002901425atural C) (@ (@ tptp.divide5121882707175180666atural A) B))))))
% 2.52/3.50 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger C) B)) A)) B) (@ (@ tptp.plus_p5714425477246183910nteger C) (@ (@ tptp.divide6298287555418463151nteger A) B))))))
% 2.52/3.50 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C) B)) A)) B) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B))))))
% 2.52/3.50 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C) B)) A)) B) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B))))))
% 2.52/3.50 (assert (forall ((B tptp.code_natural) (C tptp.code_natural) (A tptp.code_natural)) (=> (not (= B tptp.zero_z2226904508553997617atural)) (= (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural C) B)) A)) B) (@ (@ tptp.plus_p4538020629002901425atural C) (@ (@ tptp.divide5121882707175180666atural A) B))))))
% 2.52/3.50 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger B) C))) B) (@ (@ tptp.plus_p5714425477246183910nteger C) (@ (@ tptp.divide6298287555418463151nteger A) B))))))
% 2.52/3.50 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat B) C))) B) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B))))))
% 2.52/3.50 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int B) C))) B) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B))))))
% 2.52/3.50 (assert (forall ((B tptp.code_natural) (A tptp.code_natural) (C tptp.code_natural)) (=> (not (= B tptp.zero_z2226904508553997617atural)) (= (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.plus_p4538020629002901425atural A) (@ (@ tptp.times_2397367101498566445atural B) C))) B) (@ (@ tptp.plus_p4538020629002901425atural C) (@ (@ tptp.divide5121882707175180666atural A) B))))))
% 2.52/3.50 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger C) B))) B) (@ (@ tptp.plus_p5714425477246183910nteger C) (@ (@ tptp.divide6298287555418463151nteger A) B))))))
% 2.52/3.50 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat C) B))) B) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B))))))
% 2.52/3.50 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C) B))) B) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B))))))
% 2.52/3.50 (assert (forall ((B tptp.code_natural) (A tptp.code_natural) (C tptp.code_natural)) (=> (not (= B tptp.zero_z2226904508553997617atural)) (= (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.plus_p4538020629002901425atural A) (@ (@ tptp.times_2397367101498566445atural C) B))) B) (@ (@ tptp.plus_p4538020629002901425atural C) (@ (@ tptp.divide5121882707175180666atural A) B))))))
% 2.52/3.50 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int A))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger A))))
% 2.52/3.50 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (let ((_let_2 (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_z3403309356797280102nteger))) (and (=> _let_3 (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide6298287555418463151nteger A) B)))))))))
% 2.52/3.50 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat A) B)))))))))
% 2.52/3.50 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_int))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_int A) B)))))))))
% 2.52/3.50 (assert (forall ((C tptp.code_natural) (A tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural C))) (let ((_let_2 (@ (@ tptp.divide5121882707175180666atural (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_z2226904508553997617atural))) (and (=> _let_3 (= _let_2 tptp.zero_z2226904508553997617atural)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide5121882707175180666atural A) B)))))))))
% 2.52/3.50 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger A) B)))))
% 2.52/3.50 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.divide_divide_nat A) B)))))
% 2.52/3.50 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (=> (not (= C tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int A) B)))))
% 2.52/3.50 (assert (forall ((C tptp.code_natural) (A tptp.code_natural) (B tptp.code_natural)) (=> (not (= C tptp.zero_z2226904508553997617atural)) (= (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.times_2397367101498566445atural A) C)) (@ (@ tptp.times_2397367101498566445atural B) C)) (@ (@ tptp.divide5121882707175180666atural A) B)))))
% 2.52/3.50 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide6298287555418463151nteger A) B))))))
% 2.52/3.50 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (not (= C tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_nat A) B))))))
% 2.52/3.50 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_int A) B))))))
% 2.52/3.50 (assert (forall ((C tptp.code_natural) (A tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural C))) (=> (not (= C tptp.zero_z2226904508553997617atural)) (= (@ (@ tptp.divide5121882707175180666atural (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide5121882707175180666atural A) B))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) tptp.one_one_Code_integer) A)))
% 2.52/3.50 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)))
% 2.52/3.50 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)))
% 2.52/3.50 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.divide5121882707175180666atural A) tptp.one_one_Code_natural) A)))
% 2.52/3.50 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M2) N)) M2)))))
% 2.52/3.50 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (= (= (@ (@ tptp.divide_divide_nat M2) N) M2) (= N tptp.one_one_nat)))))
% 2.52/3.50 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger B) A)) B) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) tptp.one_one_Code_integer)))))
% 2.52/3.50 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat B) A)) B) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) B)) tptp.one_one_nat)))))
% 2.52/3.50 (assert (forall ((B tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int B) A)) B) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) B)) tptp.one_one_int)))))
% 2.52/3.50 (assert (forall ((B tptp.code_natural) (A tptp.code_natural)) (=> (not (= B tptp.zero_z2226904508553997617atural)) (= (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.plus_p4538020629002901425atural B) A)) B) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.divide5121882707175180666atural A) B)) tptp.one_one_Code_natural)))))
% 2.52/3.50 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) tptp.one_one_Code_integer)))))
% 2.52/3.50 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) B) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) B)) tptp.one_one_nat)))))
% 2.52/3.50 (assert (forall ((B tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) B) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) B)) tptp.one_one_int)))))
% 2.52/3.50 (assert (forall ((B tptp.code_natural) (A tptp.code_natural)) (=> (not (= B tptp.zero_z2226904508553997617atural)) (= (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.plus_p4538020629002901425atural A) B)) B) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.divide5121882707175180666atural A) B)) tptp.one_one_Code_natural)))))
% 2.52/3.50 (assert (forall ((X tptp.int) (N tptp.nat)) (=> (@ (@ tptp.nO_MATCH_int_int tptp.one_one_int) X) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int X)) N) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N)) (@ (@ tptp.power_power_int X) N))))))
% 2.52/3.50 (assert (forall ((X tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.nO_MATCH_rat_rat tptp.one_one_rat) X) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat X)) N) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N)) (@ (@ tptp.power_power_rat X) N))))))
% 2.52/3.50 (assert (forall ((X tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.nO_MAT8252062027627875367nteger tptp.one_one_Code_integer) X) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger X)) N) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N)) (@ (@ tptp.power_8256067586552552935nteger X) N))))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1))))))))))))
% 2.52/3.50 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (@ tptp.ord_less_eq_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 2.52/3.50 (assert (forall ((X tptp.int) (Y tptp.int) (Xs tptp.list_int)) (let ((_let_1 (@ (@ tptp.count_list_int Xs) Y))) (let ((_let_2 (@ (@ tptp.count_list_int (@ (@ tptp.cons_int X) Xs)) Y))) (let ((_let_3 (= X Y))) (and (=> _let_3 (= _let_2 (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))))
% 2.52/3.50 (assert (forall ((X tptp.nat) (Y tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ (@ tptp.count_list_nat Xs) Y))) (let ((_let_2 (@ (@ tptp.count_list_nat (@ (@ tptp.cons_nat X) Xs)) Y))) (let ((_let_3 (= X Y))) (and (=> _let_3 (= _let_2 (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))))
% 2.52/3.50 (assert (forall ((X tptp.nat) (Y tptp.nat) (C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.nO_MATCH_nat_rat (@ (@ tptp.divide_divide_nat X) Y)) C) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 2.52/3.50 (assert (forall ((X tptp.nat) (Y tptp.nat) (C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.nO_MATCH_nat_nat (@ (@ tptp.divide_divide_nat X) Y)) C) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C))))))
% 2.52/3.50 (assert (forall ((X tptp.nat) (Y tptp.nat) (C tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.nO_MATCH_nat_int (@ (@ tptp.divide_divide_nat X) Y)) C) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 2.52/3.50 (assert (forall ((X tptp.nat) (Y tptp.nat) (C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.nO_MAT8694959213317031834nteger (@ (@ tptp.divide_divide_nat X) Y)) C) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 2.52/3.50 (assert (forall ((X tptp.nat) (Y tptp.nat) (C tptp.code_natural) (A tptp.code_natural) (B tptp.code_natural)) (=> (@ (@ tptp.nO_MAT7518554365073749349atural (@ (@ tptp.divide_divide_nat X) Y)) C) (= (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.plus_p4538020629002901425atural A) B)) C) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural A) C)) (@ (@ tptp.times_2397367101498566445atural B) C))))))
% 2.52/3.50 (assert (forall ((X tptp.int) (Y tptp.int) (C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.nO_MATCH_int_rat (@ (@ tptp.divide_divide_int X) Y)) C) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 2.52/3.50 (assert (forall ((X tptp.int) (Y tptp.int) (C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.nO_MATCH_int_nat (@ (@ tptp.divide_divide_int X) Y)) C) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C))))))
% 2.52/3.50 (assert (forall ((X tptp.int) (Y tptp.int) (C tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.nO_MATCH_int_int (@ (@ tptp.divide_divide_int X) Y)) C) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 2.52/3.50 (assert (forall ((X tptp.int) (Y tptp.int) (C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.nO_MAT9066612773553876470nteger (@ (@ tptp.divide_divide_int X) Y)) C) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 2.52/3.50 (assert (forall ((X tptp.int) (Y tptp.int) (C tptp.code_natural) (A tptp.code_natural) (B tptp.code_natural)) (=> (@ (@ tptp.nO_MAT7890207925310593985atural (@ (@ tptp.divide_divide_int X) Y)) C) (= (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.plus_p4538020629002901425atural A) B)) C) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural A) C)) (@ (@ tptp.times_2397367101498566445atural B) C))))))
% 2.52/3.50 (assert (forall ((X tptp.nat) (Y tptp.nat) (A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (=> (@ (@ tptp.nO_MATCH_nat_rat (@ (@ tptp.divide_divide_nat X) Y)) A) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C)))))))
% 2.52/3.50 (assert (forall ((X tptp.nat) (Y tptp.nat) (A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.nO_MATCH_nat_nat (@ (@ tptp.divide_divide_nat X) Y)) A) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.plus_plus_nat (@ _let_1 B)) (@ _let_1 C)))))))
% 2.52/3.50 (assert (forall ((X tptp.nat) (Y tptp.nat) (A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.nO_MATCH_nat_int (@ (@ tptp.divide_divide_nat X) Y)) A) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C)))))))
% 2.52/3.50 (assert (forall ((X tptp.nat) (Y tptp.nat) (A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.nO_MAT8694959213317031834nteger (@ (@ tptp.divide_divide_nat X) Y)) A) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 B)) (@ _let_1 C)))))))
% 2.52/3.50 (assert (forall ((X tptp.nat) (Y tptp.nat) (A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural A))) (=> (@ (@ tptp.nO_MAT7518554365073749349atural (@ (@ tptp.divide_divide_nat X) Y)) A) (= (@ _let_1 (@ (@ tptp.plus_p4538020629002901425atural B) C)) (@ (@ tptp.plus_p4538020629002901425atural (@ _let_1 B)) (@ _let_1 C)))))))
% 2.52/3.50 (assert (forall ((X tptp.int) (Y tptp.int) (A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (=> (@ (@ tptp.nO_MATCH_int_rat (@ (@ tptp.divide_divide_int X) Y)) A) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C)))))))
% 2.52/3.50 (assert (forall ((X tptp.int) (Y tptp.int) (A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.nO_MATCH_int_nat (@ (@ tptp.divide_divide_int X) Y)) A) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.plus_plus_nat (@ _let_1 B)) (@ _let_1 C)))))))
% 2.52/3.50 (assert (forall ((X tptp.int) (Y tptp.int) (A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.nO_MATCH_int_int (@ (@ tptp.divide_divide_int X) Y)) A) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C)))))))
% 2.52/3.50 (assert (forall ((X tptp.int) (Y tptp.int) (A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.nO_MAT9066612773553876470nteger (@ (@ tptp.divide_divide_int X) Y)) A) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 B)) (@ _let_1 C)))))))
% 2.52/3.50 (assert (forall ((X tptp.int) (Y tptp.int) (A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural A))) (=> (@ (@ tptp.nO_MAT7890207925310593985atural (@ (@ tptp.divide_divide_int X) Y)) A) (= (@ _let_1 (@ (@ tptp.plus_p4538020629002901425atural B) C)) (@ (@ tptp.plus_p4538020629002901425atural (@ _let_1 B)) (@ _let_1 C)))))))
% 2.52/3.50 (assert (forall ((N tptp.nat) (A tptp.assn)) (let ((_let_1 (@ tptp.power_power_assn A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_assn (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))))
% 2.52/3.50 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))))
% 2.52/3.50 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))))
% 2.52/3.50 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))))
% 2.52/3.50 (assert (forall ((N tptp.nat) (A tptp.code_natural)) (let ((_let_1 (@ tptp.power_7079662738309270450atural A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_2397367101498566445atural (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) A) tptp.zero_zero_rat)))
% 2.52/3.50 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)))
% 2.52/3.50 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) A) tptp.zero_z3403309356797280102nteger)))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) tptp.zero_zero_rat) A)))
% 2.52/3.50 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)))
% 2.52/3.50 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) tptp.zero_z3403309356797280102nteger) A)))
% 2.52/3.50 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 2.52/3.50 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.minus_7197305767214868737atural tptp.zero_z2226904508553997617atural) A) tptp.zero_z2226904508553997617atural)))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) tptp.zero_zero_rat) A)))
% 2.52/3.50 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) tptp.zero_zero_nat) A)))
% 2.52/3.50 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)))
% 2.52/3.50 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) tptp.zero_z3403309356797280102nteger) A)))
% 2.52/3.50 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.minus_7197305767214868737atural A) tptp.zero_z2226904508553997617atural) A)))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) A) tptp.zero_zero_rat)))
% 2.52/3.50 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) A) tptp.zero_zero_nat)))
% 2.52/3.50 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)))
% 2.52/3.50 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) A) tptp.zero_z3403309356797280102nteger)))
% 2.52/3.50 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.minus_7197305767214868737atural A) A) tptp.zero_z2226904508553997617atural)))
% 2.52/3.50 (assert (forall ((V2 tptp.num) (W tptp.num) (Z tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat V2)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat W)) Z)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num V2) W))) Z))))
% 2.52/3.50 (assert (forall ((V2 tptp.num) (W tptp.num) (Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int V2)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int W)) Z)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V2) W))) Z))))
% 2.52/3.50 (assert (forall ((V2 tptp.num) (W tptp.num) (Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V2)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat W)) Z)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V2) W))) Z))))
% 2.52/3.50 (assert (forall ((V2 tptp.num) (W tptp.num) (Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger V2)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger W)) Z)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V2) W))) Z))))
% 2.52/3.50 (assert (forall ((V2 tptp.num) (W tptp.num) (Z tptp.code_natural)) (= (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural V2)) (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural W)) Z)) (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural (@ (@ tptp.times_times_num V2) W))) Z))))
% 2.52/3.50 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat M2)) (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M2) N)))))
% 2.52/3.50 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int M2)) (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M2) N)))))
% 2.52/3.50 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M2) N)))))
% 2.52/3.50 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M2) N)))))
% 2.52/3.50 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural M2)) (@ tptp.numera5444537566228673987atural N)) (@ tptp.numera5444537566228673987atural (@ (@ tptp.times_times_num M2) N)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) B) A)))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B) A)))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) B) A)))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) B) A)))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) B) A)))
% 2.52/3.50 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_rat A) B)))))
% 2.52/3.50 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_nat A) B)))))
% 2.52/3.50 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.minus_minus_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_int A) B)))))
% 2.52/3.50 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger C))) (= (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_8373710615458151222nteger A) B)))))
% 2.52/3.50 (assert (forall ((C tptp.code_natural) (A tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (@ tptp.plus_p4538020629002901425atural C))) (= (@ (@ tptp.minus_7197305767214868737atural (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_7197305767214868737atural A) B)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) A) B)))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) A) B)))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) A) B)))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) A) B)))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.minus_7197305767214868737atural (@ (@ tptp.plus_p4538020629002901425atural A) B)) A) B)))
% 2.52/3.50 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.minus_minus_rat A) B))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.minus_minus_nat A) B))))
% 2.52/3.50 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.minus_minus_int A) B))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger A) C)) (@ (@ tptp.plus_p5714425477246183910nteger B) C)) (@ (@ tptp.minus_8373710615458151222nteger A) B))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (C tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.minus_7197305767214868737atural (@ (@ tptp.plus_p4538020629002901425atural A) C)) (@ (@ tptp.plus_p4538020629002901425atural B) C)) (@ (@ tptp.minus_7197305767214868737atural A) B))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) B) A)))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) B) A)))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B) A)))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.minus_7197305767214868737atural (@ (@ tptp.plus_p4538020629002901425atural A) B)) B) A)))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.minus_minus_int B) A))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.minus_minus_rat B) A))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) (@ (@ tptp.minus_8373710615458151222nteger B) A))))
% 2.52/3.50 (assert (forall ((A tptp.assn) (M2 tptp.num) (N tptp.num) (B tptp.assn)) (let ((_let_1 (@ tptp.power_power_assn A))) (= (@ (@ tptp.times_times_assn (@ _let_1 (@ tptp.numeral_numeral_nat M2))) (@ (@ tptp.times_times_assn (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_assn (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M2) N)))) B)))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (M2 tptp.num) (N tptp.num) (B tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat M2))) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M2) N)))) B)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (M2 tptp.num) (N tptp.num) (B tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat M2))) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M2) N)))) B)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (M2 tptp.num) (N tptp.num) (B tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (= (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 (@ tptp.numeral_numeral_nat M2))) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M2) N)))) B)))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (M2 tptp.num) (N tptp.num) (B tptp.code_natural)) (let ((_let_1 (@ tptp.power_7079662738309270450atural A))) (= (@ (@ tptp.times_2397367101498566445atural (@ _let_1 (@ tptp.numeral_numeral_nat M2))) (@ (@ tptp.times_2397367101498566445atural (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_2397367101498566445atural (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M2) N)))) B)))))
% 2.52/3.50 (assert (forall ((A tptp.assn) (M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_assn A))) (= (@ (@ tptp.times_times_assn (@ _let_1 (@ tptp.numeral_numeral_nat M2))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M2) N)))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat M2))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M2) N)))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat M2))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M2) N)))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (= (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 (@ tptp.numeral_numeral_nat M2))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M2) N)))))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_7079662738309270450atural A))) (= (@ (@ tptp.times_2397367101498566445atural (@ _let_1 (@ tptp.numeral_numeral_nat M2))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M2) N)))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.minus_8373710615458151222nteger A) B)) (@ (@ tptp.ord_le3102999989581377725nteger B) A))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.ord_less_eq_rat B) A))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.ord_less_eq_int B) A))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.minus_8373710615458151222nteger A) B)) (@ (@ tptp.ord_le6747313008572928689nteger B) A))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.ord_less_rat B) A))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.ord_less_int B) A))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.minus_7197305767214868737atural A) (@ (@ tptp.plus_p4538020629002901425atural A) B)) tptp.zero_z2226904508553997617atural)))
% 2.52/3.50 (assert (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) tptp.one_one_rat) tptp.zero_zero_rat))
% 2.52/3.50 (assert (= (@ (@ tptp.minus_minus_int tptp.one_one_int) tptp.one_one_int) tptp.zero_zero_int))
% 2.52/3.50 (assert (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat) (V2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V2))) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) _let_1)) (@ (@ tptp.times_times_nat B) _let_1))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (V2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int V2))) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) _let_1)) (@ (@ tptp.times_times_int B) _let_1))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (V2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat V2))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) _let_1) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) _let_1)) (@ (@ tptp.times_times_rat B) _let_1))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (V2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger V2))) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) _let_1) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger B) _let_1))))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (V2 tptp.num)) (let ((_let_1 (@ tptp.numera5444537566228673987atural V2))) (= (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.plus_p4538020629002901425atural A) B)) _let_1) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural A) _let_1)) (@ (@ tptp.times_2397367101498566445atural B) _let_1))))))
% 2.52/3.50 (assert (forall ((V2 tptp.num) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat V2)))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.plus_plus_nat (@ _let_1 B)) (@ _let_1 C))))))
% 2.52/3.50 (assert (forall ((V2 tptp.num) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int V2)))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C))))))
% 2.52/3.50 (assert (forall ((V2 tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V2)))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 2.52/3.50 (assert (forall ((V2 tptp.num) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger V2)))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 B)) (@ _let_1 C))))))
% 2.52/3.50 (assert (forall ((V2 tptp.num) (B tptp.code_natural) (C tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural V2)))) (= (@ _let_1 (@ (@ tptp.plus_p4538020629002901425atural B) C)) (@ (@ tptp.plus_p4538020629002901425atural (@ _let_1 B)) (@ _let_1 C))))))
% 2.52/3.50 (assert (forall ((V2 tptp.num) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int V2)))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C))))))
% 2.52/3.50 (assert (forall ((V2 tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V2)))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 2.52/3.50 (assert (forall ((V2 tptp.num) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger V2)))) (= (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger B) C)) (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 B)) (@ _let_1 C))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (V2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int V2))) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) _let_1) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) _let_1)) (@ (@ tptp.times_times_int B) _let_1))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (V2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat V2))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) _let_1) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A) _let_1)) (@ (@ tptp.times_times_rat B) _let_1))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (V2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger V2))) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) _let_1) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.times_3573771949741848930nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger B) _let_1))))))
% 2.52/3.50 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) A) (@ tptp.uminus_uminus_int A))))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat tptp.zero_zero_rat) A) (@ tptp.uminus_uminus_rat A))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) A) (@ tptp.uminus1351360451143612070nteger A))))
% 2.52/3.50 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M2) N)))))
% 2.52/3.50 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M2) N)))))
% 2.52/3.50 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M2) N)))))
% 2.52/3.50 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M2) N))))))
% 2.52/3.50 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M2) N))))))
% 2.52/3.50 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M2) N))))))
% 2.52/3.50 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M2) N))))))
% 2.52/3.50 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M2) N))))))
% 2.52/3.50 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M2) N))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.plus_plus_int A) B))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.plus_plus_rat A) B))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.plus_p5714425477246183910nteger A) B))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.minus_minus_int B) A))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.minus_minus_rat B) A))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.minus_8373710615458151222nteger B) A))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) _let_1))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat A) _let_1))) (=> _let_2 (= A tptp.zero_zero_rat))))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= A (@ (@ tptp.divide_divide_rat B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_rat))))))))
% 2.52/3.50 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.minus_minus_int _let_1) _let_1) tptp.zero_zero_int)))
% 2.52/3.50 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ (@ tptp.minus_minus_rat _let_1) _let_1) tptp.zero_zero_rat)))
% 2.52/3.50 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.minus_8373710615458151222nteger _let_1) _let_1) tptp.zero_z3403309356797280102nteger)))
% 2.52/3.50 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) _let_1))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) _let_1))))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat A) _let_1))) (=> _let_2 (= A tptp.zero_zero_rat))))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= A (@ (@ tptp.divide_divide_rat B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_rat))))))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) _let_1))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C) D2)) (= (= A B) (= C D2)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (= (@ (@ tptp.minus_8373710615458151222nteger A) B) (@ (@ tptp.minus_8373710615458151222nteger C) D2)) (= (= A B) (= C D2)))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 C)) B) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) C)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ (@ tptp.minus_minus_int (@ _let_1 C)) B) (@ (@ tptp.minus_minus_int (@ _let_1 B)) C)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger A))) (= (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 C)) B) (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 B)) C)))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (C tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (@ tptp.minus_7197305767214868737atural A))) (= (@ (@ tptp.minus_7197305767214868737atural (@ _let_1 C)) B) (@ (@ tptp.minus_7197305767214868737atural (@ _let_1 B)) C)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger D2) C) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger A) C)) (@ (@ tptp.minus_8373710615458151222nteger B) D2))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (D2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat D2) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) D2))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (D2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int D2) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) D2))))))
% 2.52/3.50 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger C))) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) A) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A)) (@ _let_1 B))))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))
% 2.52/3.50 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int C))) (=> (@ (@ tptp.ord_less_eq_int B) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger A) C)) (@ (@ tptp.minus_8373710615458151222nteger B) C)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) C)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) C)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (= (@ (@ tptp.minus_8373710615458151222nteger A) B) (@ (@ tptp.minus_8373710615458151222nteger C) D2)) (= (@ (@ tptp.ord_le3102999989581377725nteger A) B) (@ (@ tptp.ord_le3102999989581377725nteger C) D2)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C) D2)) (= (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat C) D2)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C) D2)) (= (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int C) D2)))))
% 2.52/3.50 (assert (= (lambda ((Y4 tptp.rat) (Z4 tptp.rat)) (= Y4 Z4)) (lambda ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A2) B2) tptp.zero_zero_rat))))
% 2.52/3.50 (assert (= (lambda ((Y4 tptp.int) (Z4 tptp.int)) (= Y4 Z4)) (lambda ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int A2) B2) tptp.zero_zero_int))))
% 2.52/3.50 (assert (= (lambda ((Y4 tptp.code_integer) (Z4 tptp.code_integer)) (= Y4 Z4)) (lambda ((A2 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A2) B2) tptp.zero_z3403309356797280102nteger))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger D2) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.minus_8373710615458151222nteger A) C)) (@ (@ tptp.minus_8373710615458151222nteger B) D2))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (D2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat D2) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) D2))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (D2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int D2) C) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) D2))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (= (@ (@ tptp.minus_8373710615458151222nteger A) B) (@ (@ tptp.minus_8373710615458151222nteger C) D2)) (= (@ (@ tptp.ord_le6747313008572928689nteger A) B) (@ (@ tptp.ord_le6747313008572928689nteger C) D2)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C) D2)) (= (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat C) D2)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C) D2)) (= (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int C) D2)))))
% 2.52/3.50 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) A) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A)) (@ _let_1 B))))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat C))) (=> (@ (@ tptp.ord_less_rat B) A) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))))
% 2.52/3.50 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int C))) (=> (@ (@ tptp.ord_less_int B) A) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.minus_8373710615458151222nteger A) C)) (@ (@ tptp.minus_8373710615458151222nteger B) C)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) C)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) C)))))
% 2.52/3.50 (assert (forall ((A3 tptp.rat) (K tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_rat A3) B) (@ _let_1 (@ (@ tptp.minus_minus_rat A) B)))))))
% 2.52/3.50 (assert (forall ((A3 tptp.int) (K tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_int A3) B) (@ _let_1 (@ (@ tptp.minus_minus_int A) B)))))))
% 2.52/3.50 (assert (forall ((A3 tptp.code_integer) (K tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.minus_8373710615458151222nteger A3) B) (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger A) B)))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.minus_minus_rat A) B) C) (= A (@ (@ tptp.plus_plus_rat C) B)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (= (@ (@ tptp.minus_minus_int A) B) C) (= A (@ (@ tptp.plus_plus_int C) B)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (= (@ (@ tptp.minus_8373710615458151222nteger A) B) C) (= A (@ (@ tptp.plus_p5714425477246183910nteger C) B)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.minus_minus_rat C) B)) (= (@ (@ tptp.plus_plus_rat A) B) C))))
% 2.52/3.50 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.minus_minus_int C) B)) (= (@ (@ tptp.plus_plus_int A) B) C))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (= A (@ (@ tptp.minus_8373710615458151222nteger C) B)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) C))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) C)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) C)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger A))) (= (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger B) C)) (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 B)) C)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) B))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) B))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.minus_8373710615458151222nteger B) C)) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger A) C)) B))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) B))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) B))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger A) C)) B))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 C)) B)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 C)) B)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger A))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C)) (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 C)) B)))))
% 2.52/3.50 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat C) B) A) (= C (@ (@ tptp.minus_minus_rat A) B)))))
% 2.52/3.50 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat C) B) A) (= C (@ (@ tptp.minus_minus_nat A) B)))))
% 2.52/3.50 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (= (@ (@ tptp.plus_plus_int C) B) A) (= C (@ (@ tptp.minus_minus_int A) B)))))
% 2.52/3.50 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger C) B) A) (= C (@ (@ tptp.minus_8373710615458151222nteger A) B)))))
% 2.52/3.50 (assert (forall ((C tptp.code_natural) (B tptp.code_natural) (A tptp.code_natural)) (=> (= (@ (@ tptp.plus_p4538020629002901425atural C) B) A) (= C (@ (@ tptp.minus_7197305767214868737atural A) B)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ (@ tptp.minus_minus_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B) C))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger A))) (= (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C))))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (let ((_let_1 (@ tptp.minus_7197305767214868737atural A))) (= (@ (@ tptp.minus_7197305767214868737atural (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_p4538020629002901425atural B) C))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat B) C)) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) (@ _let_1 C))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger B) C)) (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 B)) (@ _let_1 C))))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural A))) (= (@ _let_1 (@ (@ tptp.minus_7197305767214868737atural B) C)) (@ (@ tptp.minus_7197305767214868737atural (@ _let_1 B)) (@ _let_1 C))))))
% 2.52/3.50 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat B) C)) A) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat B) A)) (@ (@ tptp.times_times_nat C) A)))))
% 2.52/3.50 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) C)) A) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int B) A)) (@ (@ tptp.times_times_int C) A)))))
% 2.52/3.50 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger B) C)) A) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.times_3573771949741848930nteger B) A)) (@ (@ tptp.times_3573771949741848930nteger C) A)))))
% 2.52/3.50 (assert (forall ((B tptp.code_natural) (C tptp.code_natural) (A tptp.code_natural)) (= (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.minus_7197305767214868737atural B) C)) A) (@ (@ tptp.minus_7197305767214868737atural (@ (@ tptp.times_2397367101498566445atural B) A)) (@ (@ tptp.times_2397367101498566445atural C) A)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger B) C)) (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 B)) (@ _let_1 C))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)))))
% 2.52/3.50 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int B)) A) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int A)) B))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat B)) A) (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat A)) B))))
% 2.52/3.50 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger B)) A) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 2.52/3.50 (assert (forall ((X tptp.nat) (Y tptp.nat) (C tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.nO_MATCH_nat_int (@ (@ tptp.divide_divide_nat X) Y)) C) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 2.52/3.50 (assert (forall ((X tptp.nat) (Y tptp.nat) (C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.nO_MAT8694959213317031834nteger (@ (@ tptp.divide_divide_nat X) Y)) C) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 2.52/3.50 (assert (forall ((X tptp.int) (Y tptp.int) (C tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.nO_MATCH_int_int (@ (@ tptp.divide_divide_int X) Y)) C) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 2.52/3.50 (assert (forall ((X tptp.int) (Y tptp.int) (C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.nO_MAT9066612773553876470nteger (@ (@ tptp.divide_divide_int X) Y)) C) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 2.52/3.50 (assert (forall ((X tptp.rat) (Y tptp.rat) (C tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.nO_MATCH_rat_int (@ (@ tptp.divide_divide_rat X) Y)) C) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 2.52/3.50 (assert (forall ((X tptp.rat) (Y tptp.rat) (C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.nO_MAT243659986023775650nteger (@ (@ tptp.divide_divide_rat X) Y)) C) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 2.52/3.50 (assert (forall ((X tptp.code_natural) (Y tptp.code_natural) (C tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.nO_MAT4469370267861770177al_int (@ (@ tptp.divide5121882707175180666atural X) Y)) C) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 2.52/3.50 (assert (forall ((X tptp.code_natural) (Y tptp.code_natural) (C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.nO_MAT2693162092599435762nteger (@ (@ tptp.divide5121882707175180666atural X) Y)) C) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 2.52/3.50 (assert (forall ((X tptp.nat) (Y tptp.nat) (A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.nO_MATCH_nat_int (@ (@ tptp.divide_divide_nat X) Y)) A) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C)))))))
% 2.52/3.50 (assert (forall ((X tptp.nat) (Y tptp.nat) (A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.nO_MAT8694959213317031834nteger (@ (@ tptp.divide_divide_nat X) Y)) A) (= (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger B) C)) (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 B)) (@ _let_1 C)))))))
% 2.52/3.50 (assert (forall ((X tptp.int) (Y tptp.int) (A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.nO_MATCH_int_int (@ (@ tptp.divide_divide_int X) Y)) A) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C)))))))
% 2.52/3.50 (assert (forall ((X tptp.int) (Y tptp.int) (A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.nO_MAT9066612773553876470nteger (@ (@ tptp.divide_divide_int X) Y)) A) (= (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger B) C)) (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 B)) (@ _let_1 C)))))))
% 2.52/3.50 (assert (forall ((X tptp.rat) (Y tptp.rat) (A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.nO_MATCH_rat_int (@ (@ tptp.divide_divide_rat X) Y)) A) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C)))))))
% 2.52/3.50 (assert (forall ((X tptp.rat) (Y tptp.rat) (A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.nO_MAT243659986023775650nteger (@ (@ tptp.divide_divide_rat X) Y)) A) (= (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger B) C)) (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 B)) (@ _let_1 C)))))))
% 2.52/3.50 (assert (forall ((X tptp.code_natural) (Y tptp.code_natural) (A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.nO_MAT4469370267861770177al_int (@ (@ tptp.divide5121882707175180666atural X) Y)) A) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C)))))))
% 2.52/3.50 (assert (forall ((X tptp.code_natural) (Y tptp.code_natural) (A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.nO_MAT2693162092599435762nteger (@ (@ tptp.divide5121882707175180666atural X) Y)) A) (= (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger B) C)) (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 B)) (@ _let_1 C)))))))
% 2.52/3.50 (assert (= tptp.ord_le3102999989581377725nteger (lambda ((A2 tptp.code_integer) (B2 tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger A2) B2)) tptp.zero_z3403309356797280102nteger))))
% 2.52/3.50 (assert (= tptp.ord_less_eq_rat (lambda ((A2 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A2) B2)) tptp.zero_zero_rat))))
% 2.52/3.50 (assert (= tptp.ord_less_eq_int (lambda ((A2 tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A2) B2)) tptp.zero_zero_int))))
% 2.52/3.50 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((A2 tptp.code_integer) (B2 tptp.code_integer)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.minus_8373710615458151222nteger A2) B2)) tptp.zero_z3403309356797280102nteger))))
% 2.52/3.50 (assert (= tptp.ord_less_rat (lambda ((A2 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A2) B2)) tptp.zero_zero_rat))))
% 2.52/3.50 (assert (= tptp.ord_less_int (lambda ((A2 tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A2) B2)) tptp.zero_zero_int))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C) (@ (@ tptp.ord_le3102999989581377725nteger A) (@ (@ tptp.plus_p5714425477246183910nteger C) B)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.plus_plus_rat C) B)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.plus_plus_int C) B)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger A) (@ (@ tptp.minus_8373710615458151222nteger C) B)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.minus_minus_rat C) B)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) B)) C))))
% 2.52/3.50 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.minus_minus_int C) B)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) B)) C))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B) A)) A) B))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat C) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C)) A)))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.ord_less_eq_nat C) (@ (@ tptp.minus_minus_nat B) A)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat C) A)) B)))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ _let_1 (@ (@ tptp.minus_minus_nat B) A)) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) A))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.minus_minus_nat (@ _let_1 B)) A) (@ _let_1 (@ (@ tptp.minus_minus_nat B) A)))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B) A)) C) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C)) A)))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B) A)) C)))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.minus_minus_nat C) (@ (@ tptp.minus_minus_nat B) A)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat C) A)) B)))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.minus_minus_nat B) A)) B))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat A) B))) (=> _let_1 (=> _let_1 (= (= (@ (@ tptp.minus_minus_nat B) A) C) (= B (@ (@ tptp.plus_plus_nat C) A))))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger A) (@ (@ tptp.minus_8373710615458151222nteger C) B)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.minus_minus_rat C) B)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) C))))
% 2.52/3.50 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ (@ tptp.minus_minus_int C) B)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) C))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C) (@ (@ tptp.ord_le6747313008572928689nteger A) (@ (@ tptp.plus_p5714425477246183910nteger C) B)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat C) B)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int C) B)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (E2 tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E2)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D2)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E2)) C) D2))))
% 2.52/3.50 (assert (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D2)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E2)) C) D2))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (E2 tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A) E2)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) E2)) D2)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) E2)) C) D2))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (E2 tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E2)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D2)) (= C (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E2)) D2)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D2)) (= C (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E2)) D2)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (E2 tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A) E2)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) E2)) D2)) (= C (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger B) A)) E2)) D2)))))
% 2.52/3.50 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X) Y)) (@ (@ tptp.minus_minus_rat X) Y)))))
% 2.52/3.50 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X) Y)) (@ (@ tptp.minus_minus_int X) Y)))))
% 2.52/3.50 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.times_3573771949741848930nteger X) X)) (@ (@ tptp.times_3573771949741848930nteger Y) Y)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger X) Y)) (@ (@ tptp.minus_8373710615458151222nteger X) Y)))))
% 2.52/3.50 (assert (= tptp.minus_minus_int (lambda ((A2 tptp.int) (B2 tptp.int)) (@ (@ tptp.plus_plus_int A2) (@ tptp.uminus_uminus_int B2)))))
% 2.52/3.50 (assert (= tptp.minus_minus_rat (lambda ((A2 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.plus_plus_rat A2) (@ tptp.uminus_uminus_rat B2)))))
% 2.52/3.50 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A2 tptp.code_integer) (B2 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A2) (@ tptp.uminus1351360451143612070nteger B2)))))
% 2.52/3.50 (assert (= tptp.minus_minus_int (lambda ((A2 tptp.int) (B2 tptp.int)) (@ (@ tptp.plus_plus_int A2) (@ tptp.uminus_uminus_int B2)))))
% 2.52/3.50 (assert (= tptp.minus_minus_rat (lambda ((A2 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.plus_plus_rat A2) (@ tptp.uminus_uminus_rat B2)))))
% 2.52/3.50 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A2 tptp.code_integer) (B2 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A2) (@ tptp.uminus1351360451143612070nteger B2)))))
% 2.52/3.50 (assert (forall ((B3 tptp.int) (K tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (=> (= B3 (@ (@ tptp.plus_plus_int K) B)) (= (@ _let_1 B3) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K)) (@ _let_1 B)))))))
% 2.52/3.50 (assert (forall ((B3 tptp.rat) (K tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (=> (= B3 (@ (@ tptp.plus_plus_rat K) B)) (= (@ _let_1 B3) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat K)) (@ _let_1 B)))))))
% 2.52/3.50 (assert (forall ((B3 tptp.code_integer) (K tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger A))) (=> (= B3 (@ (@ tptp.plus_p5714425477246183910nteger K) B)) (= (@ _let_1 B3) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger K)) (@ _let_1 B)))))))
% 2.52/3.50 (assert (= tptp.minus_1356011639430497352at_nat (lambda ((X2 tptp.set_Pr1261947904930325089at_nat) (Y2 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.inf_in2572325071724192079at_nat X2) (@ tptp.uminus6524753893492686040at_nat Y2)))))
% 2.52/3.50 (assert (= tptp.minus_minus_set_nat (lambda ((X2 tptp.set_nat) (Y2 tptp.set_nat)) (@ (@ tptp.inf_inf_set_nat X2) (@ tptp.uminus5710092332889474511et_nat Y2)))))
% 2.52/3.50 (assert (= tptp.minus_711738161318947805_int_o (lambda ((X2 (-> tptp.product_prod_int_int Bool)) (Y2 (-> tptp.product_prod_int_int Bool)) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ (@ tptp.inf_in3604695632404883862_int_o X2) (@ tptp.uminus7117520113953359693_int_o Y2)) __flatten_var_0))))
% 2.52/3.50 (assert (= tptp.minus_minus_assn (lambda ((X2 tptp.assn) (Y2 tptp.assn)) (@ (@ tptp.inf_inf_assn X2) (@ tptp.uminus_uminus_assn Y2)))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger N))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le1926595141338095240atural tptp.one_one_Code_natural) (@ tptp.numera5444537566228673987atural N))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.numeral_numeral_int N))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger N)) tptp.one_one_Code_integer))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le5570908160329646204atural (@ tptp.numera5444537566228673987atural N)) tptp.one_one_Code_natural))))
% 2.52/3.50 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))))
% 2.52/3.50 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))
% 2.52/3.50 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X))) (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)))))
% 2.52/3.50 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger X))) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) _let_1) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)))))
% 2.52/3.50 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera5444537566228673987atural X))) (= (@ (@ tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural) _let_1) (@ (@ tptp.plus_p4538020629002901425atural _let_1) tptp.one_one_Code_natural)))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (not (= tptp.one_one_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (not (= tptp.one_one_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_rat N) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger N) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (E2 tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A) E2)) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) E2)) D2)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) E2)) C)) D2))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (E2 tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E2)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E2)) C)) D2))))
% 2.52/3.50 (assert (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E2)) C)) D2))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (E2 tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A) E2)) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) E2)) D2)) (@ (@ tptp.ord_le3102999989581377725nteger C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger B) A)) E2)) D2)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (E2 tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E2)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D2)) (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E2)) D2)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D2)) (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E2)) D2)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (E2 tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A) E2)) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) E2)) D2)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) E2)) C)) D2))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (E2 tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E2)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E2)) C)) D2))))
% 2.52/3.50 (assert (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E2)) C)) D2))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (E2 tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A) E2)) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) E2)) D2)) (@ (@ tptp.ord_le6747313008572928689nteger C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger B) A)) E2)) D2)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (E2 tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E2)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D2)) (@ (@ tptp.ord_less_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E2)) D2)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D2)) (@ (@ tptp.ord_less_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E2)) D2)))))
% 2.52/3.50 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) X)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X) tptp.one_one_rat)) (@ (@ tptp.minus_minus_rat X) tptp.one_one_rat)))))
% 2.52/3.50 (assert (forall ((X tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X) X)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) (@ (@ tptp.minus_minus_int X) tptp.one_one_int)))))
% 2.52/3.50 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.times_3573771949741848930nteger X) X)) tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger X) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger X) tptp.one_one_Code_integer)))))
% 2.52/3.50 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X) Z)) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.times_times_rat Y) Z))) Z)))))
% 2.52/3.50 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.divide_divide_rat Y) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z)) Y)) Z)))))
% 2.52/3.50 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z)))))))
% 2.52/3.50 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.divide_divide_rat B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A) Z)) B)) Z))))))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M2))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M2))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M2))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) tptp.one_one_Code_integer)))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) tptp.one_one_rat)))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) tptp.one_one_int)))
% 2.52/3.50 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 2.52/3.50 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= _let_1 (@ (@ tptp.divide_divide_rat B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M2))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M2))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M2))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) tptp.one_one_int)))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) tptp.one_one_rat)))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) tptp.one_one_Code_integer)))
% 2.52/3.50 (assert (= tptp.neg_nu3179335615603231917ec_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat X2) X2)) tptp.one_one_rat))))
% 2.52/3.50 (assert (= tptp.neg_nu3811975205180677377ec_int (lambda ((X2 tptp.int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int X2) X2)) tptp.one_one_int))))
% 2.52/3.50 (assert (= tptp.neg_nu7757733837767384882nteger (lambda ((X2 tptp.code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger X2) X2)) tptp.one_one_Code_integer))))
% 2.52/3.50 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z))) tptp.zero_zero_rat))))))
% 2.52/3.50 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z))) tptp.zero_zero_rat))))))
% 2.52/3.50 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X) Z))) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat X)) (@ (@ tptp.times_times_rat Y) Z))) Z)))))
% 2.52/3.50 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_rat B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 2.52/3.50 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_rat B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 2.52/3.50 (assert (forall ((Y tptp.produc6575502325842934193n_assn)) (= (@ (@ tptp.count_2530312006313534765n_assn tptp.nil_Pr5671120429643327159n_assn) Y) tptp.zero_zero_nat)))
% 2.52/3.50 (assert (forall ((Y tptp.int)) (= (@ (@ tptp.count_list_int tptp.nil_int) Y) tptp.zero_zero_nat)))
% 2.52/3.50 (assert (forall ((Y tptp.nat)) (= (@ (@ tptp.count_list_nat tptp.nil_nat) Y) tptp.zero_zero_nat)))
% 2.52/3.50 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 2.52/3.50 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (@ tptp.ord_less_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 2.52/3.50 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= _let_1 (@ (@ tptp.divide_divide_rat B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 2.52/3.50 (assert (= tptp.times_times_nat (lambda ((M3 tptp.nat) (N3 tptp.nat)) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat N3) (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)) N3))))))
% 2.52/3.50 (assert (forall ((U tptp.rat) (V2 tptp.rat) (R2 tptp.rat) (S3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat U) V2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) R2) (=> (@ (@ tptp.ord_less_eq_rat R2) S3) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat U) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat R2) (@ (@ tptp.minus_minus_rat V2) U))) S3))) V2))))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1))))))))))))
% 2.52/3.50 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (@ tptp.ord_less_eq_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 2.52/3.50 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (@ tptp.ord_less_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 2.52/3.50 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (let ((_let_2 (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 M2)) (@ _let_1 N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N) M2))) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M2))))))))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 M2)) (@ _let_1 N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N) M2))) (=> (not (= A tptp.zero_zero_nat)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M2))))))))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ _let_1 M2)) (@ _let_1 N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N) M2))) (=> (not (= A tptp.zero_zero_int)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M2))))))))))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.power_7079662738309270450atural A))) (let ((_let_2 (@ (@ tptp.divide5121882707175180666atural (@ _let_1 M2)) (@ _let_1 N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N) M2))) (=> (not (= A tptp.zero_z2226904508553997617atural)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide5121882707175180666atural tptp.one_one_Code_natural) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M2))))))))))))
% 2.52/3.50 (assert (= tptp.power_power_rat (lambda ((P6 tptp.rat) (M3 tptp.nat)) (@ (@ (@ tptp.if_rat (= M3 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat P6) (@ (@ tptp.power_power_rat P6) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 2.52/3.50 (assert (= tptp.power_power_assn (lambda ((P6 tptp.assn) (M3 tptp.nat)) (@ (@ (@ tptp.if_assn (= M3 tptp.zero_zero_nat)) tptp.one_one_assn) (@ (@ tptp.times_times_assn P6) (@ (@ tptp.power_power_assn P6) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 2.52/3.50 (assert (= tptp.power_power_nat (lambda ((P6 tptp.nat) (M3 tptp.nat)) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat P6) (@ (@ tptp.power_power_nat P6) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 2.52/3.50 (assert (= tptp.power_power_int (lambda ((P6 tptp.int) (M3 tptp.nat)) (@ (@ (@ tptp.if_int (= M3 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int P6) (@ (@ tptp.power_power_int P6) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 2.52/3.50 (assert (= tptp.power_8256067586552552935nteger (lambda ((P6 tptp.code_integer) (M3 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (= M3 tptp.zero_zero_nat)) tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger P6) (@ (@ tptp.power_8256067586552552935nteger P6) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 2.52/3.50 (assert (= tptp.power_7079662738309270450atural (lambda ((P6 tptp.code_natural) (M3 tptp.nat)) (@ (@ (@ tptp.if_Code_natural (= M3 tptp.zero_zero_nat)) tptp.one_one_Code_natural) (@ (@ tptp.times_2397367101498566445atural P6) (@ (@ tptp.power_7079662738309270450atural P6) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 2.52/3.50 (assert (forall ((V2 tptp.num) (W tptp.num) (Y tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V2))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int W)) Y)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V2) W)))) Y))))
% 2.52/3.50 (assert (forall ((V2 tptp.num) (W tptp.num) (Y tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V2))) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat W)) Y)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V2) W)))) Y))))
% 2.52/3.50 (assert (forall ((V2 tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V2))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger W)) Y)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V2) W)))) Y))))
% 2.52/3.50 (assert (forall ((V2 tptp.num) (W tptp.num) (Y tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int V2)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) Y)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V2) W)))) Y))))
% 2.52/3.50 (assert (forall ((V2 tptp.num) (W tptp.num) (Y tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V2)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W))) Y)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V2) W)))) Y))))
% 2.52/3.50 (assert (forall ((V2 tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger V2)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W))) Y)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V2) W)))) Y))))
% 2.52/3.50 (assert (forall ((V2 tptp.num) (W tptp.num) (Y tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V2))) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) Y)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V2) W))) Y))))
% 2.52/3.50 (assert (forall ((V2 tptp.num) (W tptp.num) (Y tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V2))) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W))) Y)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V2) W))) Y))))
% 2.52/3.50 (assert (forall ((V2 tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V2))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W))) Y)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V2) W))) Y))))
% 2.52/3.50 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 2.52/3.50 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 2.52/3.50 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 2.52/3.50 (assert (forall ((W tptp.num) (X tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int W))) (= (@ (@ tptp.times_times_int _let_1) (@ tptp.uminus_uminus_int X)) (@ (@ tptp.times_times_int X) (@ tptp.uminus_uminus_int _let_1))))))
% 2.52/3.50 (assert (forall ((W tptp.num) (X tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.times_times_rat _let_1) (@ tptp.uminus_uminus_rat X)) (@ (@ tptp.times_times_rat X) (@ tptp.uminus_uminus_rat _let_1))))))
% 2.52/3.50 (assert (forall ((W tptp.num) (X tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger W))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ tptp.uminus1351360451143612070nteger X)) (@ (@ tptp.times_3573771949741848930nteger X) (@ tptp.uminus1351360451143612070nteger _let_1))))))
% 2.52/3.50 (assert (forall ((Begin tptp.nat) (End tptp.nat) (X tptp.int) (Xs tptp.list_int)) (let ((_let_1 (@ (@ tptp.minus_minus_nat End) tptp.one_one_nat))) (let ((_let_2 (@ tptp.cons_int X))) (let ((_let_3 (@ tptp.slice_int Begin))) (let ((_let_4 (@ (@ _let_3 End) (@ _let_2 Xs)))) (let ((_let_5 (and (= Begin tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) End)))) (and (=> _let_5 (= _let_4 (@ _let_2 (@ (@ _let_3 _let_1) Xs)))) (=> (not _let_5) (= _let_4 (@ (@ (@ tptp.slice_int (@ (@ tptp.minus_minus_nat Begin) tptp.one_one_nat)) _let_1) Xs)))))))))))
% 2.52/3.50 (assert (forall ((Begin tptp.nat) (End tptp.nat) (X tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat End) tptp.one_one_nat))) (let ((_let_2 (@ tptp.cons_nat X))) (let ((_let_3 (@ tptp.slice_nat Begin))) (let ((_let_4 (@ (@ _let_3 End) (@ _let_2 Xs)))) (let ((_let_5 (and (= Begin tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) End)))) (and (=> _let_5 (= _let_4 (@ _let_2 (@ (@ _let_3 _let_1) Xs)))) (=> (not _let_5) (= _let_4 (@ (@ (@ tptp.slice_nat (@ (@ tptp.minus_minus_nat Begin) tptp.one_one_nat)) _let_1) Xs)))))))))))
% 2.52/3.50 (assert (forall ((P2 (-> tptp.int Bool)) (D tptp.int) (Q2 (-> tptp.int Bool))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P2 X3) (@ P2 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D))))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ Q2 X3) (@ Q2 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D))))) (forall ((X4 tptp.int) (K3 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K3) D)))) (= (and (@ P2 X4) (@ Q2 X4)) (and (@ P2 _let_1) (@ Q2 _let_1)))))))))
% 2.52/3.50 (assert (forall ((P2 (-> tptp.code_integer Bool)) (D tptp.code_integer) (Q2 (-> tptp.code_integer Bool))) (=> (forall ((X3 tptp.code_integer) (K2 tptp.code_integer)) (= (@ P2 X3) (@ P2 (@ (@ tptp.minus_8373710615458151222nteger X3) (@ (@ tptp.times_3573771949741848930nteger K2) D))))) (=> (forall ((X3 tptp.code_integer) (K2 tptp.code_integer)) (= (@ Q2 X3) (@ Q2 (@ (@ tptp.minus_8373710615458151222nteger X3) (@ (@ tptp.times_3573771949741848930nteger K2) D))))) (forall ((X4 tptp.code_integer) (K3 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.minus_8373710615458151222nteger X4) (@ (@ tptp.times_3573771949741848930nteger K3) D)))) (= (and (@ P2 X4) (@ Q2 X4)) (and (@ P2 _let_1) (@ Q2 _let_1)))))))))
% 2.52/3.50 (assert (forall ((P2 (-> tptp.int Bool)) (D tptp.int) (Q2 (-> tptp.int Bool))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P2 X3) (@ P2 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D))))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ Q2 X3) (@ Q2 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D))))) (forall ((X4 tptp.int) (K3 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K3) D)))) (= (or (@ P2 X4) (@ Q2 X4)) (or (@ P2 _let_1) (@ Q2 _let_1)))))))))
% 2.52/3.50 (assert (forall ((P2 (-> tptp.code_integer Bool)) (D tptp.code_integer) (Q2 (-> tptp.code_integer Bool))) (=> (forall ((X3 tptp.code_integer) (K2 tptp.code_integer)) (= (@ P2 X3) (@ P2 (@ (@ tptp.minus_8373710615458151222nteger X3) (@ (@ tptp.times_3573771949741848930nteger K2) D))))) (=> (forall ((X3 tptp.code_integer) (K2 tptp.code_integer)) (= (@ Q2 X3) (@ Q2 (@ (@ tptp.minus_8373710615458151222nteger X3) (@ (@ tptp.times_3573771949741848930nteger K2) D))))) (forall ((X4 tptp.code_integer) (K3 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.minus_8373710615458151222nteger X4) (@ (@ tptp.times_3573771949741848930nteger K3) D)))) (= (or (@ P2 X4) (@ Q2 X4)) (or (@ P2 _let_1) (@ Q2 _let_1)))))))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc N))))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.inc N))))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc N))))))
% 2.52/3.50 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) (@ (@ tptp.minus_1356011639430497352at_nat B3) A3)) tptp.bot_bo2099793752762293965at_nat)))
% 2.52/3.50 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A3) (@ (@ tptp.minus_minus_set_nat B3) A3)) tptp.bot_bot_set_nat)))
% 2.52/3.50 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int A3) (@ (@ tptp.minus_minus_set_int B3) A3)) tptp.bot_bot_set_int)))
% 2.52/3.50 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) (@ tptp.uminus6524753893492686040at_nat B3)) (@ (@ tptp.minus_1356011639430497352at_nat A3) B3))))
% 2.52/3.50 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A3) (@ tptp.uminus5710092332889474511et_nat B3)) (@ (@ tptp.minus_minus_set_nat A3) B3))))
% 2.52/3.50 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.minus_1356011639430497352at_nat A3) (@ tptp.uminus6524753893492686040at_nat B3)) (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3))))
% 2.52/3.50 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat A3) (@ tptp.uminus5710092332889474511et_nat B3)) (@ (@ tptp.inf_inf_set_nat A3) B3))))
% 2.52/3.50 (assert (forall ((Begin tptp.nat) (End tptp.nat)) (= (@ (@ (@ tptp.slice_7964966981652229398n_assn Begin) End) tptp.nil_Pr5671120429643327159n_assn) tptp.nil_Pr5671120429643327159n_assn)))
% 2.52/3.50 (assert (forall ((Begin tptp.nat) (End tptp.nat)) (= (@ (@ (@ tptp.slice_int Begin) End) tptp.nil_int) tptp.nil_int)))
% 2.52/3.50 (assert (forall ((Begin tptp.nat) (End tptp.nat)) (= (@ (@ (@ tptp.slice_nat Begin) End) tptp.nil_nat) tptp.nil_nat)))
% 2.52/3.50 (assert (forall ((I2 tptp.nat) (Xs tptp.list_P8527749157015355191n_assn)) (= (@ (@ (@ tptp.slice_7964966981652229398n_assn I2) I2) Xs) tptp.nil_Pr5671120429643327159n_assn)))
% 2.52/3.50 (assert (forall ((I2 tptp.nat) (Xs tptp.list_int)) (= (@ (@ (@ tptp.slice_int I2) I2) Xs) tptp.nil_int)))
% 2.52/3.50 (assert (forall ((I2 tptp.nat) (Xs tptp.list_nat)) (= (@ (@ (@ tptp.slice_nat I2) I2) Xs) tptp.nil_nat)))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc M2))))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.inc M2))))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc M2))))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc N))))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.inc N))))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc N))))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.inc M2)))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat (@ tptp.inc M2)))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.inc M2)))))
% 2.52/3.50 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A3))) (= (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_1 B3)) C2) (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat B3) C2))))))
% 2.52/3.50 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A3))) (= (@ (@ tptp.minus_minus_set_nat (@ _let_1 B3)) C2) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B3) C2))))))
% 2.52/3.50 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A3) C2)))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B3) C2)) (@ _let_1 B3)))))
% 2.52/3.50 (assert (forall ((A3 tptp.set_nat) (C2 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat (@ (@ tptp.inf_inf_set_nat A3) C2)))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat B3) C2)) (@ _let_1 B3)))))
% 2.52/3.50 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat A3))) (= (@ _let_1 (@ _let_1 B3)) (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)))))
% 2.52/3.50 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A3))) (= (@ _let_1 (@ _let_1 B3)) (@ (@ tptp.inf_inf_set_nat A3) B3)))))
% 2.52/3.50 (assert (forall ((C2 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat C2))) (= (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A3) B3)) (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_1 A3)) (@ _let_1 B3))))))
% 2.52/3.50 (assert (forall ((C2 tptp.set_nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat C2))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B3)) (@ (@ tptp.minus_minus_set_nat (@ _let_1 A3)) (@ _let_1 B3))))))
% 2.52/3.50 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.minus_1356011639430497352at_nat A3) B3)) C2) (@ (@ tptp.minus_1356011639430497352at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A3) C2)) (@ (@ tptp.inf_in2572325071724192079at_nat B3) C2)))))
% 2.52/3.50 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C2 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.minus_minus_set_nat A3) B3)) C2) (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.inf_inf_set_nat A3) C2)) (@ (@ tptp.inf_inf_set_nat B3) C2)))))
% 2.52/3.50 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le7866589430770878221at_nat (@ (@ tptp.minus_1356011639430497352at_nat A3) B3)) A3) (not (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3) tptp.bot_bo2099793752762293965at_nat)))))
% 2.52/3.50 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (@ (@ tptp.ord_less_set_nat (@ (@ tptp.minus_minus_set_nat A3) B3)) A3) (not (= (@ (@ tptp.inf_inf_set_nat A3) B3) tptp.bot_bot_set_nat)))))
% 2.52/3.50 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (@ (@ tptp.ord_less_set_int (@ (@ tptp.minus_minus_set_int A3) B3)) A3) (not (= (@ (@ tptp.inf_inf_set_int A3) B3) tptp.bot_bot_set_int)))))
% 2.52/3.50 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.minus_1356011639430497352at_nat A3) B3) A3) (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3) tptp.bot_bo2099793752762293965at_nat))))
% 2.52/3.50 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat A3) B3) A3) (= (@ (@ tptp.inf_inf_set_nat A3) B3) tptp.bot_bot_set_nat))))
% 2.52/3.50 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int A3) B3) A3) (= (@ (@ tptp.inf_inf_set_int A3) B3) tptp.bot_bot_set_int))))
% 2.52/3.50 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (not (= (@ (@ tptp.minus_1356011639430497352at_nat A3) B3) A3)) (not (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3) tptp.bot_bo2099793752762293965at_nat)))))
% 2.52/3.50 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (not (= (@ (@ tptp.minus_minus_set_nat A3) B3) A3)) (not (= (@ (@ tptp.inf_inf_set_nat A3) B3) tptp.bot_bot_set_nat)))))
% 2.52/3.50 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (not (= (@ (@ tptp.minus_minus_set_int A3) B3) A3)) (not (= (@ (@ tptp.inf_inf_set_int A3) B3) tptp.bot_bot_set_int)))))
% 2.52/3.50 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (=> (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3) tptp.bot_bo2099793752762293965at_nat) (= (@ (@ tptp.minus_1356011639430497352at_nat A3) B3) A3))))
% 2.52/3.50 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (=> (= (@ (@ tptp.inf_inf_set_nat A3) B3) tptp.bot_bot_set_nat) (= (@ (@ tptp.minus_minus_set_nat A3) B3) A3))))
% 2.52/3.50 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (=> (= (@ (@ tptp.inf_inf_set_int A3) B3) tptp.bot_bot_set_int) (= (@ (@ tptp.minus_minus_set_int A3) B3) A3))))
% 2.52/3.50 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)) (@ (@ tptp.minus_1356011639430497352at_nat A3) B3)) tptp.bot_bo2099793752762293965at_nat)))
% 2.52/3.50 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.inf_inf_set_nat A3) B3)) (@ (@ tptp.minus_minus_set_nat A3) B3)) tptp.bot_bot_set_nat)))
% 2.52/3.50 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int (@ (@ tptp.inf_inf_set_int A3) B3)) (@ (@ tptp.minus_minus_set_int A3) B3)) tptp.bot_bot_set_int)))
% 2.52/3.50 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat A3))) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat B3) C2)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 B3)) (@ _let_1 C2))))))
% 2.52/3.50 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A3))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat B3) C2)) (@ (@ tptp.inf_inf_set_nat (@ _let_1 B3)) (@ _let_1 C2))))))
% 2.52/3.50 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat A3))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B3) C2)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 B3)) (@ _let_1 C2))))))
% 2.52/3.50 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C2 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A3))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat B3) C2)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 B3)) (@ _let_1 C2))))))
% 2.52/3.50 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)) (@ (@ tptp.minus_1356011639430497352at_nat A3) B3)) A3)))
% 2.52/3.50 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat A3) B3)) (@ (@ tptp.minus_minus_set_nat A3) B3)) A3)))
% 2.52/3.50 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.minus_1356011639430497352at_nat A3) B3)) (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)) A3)))
% 2.52/3.50 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.minus_minus_set_nat A3) B3)) (@ (@ tptp.inf_inf_set_nat A3) B3)) A3)))
% 2.52/3.50 (assert (= tptp.minus_minus_assn (lambda ((A2 tptp.assn) (B2 tptp.assn)) (@ (@ tptp.inf_inf_assn A2) (@ tptp.uminus_uminus_assn B2)))))
% 2.52/3.50 (assert (forall ((X tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.inc X)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat X)) tptp.one_one_nat))))
% 2.52/3.50 (assert (forall ((X tptp.num)) (= (@ tptp.numeral_numeral_int (@ tptp.inc X)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int X)) tptp.one_one_int))))
% 2.52/3.50 (assert (forall ((X tptp.num)) (= (@ tptp.numeral_numeral_rat (@ tptp.inc X)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat X)) tptp.one_one_rat))))
% 2.52/3.50 (assert (forall ((X tptp.num)) (= (@ tptp.numera6620942414471956472nteger (@ tptp.inc X)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.numera6620942414471956472nteger X)) tptp.one_one_Code_integer))))
% 2.52/3.50 (assert (forall ((X tptp.num)) (= (@ tptp.numera5444537566228673987atural (@ tptp.inc X)) (@ (@ tptp.plus_p4538020629002901425atural (@ tptp.numera5444537566228673987atural X)) tptp.one_one_Code_natural))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M2) tptp.one))))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M2) tptp.one))))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M2) tptp.one))))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 2.52/3.50 (assert (forall ((N tptp.nat) (X tptp.int) (Xs tptp.list_int)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.nth_int (@ (@ tptp.cons_int X) Xs)) N) (@ (@ tptp.nth_int Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 2.52/3.50 (assert (forall ((N tptp.nat) (X tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X) Xs)) N) (@ (@ tptp.nth_nat Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural) (@ tptp.numera5444537566228673987atural N)) (@ tptp.numera5444537566228673987atural (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.numera6620942414471956472nteger N)) tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_p4538020629002901425atural (@ tptp.numera5444537566228673987atural N)) tptp.one_one_Code_natural) (@ tptp.numera5444537566228673987atural (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.uminus_uminus_int tptp.one_one_int)) (not (= M2 tptp.one)))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (not (= M2 tptp.one)))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (not (= M2 tptp.one)))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (= (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2)))) (not (= M2 tptp.one)))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2)))) (not (= M2 tptp.one)))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2)))) (not (= M2 tptp.one)))))
% 2.52/3.50 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) N))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_nat N) tptp.one_one_nat) (= N tptp.one))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_int N) tptp.one_one_int) (= N tptp.one))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_rat N) tptp.one_one_rat) (= N tptp.one))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (= (@ tptp.numera6620942414471956472nteger N) tptp.one_one_Code_integer) (= N tptp.one))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (= (@ tptp.numera5444537566228673987atural N) tptp.one_one_Code_natural) (= N tptp.one))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (= tptp.one_one_nat (@ tptp.numeral_numeral_nat N)) (= tptp.one N))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (= tptp.one_one_int (@ tptp.numeral_numeral_int N)) (= tptp.one N))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (= tptp.one_one_rat (@ tptp.numeral_numeral_rat N)) (= tptp.one N))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (= tptp.one_one_Code_integer (@ tptp.numera6620942414471956472nteger N)) (= tptp.one N))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (= tptp.one_one_Code_natural (@ tptp.numera5444537566228673987atural N)) (= tptp.one N))))
% 2.52/3.50 (assert (forall ((X tptp.int) (Xs tptp.list_int)) (= (@ (@ tptp.nth_int (@ (@ tptp.cons_int X) Xs)) tptp.zero_zero_nat) X)))
% 2.52/3.50 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (= (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X) Xs)) tptp.zero_zero_nat) X)))
% 2.52/3.50 (assert (forall ((X tptp.int) (Xs tptp.list_int) (N tptp.nat)) (= (@ (@ tptp.nth_int (@ (@ tptp.cons_int X) Xs)) (@ tptp.suc N)) (@ (@ tptp.nth_int Xs) N))))
% 2.52/3.50 (assert (forall ((X tptp.nat) (Xs tptp.list_nat) (N tptp.nat)) (= (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X) Xs)) (@ tptp.suc N)) (@ (@ tptp.nth_nat Xs) N))))
% 2.52/3.50 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N)) tptp.one_one_nat) N)))
% 2.52/3.50 (assert (forall ((N tptp.nat) (X tptp.int) (Xs tptp.list_int)) (= (@ (@ tptp.enumerate_int N) (@ (@ tptp.cons_int X) Xs)) (@ (@ tptp.cons_P2335045147070616083at_int (@ (@ tptp.product_Pair_nat_int N) X)) (@ (@ tptp.enumerate_int (@ tptp.suc N)) Xs)))))
% 2.52/3.50 (assert (forall ((N tptp.nat) (X tptp.nat) (Xs tptp.list_nat)) (= (@ (@ tptp.enumerate_nat N) (@ (@ tptp.cons_nat X) Xs)) (@ (@ tptp.cons_P6512896166579812791at_nat (@ (@ tptp.product_Pair_nat_nat N) X)) (@ (@ tptp.enumerate_nat (@ tptp.suc N)) Xs)))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger N)) tptp.one_one_Code_integer) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_le1926595141338095240atural (@ tptp.numera5444537566228673987atural N)) tptp.one_one_Code_natural) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.numeral_numeral_int N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_le5570908160329646204atural tptp.one_one_Code_natural) (@ tptp.numera5444537566228673987atural N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int tptp.one_one_int)) (= N tptp.one))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (= N tptp.one))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (= N tptp.one))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (= N tptp.one))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (= N tptp.one))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (= N tptp.one))))
% 2.52/3.50 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M2) (= (@ tptp.suc (@ _let_1 M2)) (@ _let_1 (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat))))))))
% 2.52/3.50 (assert (forall ((X tptp.int) (Xs tptp.list_int) (V2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V2))) (= (@ (@ tptp.nth_int (@ (@ tptp.cons_int X) Xs)) _let_1) (@ (@ tptp.nth_int Xs) (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))))))
% 2.52/3.50 (assert (forall ((X tptp.nat) (Xs tptp.list_nat) (V2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V2))) (= (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X) Xs)) _let_1) (@ (@ tptp.nth_nat Xs) (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))))))
% 2.52/3.50 (assert (forall ((A tptp.assn) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_assn A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_assn A) (@ _let_1 N))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat A) (@ _let_1 N))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int A) (@ _let_1 N))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_3573771949741848930nteger A) (@ _let_1 N))))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (N tptp.nat)) (let ((_let_1 (@ tptp.power_7079662738309270450atural A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_2397367101498566445atural A) (@ _let_1 N))))))
% 2.52/3.50 (assert (forall ((A tptp.assn) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_assn A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_assn (@ _let_1 N)) A)))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat (@ _let_1 N)) A)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int (@ _let_1 N)) A)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 N)) A)))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (N tptp.nat)) (let ((_let_1 (@ tptp.power_7079662738309270450atural A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_2397367101498566445atural (@ _let_1 N)) A)))))
% 2.52/3.50 (assert (= tptp.one_one_nat (@ tptp.suc tptp.zero_zero_nat)))
% 2.52/3.50 (assert (= tptp.suc (lambda ((N3 tptp.nat)) (@ (@ tptp.plus_plus_nat N3) tptp.one_one_nat))))
% 2.52/3.50 (assert (= (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.suc))
% 2.52/3.50 (assert (= tptp.suc (@ tptp.plus_plus_nat tptp.one_one_nat)))
% 2.52/3.50 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M2))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat (@ _let_1 tptp.one_one_nat)) N)))))
% 2.52/3.50 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) (@ tptp.numeral_numeral_nat tptp.one)) A)))
% 2.52/3.50 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) (@ tptp.numeral_numeral_int tptp.one)) A)))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) (@ tptp.numeral_numeral_rat tptp.one)) A)))
% 2.52/3.50 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger A) (@ tptp.numera6620942414471956472nteger tptp.one)) A)))
% 2.52/3.50 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.times_2397367101498566445atural A) (@ tptp.numera5444537566228673987atural tptp.one)) A)))
% 2.52/3.50 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat tptp.one)) A) A)))
% 2.52/3.50 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int tptp.one)) A) A)))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat tptp.one)) A) A)))
% 2.52/3.50 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger tptp.one)) A) A)))
% 2.52/3.50 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural tptp.one)) A) A)))
% 2.52/3.50 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 2.52/3.50 (assert (= (@ tptp.numeral_numeral_int tptp.one) tptp.one_one_int))
% 2.52/3.50 (assert (= (@ tptp.numeral_numeral_rat tptp.one) tptp.one_one_rat))
% 2.52/3.50 (assert (= (@ tptp.numera6620942414471956472nteger tptp.one) tptp.one_one_Code_integer))
% 2.52/3.50 (assert (= (@ tptp.numera5444537566228673987atural tptp.one) tptp.one_one_Code_natural))
% 2.52/3.50 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 2.52/3.50 (assert (forall ((N tptp.nat) (X tptp.int) (Xs tptp.list_int)) (= (@ (@ tptp.gen_length_int N) (@ (@ tptp.cons_int X) Xs)) (@ (@ tptp.gen_length_int (@ tptp.suc N)) Xs))))
% 2.52/3.50 (assert (forall ((N tptp.nat) (X tptp.nat) (Xs tptp.list_nat)) (= (@ (@ tptp.gen_length_nat N) (@ (@ tptp.cons_nat X) Xs)) (@ (@ tptp.gen_length_nat (@ tptp.suc N)) Xs))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.suc N)))))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) (@ tptp.suc N)))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) (@ tptp.suc N)))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) (@ tptp.suc N)))))))
% 2.52/3.50 (assert (forall ((N tptp.nat) (P2 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ P2 tptp.one_one_nat) (=> (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4) (=> (@ P2 N4) (@ P2 (@ tptp.suc N4))))) (@ P2 N))))))
% 2.52/3.50 (assert (forall ((B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one))) B) (@ tptp.uminus_uminus_int B))))
% 2.52/3.50 (assert (forall ((B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one))) B) (@ tptp.uminus_uminus_rat B))))
% 2.52/3.50 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) B) (@ tptp.uminus1351360451143612070nteger B))))
% 2.52/3.50 (assert (forall ((B tptp.int)) (= (@ (@ tptp.times_times_int B) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one))) (@ tptp.uminus_uminus_int B))))
% 2.52/3.50 (assert (forall ((B tptp.rat)) (= (@ (@ tptp.times_times_rat B) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one))) (@ tptp.uminus_uminus_rat B))))
% 2.52/3.50 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger B) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) (@ tptp.uminus1351360451143612070nteger B))))
% 2.52/3.50 (assert (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one)) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 2.52/3.50 (assert (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 2.52/3.50 (assert (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 2.52/3.50 (assert (forall ((N tptp.nat) (X tptp.int) (Xs tptp.list_int)) (let ((_let_1 (@ (@ tptp.nth_int (@ (@ tptp.cons_int X) Xs)) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_int Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))))
% 2.52/3.50 (assert (forall ((N tptp.nat) (X tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X) Xs)) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_nat Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.suc N))) A)))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (N tptp.nat)) (=> (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) A) (=> (@ (@ tptp.ord_le1926595141338095240atural A) tptp.one_one_Code_natural) (@ (@ tptp.ord_le1926595141338095240atural (@ (@ tptp.power_7079662738309270450atural A) (@ tptp.suc N))) A)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) (@ tptp.suc N))) A)))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) (@ tptp.suc N))) A)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) (@ tptp.suc N))) A)))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (N tptp.nat)) (=> (@ (@ tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural) A) (=> (@ (@ tptp.ord_le5570908160329646204atural A) tptp.one_one_Code_natural) (@ (@ tptp.ord_le5570908160329646204atural (@ (@ tptp.power_7079662738309270450atural A) (@ tptp.suc N))) tptp.one_one_Code_natural)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.suc N))) tptp.one_one_Code_integer)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) (@ tptp.suc N))) tptp.one_one_rat)))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) (@ tptp.suc N))) tptp.one_one_nat)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) (@ tptp.suc N))) tptp.one_one_int)))))
% 2.52/3.50 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M2)) N) (@ (@ tptp.minus_minus_nat M2) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 2.52/3.50 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= N (@ tptp.suc (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 2.52/3.50 (assert (= tptp.plus_plus_nat (lambda ((M3 tptp.nat) (N3 tptp.nat)) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) N3) (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)) N3))))))
% 2.52/3.50 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) M2) (= (@ tptp.suc (@ _let_1 M2)) (@ _let_1 (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat))))))))
% 2.52/3.50 (assert (forall ((X tptp.int) (Y tptp.int) (Xs tptp.list_int) (N tptp.nat)) (=> (not (= X Y)) (= (= (@ (@ tptp.nth_int (@ (@ tptp.cons_int X) Xs)) N) Y) (and (= (@ (@ tptp.nth_int Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) Y) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))))
% 2.52/3.50 (assert (forall ((X tptp.nat) (Y tptp.nat) (Xs tptp.list_nat) (N tptp.nat)) (=> (not (= X Y)) (= (= (@ (@ tptp.nth_nat (@ (@ tptp.cons_nat X) Xs)) N) Y) (and (= (@ (@ tptp.nth_nat Xs) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) Y) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.produc8508995932063986495nteger (@ (@ tptp.unique3479559517661332726nteger tptp.one) N)))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N)) (@ tptp.product_fst_nat_nat (@ (@ tptp.unique5055182867167087721od_nat tptp.one) N)))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int N)) (@ tptp.product_fst_int_int (@ (@ tptp.unique5052692396658037445od_int tptp.one) N)))))
% 2.52/3.50 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_int)))
% 2.52/3.50 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_rat)))
% 2.52/3.50 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_Code_integer)))
% 2.52/3.50 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.power_power_int _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))))
% 2.52/3.50 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ (@ tptp.power_power_rat _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))))
% 2.52/3.50 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.power_8256067586552552935nteger _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))))
% 2.52/3.50 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int X) Y)) _let_2) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_2)) (@ (@ tptp.power_power_int Y) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X)) Y)))))))
% 2.52/3.50 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat X) Y)) _let_2) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_2)) (@ (@ tptp.power_power_rat Y) _let_2))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X)) Y)))))))
% 2.52/3.50 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.minus_8373710615458151222nteger X) Y)) _let_2) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.power_8256067586552552935nteger X) _let_2)) (@ (@ tptp.power_8256067586552552935nteger Y) _let_2))) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger _let_1)) X)) Y)))))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.neg_numeral_sub_int tptp.one) M2))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ (@ tptp.neg_numeral_sub_rat tptp.one) M2))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.neg_nu5755505904847501662nteger tptp.one) M2))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ (@ tptp.neg_numeral_sub_int N) tptp.one))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ (@ tptp.neg_numeral_sub_rat N) tptp.one))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ (@ tptp.neg_nu5755505904847501662nteger N) tptp.one))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ (@ tptp.neg_numeral_sub_int M2) tptp.one))) tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2)))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.neg_numeral_sub_rat M2) tptp.one))) tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2)))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.neg_nu5755505904847501662nteger M2) tptp.one))) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2)))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) (@ (@ tptp.neg_numeral_sub_int tptp.one) M2))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) (@ (@ tptp.neg_numeral_sub_rat tptp.one) M2))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) (@ (@ tptp.neg_nu5755505904847501662nteger tptp.one) M2))))
% 2.52/3.50 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 2.52/3.50 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 2.52/3.50 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 2.52/3.50 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))
% 2.52/3.50 (assert (= (@ (@ tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural) tptp.one_one_Code_natural) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))
% 2.52/3.50 (assert (= (@ tptp.suc tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M2)) tptp.one_one_int) (@ (@ tptp.neg_numeral_sub_int M2) tptp.one))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat M2)) tptp.one_one_rat) (@ (@ tptp.neg_numeral_sub_rat M2) tptp.one))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.numera6620942414471956472nteger M2)) tptp.one_one_Code_integer) (@ (@ tptp.neg_nu5755505904847501662nteger M2) tptp.one))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.numeral_numeral_int N)) (@ (@ tptp.neg_numeral_sub_int tptp.one) N))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.neg_numeral_sub_rat tptp.one) N))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger N)) (@ (@ tptp.neg_nu5755505904847501662nteger tptp.one) N))))
% 2.52/3.50 (assert (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger))
% 2.52/3.50 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 2.52/3.50 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 2.52/3.50 (assert (= (@ (@ tptp.divide5121882707175180666atural tptp.one_one_Code_natural) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) tptp.zero_z2226904508553997617atural))
% 2.52/3.50 (assert (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger))
% 2.52/3.50 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 2.52/3.50 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 2.52/3.50 (assert (= (@ (@ tptp.divide5121882707175180666atural tptp.one_one_Code_natural) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) tptp.zero_z2226904508553997617atural))
% 2.52/3.50 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.plus_plus_int _let_1) _let_1) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 2.52/3.50 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ (@ tptp.plus_plus_rat _let_1) _let_1) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))
% 2.52/3.50 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 2.52/3.50 (assert (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))
% 2.52/3.50 (assert (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))
% 2.52/3.50 (assert (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 2.52/3.50 (assert (= (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 2.52/3.50 (assert (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 2.52/3.50 (assert (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))
% 2.52/3.50 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.divide_divide_int _let_1) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)))
% 2.52/3.50 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.divide6298287555418463151nteger _let_1) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1)))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int N)) (@ (@ tptp.neg_numeral_sub_int N) tptp.one))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.neg_numeral_sub_rat N) tptp.one))))
% 2.52/3.50 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger N)) (@ (@ tptp.neg_nu5755505904847501662nteger N) tptp.one))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int M2)) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.neg_numeral_sub_int M2) tptp.one))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat M2)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ (@ tptp.neg_numeral_sub_rat M2) tptp.one))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.numera6620942414471956472nteger M2)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.neg_nu5755505904847501662nteger M2) tptp.one))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2))) tptp.one_one_int) (@ (@ tptp.neg_numeral_sub_int tptp.one) M2))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M2))) tptp.one_one_rat) (@ (@ tptp.neg_numeral_sub_rat tptp.one) M2))))
% 2.52/3.50 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M2))) tptp.one_one_Code_integer) (@ (@ tptp.neg_nu5755505904847501662nteger tptp.one) M2))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 B))) (@ _let_1 A)) (@ (@ tptp.divide_divide_int B) A))))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 B))) (@ _let_1 A)) (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int B) tptp.one_one_int)) A))))))
% 2.52/3.50 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.divide_divide_int _let_1) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) _let_1))))
% 2.52/3.50 (assert (forall ((P2 (-> tptp.int Bool)) (K tptp.int)) (=> (@ P2 tptp.zero_zero_int) (=> (@ P2 (@ tptp.uminus_uminus_int tptp.one_one_int)) (=> (forall ((K2 tptp.int)) (=> (@ P2 K2) (=> (not (= K2 tptp.zero_zero_int)) (@ P2 (@ (@ tptp.times_times_int K2) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))) (=> (forall ((K2 tptp.int)) (=> (@ P2 K2) (=> (not (= K2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ P2 (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int K2) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))) (@ P2 K)))))))
% 2.52/3.50 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) B)))))
% 2.52/3.50 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) B)))))
% 2.52/3.50 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) A)) B)))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)) B)))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (@ tptp.plus_p4538020629002901425atural A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) A)) B)))))
% 2.52/3.50 (assert (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat Z) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_nat Z) Z))))
% 2.52/3.50 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_int Z) Z))))
% 2.52/3.50 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat Z) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_rat Z) Z))))
% 2.52/3.50 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger Z) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_p5714425477246183910nteger Z) Z))))
% 2.52/3.50 (assert (forall ((Z tptp.code_natural)) (= (@ (@ tptp.times_2397367101498566445atural Z) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_p4538020629002901425atural Z) Z))))
% 2.52/3.50 (assert (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_nat Z) Z))))
% 2.52/3.50 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_int Z) Z))))
% 2.52/3.50 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_rat Z) Z))))
% 2.52/3.50 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_p5714425477246183910nteger Z) Z))))
% 2.52/3.50 (assert (forall ((Z tptp.code_natural)) (= (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_p4538020629002901425atural Z) Z))))
% 2.52/3.50 (assert (forall ((A tptp.assn)) (= (@ (@ tptp.power_power_assn A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_assn A) A))))
% 2.52/3.50 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_nat A) A))))
% 2.52/3.50 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_int A) A))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_3573771949741848930nteger A) A))))
% 2.52/3.50 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.power_7079662738309270450atural A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_2397367101498566445atural A) A))))
% 2.52/3.50 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.power_power_assn X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn X) X)) X)) X))))
% 2.52/3.50 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.power_power_nat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat X) X)) X)) X))))
% 2.52/3.50 (assert (forall ((X tptp.int)) (= (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int X) X)) X)) X))))
% 2.52/3.50 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.power_8256067586552552935nteger X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger X) X)) X)) X))))
% 2.52/3.50 (assert (forall ((X tptp.code_natural)) (= (@ (@ tptp.power_7079662738309270450atural X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.times_2397367101498566445atural X) X)) X)) X))))
% 2.52/3.50 (assert (= (@ (@ tptp.power_8256067586552552935nteger tptp.one_one_Code_integer) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 2.52/3.50 (assert (= (@ (@ tptp.power_power_rat tptp.one_one_rat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat))
% 2.52/3.50 (assert (= (@ (@ tptp.power_power_int tptp.one_one_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 2.52/3.50 (assert (= (@ (@ tptp.power_power_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 2.52/3.50 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 2.52/3.50 (assert (forall ((A tptp.int)) (= (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int) (or (= A tptp.one_one_int) (= A (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 2.52/3.50 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat) (or (= A tptp.one_one_rat) (= A (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 2.52/3.50 (assert (forall ((A tptp.code_integer)) (= (= (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer) (or (= A tptp.one_one_Code_integer) (= A (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))))
% 2.52/3.51 (assert (forall ((P2 (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P2 tptp.zero_zero_nat) (=> (@ P2 tptp.one_one_nat) (=> (forall ((N4 tptp.nat)) (=> (@ P2 N4) (@ P2 (@ (@ tptp.plus_plus_nat N4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ P2 N))))))
% 2.52/3.51 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat X) Y)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat X) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat _let_1) X)) Y))))))
% 2.52/3.51 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int X) Y)) _let_2) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_2)) (@ (@ tptp.power_power_int Y) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X)) Y)))))))
% 2.52/3.51 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat X) Y)) _let_2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_2)) (@ (@ tptp.power_power_rat Y) _let_2))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X)) Y)))))))
% 2.52/3.51 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.plus_p5714425477246183910nteger X) Y)) _let_2) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.power_8256067586552552935nteger X) _let_2)) (@ (@ tptp.power_8256067586552552935nteger Y) _let_2))) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger _let_1)) X)) Y)))))))
% 2.52/3.51 (assert (forall ((X tptp.code_natural) (Y tptp.code_natural)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_7079662738309270450atural (@ (@ tptp.plus_p4538020629002901425atural X) Y)) _let_2) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.power_7079662738309270450atural X) _let_2)) (@ (@ tptp.power_7079662738309270450atural Y) _let_2))) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural _let_1)) X)) Y)))))))
% 2.52/3.51 (assert (forall ((X tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X) (=> (@ (@ tptp.ord_le3102999989581377725nteger X) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer)))))
% 2.52/3.51 (assert (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) X) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat)))))
% 2.52/3.51 (assert (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) X) (=> (@ (@ tptp.ord_less_eq_int X) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int)))))
% 2.52/3.51 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N))) (= (@ (@ tptp.times_times_int _let_1) _let_1) (@ (@ tptp.power_power_int A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 2.52/3.51 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) (@ (@ tptp.power_power_rat A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 2.52/3.51 (assert (forall ((A tptp.assn) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_assn A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_times_assn A) (@ (@ tptp.power_power_assn (@ _let_2 N)) _let_1)))))))
% 2.52/3.51 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_times_nat A) (@ (@ tptp.power_power_nat (@ _let_2 N)) _let_1)))))))
% 2.52/3.51 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_times_int A) (@ (@ tptp.power_power_int (@ _let_2 N)) _let_1)))))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_3573771949741848930nteger A) (@ (@ tptp.power_8256067586552552935nteger (@ _let_2 N)) _let_1)))))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_7079662738309270450atural A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_2397367101498566445atural A) (@ (@ tptp.power_7079662738309270450atural (@ _let_2 N)) _let_1)))))))
% 2.52/3.51 (assert (forall ((B tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ _let_1 B) (=> (@ _let_1 K) (exists ((N4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (and (@ (@ tptp.ord_less_nat (@ _let_1 N4)) K) (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N4) tptp.one_one_nat)))))))))))
% 2.52/3.51 (assert (forall ((B tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) K) (exists ((N4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N4)) K) (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N4) tptp.one_one_nat))))))))))
% 2.52/3.51 (assert (forall ((L tptp.num) (R2 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ (@ tptp.unique5026877609467782581ep_nat L) (@ (@ tptp.product_Pair_nat_nat Q4) R2)))) (let ((_let_3 (@ tptp.numeral_numeral_nat L))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat _let_3) R2))) (and (=> _let_4 (= _let_2 (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R2) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.product_Pair_nat_nat _let_1) R2))))))))))
% 2.52/3.51 (assert (forall ((L tptp.num) (R2 tptp.int) (Q4 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ (@ tptp.unique5024387138958732305ep_int L) (@ (@ tptp.product_Pair_int_int Q4) R2)))) (let ((_let_3 (@ tptp.numeral_numeral_int L))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_3) R2))) (and (=> _let_4 (= _let_2 (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R2) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.product_Pair_int_int _let_1) R2))))))))))
% 2.52/3.51 (assert (forall ((L tptp.num) (R2 tptp.code_integer) (Q4 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ (@ tptp.unique4921790084139445826nteger L) (@ (@ tptp.produc1086072967326762835nteger Q4) R2)))) (let ((_let_3 (@ tptp.numera6620942414471956472nteger L))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_3) R2))) (and (=> _let_4 (= _let_2 (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R2) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.produc1086072967326762835nteger _let_1) R2))))))))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2793503036327961859nteger tptp.zero_zero_nat) A) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1)))))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1617098188084679374atural tptp.zero_zero_nat) A) (@ (@ tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural) (@ (@ tptp.times_2397367101498566445atural _let_1) (@ (@ tptp.divide5121882707175180666atural A) _let_1)))))))
% 2.52/3.51 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7882103937844011126it_nat tptp.zero_zero_nat) A) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1)))))))
% 2.52/3.51 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7879613467334960850it_int tptp.zero_zero_nat) A) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1)))))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se8260200283734997820nteger tptp.zero_zero_nat) A) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))
% 2.52/3.51 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4205575877204974255it_nat tptp.zero_zero_nat) A) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1))))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7083795435491715335atural tptp.zero_zero_nat) A) (@ (@ tptp.times_2397367101498566445atural _let_1) (@ (@ tptp.divide5121882707175180666atural A) _let_1))))))
% 2.52/3.51 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4203085406695923979it_int tptp.zero_zero_nat) A) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1))))))
% 2.52/3.51 (assert (= (@ tptp.neg_numeral_dbl_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))
% 2.52/3.51 (assert (= (@ tptp.neg_numeral_dbl_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))
% 2.52/3.51 (assert (= (@ tptp.neg_nu8804712462038260780nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 2.52/3.51 (assert (= (@ tptp.neg_numeral_dbl_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 2.52/3.51 (assert (= (@ tptp.neg_numeral_dbl_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 2.52/3.51 (assert (= (@ tptp.neg_nu8804712462038260780nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) A)) _let_2) (@ (@ tptp.divide6298287555418463151nteger A) _let_2))))))))
% 2.52/3.51 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_nat _let_1) N))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) A)) _let_2) (@ (@ tptp.divide_divide_nat A) _let_2))))))))
% 2.52/3.51 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) _let_2) (@ (@ tptp.divide_divide_int A) _let_2))))))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural) (N tptp.nat)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_7079662738309270450atural _let_1) N))) (=> (@ (@ tptp.dvd_dvd_Code_natural _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural) A)) _let_2) (@ (@ tptp.divide5121882707175180666atural A) _let_2))))))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger _let_1))) (let ((_let_3 (@ tptp.dvd_dvd_Code_integer _let_1))) (let ((_let_4 (@ _let_2 N))) (= (@ _let_3 (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) (@ _let_2 M2))) _let_4)) (or (@ (@ tptp.ord_less_nat N) M2) (= _let_4 tptp.zero_z3403309356797280102nteger) (and (@ (@ tptp.ord_less_eq_nat M2) N) (@ _let_3 (@ (@ tptp.divide6298287555418463151nteger A) (@ _let_2 (@ (@ tptp.minus_minus_nat N) M2)))))))))))))
% 2.52/3.51 (assert (forall ((A tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (let ((_let_3 (@ tptp.dvd_dvd_nat _let_1))) (let ((_let_4 (@ _let_2 N))) (= (@ _let_3 (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) (@ _let_2 M2))) _let_4)) (or (@ (@ tptp.ord_less_nat N) M2) (= _let_4 tptp.zero_zero_nat) (and (@ (@ tptp.ord_less_eq_nat M2) N) (@ _let_3 (@ (@ tptp.divide_divide_nat A) (@ _let_2 (@ (@ tptp.minus_minus_nat N) M2)))))))))))))
% 2.52/3.51 (assert (forall ((A tptp.int) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int _let_1))) (let ((_let_3 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_4 (@ _let_2 N))) (= (@ _let_3 (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) (@ _let_2 M2))) _let_4)) (or (@ (@ tptp.ord_less_nat N) M2) (= _let_4 tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_nat M2) N) (@ _let_3 (@ (@ tptp.divide_divide_int A) (@ _let_2 (@ (@ tptp.minus_minus_nat N) M2)))))))))))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_7079662738309270450atural _let_1))) (let ((_let_3 (@ tptp.dvd_dvd_Code_natural _let_1))) (let ((_let_4 (@ _let_2 N))) (= (@ _let_3 (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.times_2397367101498566445atural A) (@ _let_2 M2))) _let_4)) (or (@ (@ tptp.ord_less_nat N) M2) (= _let_4 tptp.zero_z2226904508553997617atural) (and (@ (@ tptp.ord_less_eq_nat M2) N) (@ _let_3 (@ (@ tptp.divide5121882707175180666atural A) (@ _let_2 (@ (@ tptp.minus_minus_nat N) M2)))))))))))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) (@ (@ tptp.modulo364778990260209775nteger A) _let_3)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 (@ _let_1 _let_3))) tptp.one_one_Code_integer) (@ _let_1 B))))))))))
% 2.52/3.51 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (let ((_let_2 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat B) (@ (@ tptp.modulo_modulo_nat A) _let_3)) (= (@ (@ tptp.plus_plus_nat (@ _let_2 (@ _let_1 _let_3))) tptp.one_one_nat) (@ _let_1 B))))))))))
% 2.52/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int B) (@ (@ tptp.modulo_modulo_int A) _let_3)) (= (@ (@ tptp.plus_plus_int (@ _let_2 (@ _let_1 _let_3))) tptp.one_one_int) (@ _let_1 B))))))))))
% 2.52/3.51 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat M2) tptp.one_one_nat) (= M2 tptp.one_one_nat))))
% 2.52/3.51 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat B) A)) (@ (@ tptp.times_times_nat C) A)) (@ (@ tptp.dvd_dvd_nat B) C)))))
% 2.52/3.51 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int B) A)) (@ (@ tptp.times_times_int C) A)) (@ (@ tptp.dvd_dvd_int B) C)))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger B) A)) (@ (@ tptp.times_3573771949741848930nteger C) A)) (@ (@ tptp.dvd_dvd_Code_integer B) C)))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (=> (not (= A tptp.zero_z2226904508553997617atural)) (= (@ (@ tptp.dvd_dvd_Code_natural (@ (@ tptp.times_2397367101498566445atural B) A)) (@ (@ tptp.times_2397367101498566445atural C) A)) (@ (@ tptp.dvd_dvd_Code_natural B) C)))))
% 2.52/3.51 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 B)) (@ _let_1 C)) (@ (@ tptp.dvd_dvd_nat B) C))))))
% 2.52/3.51 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 B)) (@ _let_1 C)) (@ (@ tptp.dvd_dvd_int B) C))))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 B)) (@ _let_1 C)) (@ (@ tptp.dvd_dvd_Code_integer B) C))))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural A))) (=> (not (= A tptp.zero_z2226904508553997617atural)) (= (@ (@ tptp.dvd_dvd_Code_natural (@ _let_1 B)) (@ _let_1 C)) (@ (@ tptp.dvd_dvd_Code_natural B) C))))))
% 2.52/3.51 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (or (= C tptp.zero_zero_rat) (@ (@ tptp.dvd_dvd_rat A) B)))))
% 2.52/3.51 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (or (= C tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int A) B)))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (or (= C tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer A) B)))))
% 2.52/3.51 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.dvd_dvd_rat (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_zero_rat) (@ (@ tptp.dvd_dvd_rat A) B))))))
% 2.52/3.51 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int A) B))))))
% 2.52/3.51 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer A) B))))))
% 2.52/3.51 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) (@ (@ tptp.times_times_rat C) A))) (@ _let_1 B)))))
% 2.52/3.51 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) (@ (@ tptp.times_times_nat C) A))) (@ _let_1 B)))))
% 2.52/3.51 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) (@ (@ tptp.times_times_int C) A))) (@ _let_1 B)))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) (@ (@ tptp.times_3573771949741848930nteger C) A))) (@ _let_1 B)))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (let ((_let_1 (@ tptp.dvd_dvd_Code_natural A))) (= (@ _let_1 (@ (@ tptp.plus_p4538020629002901425atural B) (@ (@ tptp.times_2397367101498566445atural C) A))) (@ _let_1 B)))))
% 2.52/3.51 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat C) A)) B)) (@ _let_1 B)))))
% 2.52/3.51 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C) A)) B)) (@ _let_1 B)))))
% 2.52/3.51 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C) A)) B)) (@ _let_1 B)))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger C) A)) B)) (@ _let_1 B)))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural) (C tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (@ tptp.dvd_dvd_Code_natural A))) (= (@ _let_1 (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural C) A)) B)) (@ _let_1 B)))))
% 2.52/3.51 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) tptp.one_one_nat)))))
% 2.52/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) tptp.one_one_int)))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.one_one_Code_integer)))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural A) tptp.one_one_Code_natural) (=> (@ (@ tptp.dvd_dvd_Code_natural B) tptp.one_one_Code_natural) (@ (@ tptp.dvd_dvd_Code_natural (@ (@ tptp.times_2397367101498566445atural A) B)) tptp.one_one_Code_natural)))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 2.52/3.51 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) B) tptp.zero_zero_nat)))
% 2.52/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) B) tptp.zero_zero_int)))
% 2.52/3.51 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.times_2397367101498566445atural A) B)) B) tptp.zero_z2226904508553997617atural)))
% 2.52/3.51 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger B) A)) B) tptp.zero_z3403309356797280102nteger)))
% 2.52/3.51 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat B) A)) B) tptp.zero_zero_nat)))
% 2.52/3.51 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int B) A)) B) tptp.zero_zero_int)))
% 2.52/3.51 (assert (forall ((B tptp.code_natural) (A tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.times_2397367101498566445atural B) A)) B) tptp.zero_z2226904508553997617atural)))
% 2.52/3.51 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 2.52/3.51 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)))
% 2.52/3.51 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)))
% 2.52/3.51 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural A) tptp.one_one_Code_natural) tptp.zero_z2226904508553997617atural)))
% 2.52/3.51 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 2.52/3.51 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)))
% 2.52/3.51 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)))
% 2.52/3.51 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural A) tptp.one_one_Code_natural) tptp.zero_z2226904508553997617atural)))
% 2.52/3.51 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) C)) A)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 2.52/3.51 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) C)) A)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 2.52/3.51 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) C)) A)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 2.52/3.51 (assert (forall ((B tptp.code_natural) (C tptp.code_natural) (A tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural B) C)) A)) B) (@ (@ tptp.modulo8411746178871703098atural A) B))))
% 2.52/3.51 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger C) B)) A)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 2.52/3.51 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C) B)) A)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 2.52/3.51 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C) B)) A)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 2.52/3.51 (assert (forall ((C tptp.code_natural) (B tptp.code_natural) (A tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural C) B)) A)) B) (@ (@ tptp.modulo8411746178871703098atural A) B))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger B) C))) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 2.52/3.51 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat B) C))) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 2.52/3.51 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int B) C))) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.plus_p4538020629002901425atural A) (@ (@ tptp.times_2397367101498566445atural B) C))) B) (@ (@ tptp.modulo8411746178871703098atural A) B))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger C) B))) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 2.52/3.51 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat C) B))) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 2.52/3.51 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C) B))) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural) (C tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.plus_p4538020629002901425atural A) (@ (@ tptp.times_2397367101498566445atural C) B))) B) (@ (@ tptp.modulo8411746178871703098atural A) B))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger B) A)) A) B))))
% 2.52/3.51 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B) A)) A) B))))
% 2.52/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B) A)) A) B))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural A) B) (= (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural B) A)) A) B))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (@ (@ tptp.times_3573771949741848930nteger A) (@ (@ tptp.divide6298287555418463151nteger B) A)) B))))
% 2.52/3.51 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (@ (@ tptp.times_times_nat A) (@ (@ tptp.divide_divide_nat B) A)) B))))
% 2.52/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (@ (@ tptp.times_times_int A) (@ (@ tptp.divide_divide_int B) A)) B))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural A) B) (= (@ (@ tptp.times_2397367101498566445atural A) (@ (@ tptp.divide5121882707175180666atural B) A)) B))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger A) B)) tptp.one_one_Code_integer)))))
% 2.52/3.51 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A) B)) tptp.one_one_nat)))))
% 2.52/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A) B)) tptp.one_one_int)))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural A) tptp.one_one_Code_natural) (=> (@ (@ tptp.dvd_dvd_Code_natural B) tptp.one_one_Code_natural) (@ (@ tptp.dvd_dvd_Code_natural (@ (@ tptp.divide5121882707175180666atural A) B)) tptp.one_one_Code_natural)))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) A)) tptp.one_one_Code_integer))))
% 2.52/3.51 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat tptp.one_one_nat) A)) tptp.one_one_nat))))
% 2.52/3.51 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int tptp.one_one_int) A)) tptp.one_one_int))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural A) tptp.one_one_Code_natural) (@ (@ tptp.dvd_dvd_Code_natural (@ (@ tptp.divide5121882707175180666atural tptp.one_one_Code_natural) A)) tptp.one_one_Code_natural))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer))) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (@ _let_1 (@ _let_1 A)) A)))))
% 2.52/3.51 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat tptp.one_one_nat))) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ _let_1 (@ _let_1 A)) A)))))
% 2.52/3.51 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int tptp.one_one_int))) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ _let_1 (@ _let_1 A)) A)))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural)) (let ((_let_1 (@ tptp.divide5121882707175180666atural tptp.one_one_Code_natural))) (=> (@ (@ tptp.dvd_dvd_Code_natural A) tptp.one_one_Code_natural) (= (@ _let_1 (@ _let_1 A)) A)))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger B) A)) A) B))))
% 2.52/3.51 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B) A)) A) B))))
% 2.52/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B) A)) A) B))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural A) tptp.one_one_Code_natural) (= (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural B) A)) A) B))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) A)) (@ (@ tptp.divide6298287555418463151nteger B) A)))))
% 2.52/3.51 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat tptp.one_one_nat) A)) (@ (@ tptp.divide_divide_nat B) A)))))
% 2.52/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int tptp.one_one_int) A)) (@ (@ tptp.divide_divide_int B) A)))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural A) tptp.one_one_Code_natural) (= (@ (@ tptp.times_2397367101498566445atural B) (@ (@ tptp.divide5121882707175180666atural tptp.one_one_Code_natural) A)) (@ (@ tptp.divide5121882707175180666atural B) A)))))
% 2.52/3.51 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int)))
% 2.52/3.51 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger)))
% 2.52/3.51 (assert (forall ((K tptp.num) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (=> (not (= _let_1 tptp.one_one_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) _let_1) tptp.one_one_nat)))))
% 2.52/3.51 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.times_times_nat A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 2.52/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.times_times_int A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (@ tptp.dvd_dvd_Code_natural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.times_2397367101498566445atural A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 2.52/3.51 (assert (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 2.52/3.51 (assert (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 2.52/3.51 (assert (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 2.52/3.51 (assert (= (@ (@ tptp.modulo8411746178871703098atural tptp.one_one_Code_natural) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) tptp.one_one_Code_natural))
% 2.52/3.51 (assert (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 2.52/3.51 (assert (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 2.52/3.51 (assert (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 2.52/3.51 (assert (= (@ (@ tptp.modulo8411746178871703098atural tptp.one_one_Code_natural) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) tptp.one_one_Code_natural))
% 2.52/3.51 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) (not (@ _let_1 A))))))
% 2.52/3.51 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) (not (@ _let_1 A))))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer)) (not (@ _let_1 A))))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural)) (let ((_let_1 (@ tptp.dvd_dvd_Code_natural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_p4538020629002901425atural A) tptp.one_one_Code_natural)) (not (@ _let_1 A))))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_z3403309356797280102nteger)) (= _let_1 tptp.one_one_Code_integer)))))
% 2.52/3.51 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_zero_nat)) (= _let_1 tptp.one_one_nat)))))
% 2.52/3.51 (assert (forall ((A tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_zero_int)) (= _let_1 tptp.one_one_int)))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural)) (let ((_let_1 (@ (@ tptp.modulo8411746178871703098atural A) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_z2226904508553997617atural)) (= _let_1 tptp.one_one_Code_natural)))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_Code_integer)) (= _let_1 tptp.zero_z3403309356797280102nteger)))))
% 2.52/3.51 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_nat)) (= _let_1 tptp.zero_zero_nat)))))
% 2.52/3.51 (assert (forall ((A tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_int)) (= _let_1 tptp.zero_zero_int)))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural)) (let ((_let_1 (@ (@ tptp.modulo8411746178871703098atural A) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_Code_natural)) (= _let_1 tptp.zero_z2226904508553997617atural)))))
% 2.52/3.51 (assert (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 2.52/3.51 (assert (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 2.52/3.51 (assert (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 2.52/3.51 (assert (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 2.52/3.51 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N) tptp.one_one_int))))
% 2.52/3.51 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N) tptp.one_one_rat))))
% 2.52/3.51 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N) tptp.one_one_Code_integer))))
% 2.52/3.51 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_int _let_1) N) _let_1)))))
% 2.52/3.51 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_rat _let_1) N) _let_1)))))
% 2.52/3.51 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_8256067586552552935nteger _let_1) N) _let_1)))))
% 2.52/3.51 (assert (forall ((M2 tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat M2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (= _let_1 tptp.one_one_nat)))))
% 2.52/3.51 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.produc6174133586879617921nteger (@ (@ tptp.unique3479559517661332726nteger tptp.one) N)))))
% 2.52/3.51 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N)) (@ tptp.product_snd_nat_nat (@ (@ tptp.unique5055182867167087721od_nat tptp.one) N)))))
% 2.52/3.51 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int N)) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int tptp.one) N)))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) A)) _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))
% 2.52/3.51 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) A)) _let_1) (@ (@ tptp.divide_divide_nat A) _let_1))))))
% 2.52/3.51 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) _let_1) (@ (@ tptp.divide_divide_int A) _let_1))))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_Code_natural _let_1) A) (= (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural) A)) _let_1) (@ (@ tptp.divide5121882707175180666atural A) _let_1))))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer)) _let_1) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) _let_1)) tptp.one_one_Code_integer))))))
% 2.52/3.51 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) A)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) _let_1)) tptp.one_one_nat))))))
% 2.52/3.51 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_int _let_1) A)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) _let_1)) tptp.one_one_int))))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_Code_natural _let_1) A)) (= (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.plus_p4538020629002901425atural A) tptp.one_one_Code_natural)) _let_1) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.divide5121882707175180666atural A) _let_1)) tptp.one_one_Code_natural))))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer)) _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))
% 2.52/3.51 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) _let_1) (@ (@ tptp.divide_divide_nat A) _let_1))))))
% 2.52/3.51 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) _let_1) (@ (@ tptp.divide_divide_int A) _let_1))))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_Code_natural _let_1) A) (= (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.plus_p4538020629002901425atural A) tptp.one_one_Code_natural)) _let_1) (@ (@ tptp.divide5121882707175180666atural A) _let_1))))))
% 2.52/3.51 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N)) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat N) _let_1)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))) tptp.one_one_Code_integer) A)))))
% 2.52/3.51 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) A)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1))) tptp.one_one_nat) A)))))
% 2.52/3.51 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_int _let_1) A)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1))) tptp.one_one_int) A)))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_Code_natural _let_1) A)) (= (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural _let_1) (@ (@ tptp.divide5121882707175180666atural A) _let_1))) tptp.one_one_Code_natural) A)))))
% 2.52/3.51 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat _let_1) N)) tptp.one_one_nat)) (= N tptp.zero_zero_nat)))))
% 2.52/3.51 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int _let_1) N)) tptp.one_one_int)) (= N tptp.zero_zero_nat)))))
% 2.52/3.51 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger _let_1) N)) tptp.one_one_Code_integer)) (= N tptp.zero_zero_nat)))))
% 2.52/3.51 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_Code_natural _let_1) (@ (@ tptp.minus_7197305767214868737atural (@ (@ tptp.power_7079662738309270450atural _let_1) N)) tptp.one_one_Code_natural)) (= N tptp.zero_zero_nat)))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N))) (let ((_let_3 (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo364778990260209775nteger A) _let_2))))))))))
% 2.52/3.51 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_nat _let_1) N))) (let ((_let_3 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.modulo_modulo_nat (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo_modulo_nat A) _let_2))))))))))
% 2.52/3.51 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N))) (let ((_let_3 (@ tptp.plus_plus_int tptp.one_one_int))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.modulo_modulo_int (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo_modulo_int A) _let_2))))))))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural) (N tptp.nat)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_7079662738309270450atural _let_1) N))) (let ((_let_3 (@ tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural))) (=> (@ (@ tptp.dvd_dvd_Code_natural _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.modulo8411746178871703098atural (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo8411746178871703098atural A) _let_2))))))))))
% 2.52/3.51 (assert (forall ((K tptp.int) (L tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K) L)) tptp.zero_zero_int) (= (@ (@ tptp.divide_divide_int K) L) (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 2.52/3.51 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) L) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int K)) L) (@ (@ tptp.minus_minus_int (@ (@ tptp.minus_minus_int L) tptp.one_one_int)) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) L))))))
% 2.52/3.51 (assert (forall ((B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) B) (@ (@ tptp.minus_minus_int B) tptp.one_one_int)))))
% 2.52/3.51 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L) (=> (@ (@ tptp.ord_less_eq_int L) K) (= (@ (@ tptp.divide_divide_int K) L) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int K) L)) L)) tptp.one_one_int))))))
% 2.52/3.51 (assert (forall ((X tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) K) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int X) K)) X)))))
% 2.52/3.51 (assert (forall ((B tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.divide_divide_int _let_1) B) _let_1)))))
% 2.52/3.51 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int A) B)))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B))) (let ((_let_3 (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int))) (=> (not (= B tptp.zero_zero_int)) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_int _let_1) tptp.one_one_int))))))))))
% 2.52/3.51 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ _let_1 B)))) (let ((_let_3 (@ _let_1 (@ tptp.uminus_uminus_int B)))) (let ((_let_4 (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int))) (=> (not (= B tptp.zero_zero_int)) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)))))))))))
% 2.52/3.51 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.modulo364778990260209775nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 2.52/3.51 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat))))
% 2.52/3.51 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int))))
% 2.52/3.51 (assert (forall ((B tptp.code_natural) (A tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural B) tptp.one_one_Code_natural) (= (@ (@ tptp.modulo8411746178871703098atural A) B) tptp.zero_z2226904508553997617atural))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 B)) C)))))
% 2.52/3.51 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.modulo_modulo_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat B) C))) C) (@ (@ tptp.modulo_modulo_nat (@ _let_1 B)) C)))))
% 2.52/3.51 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ _let_1 B)) C)))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural A))) (= (@ (@ tptp.modulo8411746178871703098atural (@ _let_1 (@ (@ tptp.modulo8411746178871703098atural B) C))) C) (@ (@ tptp.modulo8411746178871703098atural (@ _let_1 B)) C)))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) C))))
% 2.52/3.51 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) C)) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C))))
% 2.52/3.51 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) C)) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural) (C tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.modulo8411746178871703098atural A) C)) B)) C) (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.times_2397367101498566445atural A) B)) C))))
% 2.52/3.51 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 A)) (@ _let_1 B))))))
% 2.52/3.51 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.modulo_modulo_nat (@ _let_1 A)) (@ _let_1 B))))))
% 2.52/3.51 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.modulo_modulo_int (@ _let_1 A)) (@ _let_1 B))))))
% 2.52/3.51 (assert (forall ((C tptp.code_natural) (A tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural C))) (= (@ _let_1 (@ (@ tptp.modulo8411746178871703098atural A) B)) (@ (@ tptp.modulo8411746178871703098atural (@ _let_1 A)) (@ _let_1 B))))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) C))))
% 2.52/3.51 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) B)) C))))
% 2.52/3.51 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) B)) C))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural) (C tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.times_2397367101498566445atural A) C)) (@ (@ tptp.times_2397367101498566445atural B) C)) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.modulo8411746178871703098atural A) B)) C))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (A5 tptp.code_integer) (B tptp.code_integer) (B6 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger A5) C)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B) C) (@ (@ tptp.modulo364778990260209775nteger B6) C)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A5) B6)) C))))))
% 2.52/3.51 (assert (forall ((A tptp.nat) (C tptp.nat) (A5 tptp.nat) (B tptp.nat) (B6 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) C) (@ (@ tptp.modulo_modulo_nat A5) C)) (=> (= (@ (@ tptp.modulo_modulo_nat B) C) (@ (@ tptp.modulo_modulo_nat B6) C)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A5) B6)) C))))))
% 2.52/3.51 (assert (forall ((A tptp.int) (C tptp.int) (A5 tptp.int) (B tptp.int) (B6 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A5) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B6) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A5) B6)) C))))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural) (C tptp.code_natural) (A5 tptp.code_natural) (B tptp.code_natural) (B6 tptp.code_natural)) (=> (= (@ (@ tptp.modulo8411746178871703098atural A) C) (@ (@ tptp.modulo8411746178871703098atural A5) C)) (=> (= (@ (@ tptp.modulo8411746178871703098atural B) C) (@ (@ tptp.modulo8411746178871703098atural B6) C)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.times_2397367101498566445atural A) B)) C) (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.times_2397367101498566445atural A5) B6)) C))))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) C))))
% 2.52/3.51 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) C)) (@ (@ tptp.modulo_modulo_nat B) C))) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C))))
% 2.52/3.51 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) C)) (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural) (C tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.modulo8411746178871703098atural A) C)) (@ (@ tptp.modulo8411746178871703098atural B) C))) C) (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.times_2397367101498566445atural A) B)) C))))
% 2.52/3.51 (assert (forall ((A tptp.assn) (B tptp.assn)) (@ (@ tptp.dvd_dvd_assn A) (@ (@ tptp.times_times_assn B) A))))
% 2.52/3.51 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B) A))))
% 2.52/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B) A))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger B) A))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (@ (@ tptp.dvd_dvd_Code_natural A) (@ (@ tptp.times_2397367101498566445atural B) A))))
% 2.52/3.51 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (=> (@ (@ tptp.dvd_dvd_assn (@ (@ tptp.times_times_assn A) B)) C) (@ (@ tptp.dvd_dvd_assn B) C))))
% 2.52/3.51 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat B) C))))
% 2.52/3.51 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.dvd_dvd_int B) C))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer B) C))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural (@ (@ tptp.times_2397367101498566445atural A) B)) C) (@ (@ tptp.dvd_dvd_Code_natural B) C))))
% 2.52/3.51 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn) (D2 tptp.assn)) (=> (@ (@ tptp.dvd_dvd_assn A) B) (=> (@ (@ tptp.dvd_dvd_assn C) D2) (@ (@ tptp.dvd_dvd_assn (@ (@ tptp.times_times_assn A) C)) (@ (@ tptp.times_times_assn B) D2))))))
% 2.52/3.51 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (=> (@ (@ tptp.dvd_dvd_nat C) D2) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D2))))))
% 2.52/3.51 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (=> (@ (@ tptp.dvd_dvd_int C) D2) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D2))))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (=> (@ (@ tptp.dvd_dvd_Code_integer C) D2) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D2))))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural) (D2 tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural A) B) (=> (@ (@ tptp.dvd_dvd_Code_natural C) D2) (@ (@ tptp.dvd_dvd_Code_natural (@ (@ tptp.times_2397367101498566445atural A) C)) (@ (@ tptp.times_2397367101498566445atural B) D2))))))
% 2.52/3.51 (assert (forall ((A tptp.assn) (B tptp.assn)) (@ (@ tptp.dvd_dvd_assn A) (@ (@ tptp.times_times_assn A) B))))
% 2.52/3.51 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat A) B))))
% 2.52/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int A) B))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger A) B))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (@ (@ tptp.dvd_dvd_Code_natural A) (@ (@ tptp.times_2397367101498566445atural A) B))))
% 2.52/3.51 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (=> (@ (@ tptp.dvd_dvd_assn (@ (@ tptp.times_times_assn A) B)) C) (@ (@ tptp.dvd_dvd_assn A) C))))
% 2.52/3.51 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat A) C))))
% 2.52/3.51 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.dvd_dvd_int A) C))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer A) C))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural (@ (@ tptp.times_2397367101498566445atural A) B)) C) (@ (@ tptp.dvd_dvd_Code_natural A) C))))
% 2.52/3.51 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.dvd_dvd_assn A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_assn B) C))))))
% 2.52/3.51 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))))
% 2.52/3.51 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_int B) C))))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (let ((_let_1 (@ tptp.dvd_dvd_Code_natural A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_2397367101498566445atural B) C))))))
% 2.52/3.51 (assert (forall ((A tptp.assn) (C tptp.assn) (B tptp.assn)) (let ((_let_1 (@ tptp.dvd_dvd_assn A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_assn B) C))))))
% 2.52/3.51 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))))
% 2.52/3.51 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_int B) C))))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural) (C tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (@ tptp.dvd_dvd_Code_natural A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_2397367101498566445atural B) C))))))
% 2.52/3.51 (assert (= tptp.dvd_dvd_assn (lambda ((B2 tptp.assn) (A2 tptp.assn)) (exists ((K4 tptp.assn)) (= A2 (@ (@ tptp.times_times_assn B2) K4))))))
% 2.52/3.51 (assert (= tptp.dvd_dvd_nat (lambda ((B2 tptp.nat) (A2 tptp.nat)) (exists ((K4 tptp.nat)) (= A2 (@ (@ tptp.times_times_nat B2) K4))))))
% 2.52/3.51 (assert (= tptp.dvd_dvd_int (lambda ((B2 tptp.int) (A2 tptp.int)) (exists ((K4 tptp.int)) (= A2 (@ (@ tptp.times_times_int B2) K4))))))
% 2.52/3.51 (assert (= tptp.dvd_dvd_Code_integer (lambda ((B2 tptp.code_integer) (A2 tptp.code_integer)) (exists ((K4 tptp.code_integer)) (= A2 (@ (@ tptp.times_3573771949741848930nteger B2) K4))))))
% 2.52/3.51 (assert (= tptp.dvd_dvd_Code_natural (lambda ((B2 tptp.code_natural) (A2 tptp.code_natural)) (exists ((K4 tptp.code_natural)) (= A2 (@ (@ tptp.times_2397367101498566445atural B2) K4))))))
% 2.52/3.51 (assert (forall ((A tptp.assn) (B tptp.assn) (K tptp.assn)) (=> (= A (@ (@ tptp.times_times_assn B) K)) (@ (@ tptp.dvd_dvd_assn B) A))))
% 2.52/3.51 (assert (forall ((A tptp.nat) (B tptp.nat) (K tptp.nat)) (=> (= A (@ (@ tptp.times_times_nat B) K)) (@ (@ tptp.dvd_dvd_nat B) A))))
% 2.52/3.51 (assert (forall ((A tptp.int) (B tptp.int) (K tptp.int)) (=> (= A (@ (@ tptp.times_times_int B) K)) (@ (@ tptp.dvd_dvd_int B) A))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (K tptp.code_integer)) (=> (= A (@ (@ tptp.times_3573771949741848930nteger B) K)) (@ (@ tptp.dvd_dvd_Code_integer B) A))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (K tptp.code_natural)) (=> (= A (@ (@ tptp.times_2397367101498566445atural B) K)) (@ (@ tptp.dvd_dvd_Code_natural B) A))))
% 2.52/3.51 (assert (forall ((B tptp.assn) (A tptp.assn)) (=> (@ (@ tptp.dvd_dvd_assn B) A) (not (forall ((K2 tptp.assn)) (not (= A (@ (@ tptp.times_times_assn B) K2))))))))
% 2.52/3.51 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (not (forall ((K2 tptp.nat)) (not (= A (@ (@ tptp.times_times_nat B) K2))))))))
% 2.52/3.51 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (not (forall ((K2 tptp.int)) (not (= A (@ (@ tptp.times_times_int B) K2))))))))
% 2.52/3.51 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (not (forall ((K2 tptp.code_integer)) (not (= A (@ (@ tptp.times_3573771949741848930nteger B) K2))))))))
% 2.52/3.51 (assert (forall ((B tptp.code_natural) (A tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural B) A) (not (forall ((K2 tptp.code_natural)) (not (= A (@ (@ tptp.times_2397367101498566445atural B) K2))))))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (@ _let_1 tptp.one_one_Code_integer))))))
% 2.52/3.51 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (@ _let_1 tptp.one_one_nat))))))
% 2.52/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (@ _let_1 tptp.one_one_int))))))
% 2.52/3.51 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer B))) (=> (@ _let_1 tptp.one_one_Code_integer) (@ _let_1 A)))))
% 2.52/3.51 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat B))) (=> (@ _let_1 tptp.one_one_nat) (@ _let_1 A)))))
% 2.52/3.51 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int B))) (=> (@ _let_1 tptp.one_one_int) (@ _let_1 A)))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer tptp.one_one_Code_integer) A)))
% 2.52/3.51 (assert (forall ((A tptp.assn)) (@ (@ tptp.dvd_dvd_assn tptp.one_one_assn) A)))
% 2.52/3.51 (assert (forall ((A tptp.rat)) (@ (@ tptp.dvd_dvd_rat tptp.one_one_rat) A)))
% 2.52/3.51 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat tptp.one_one_nat) A)))
% 2.52/3.51 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int tptp.one_one_int) A)))
% 2.52/3.51 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)) (= (@ (@ tptp.modulo364778990260209775nteger A) _let_1) tptp.one_one_Code_integer)))))
% 2.52/3.51 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (not (@ (@ tptp.dvd_dvd_nat _let_1) A)) (= (@ (@ tptp.modulo_modulo_nat A) _let_1) tptp.one_one_nat)))))
% 2.52/3.51 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (not (@ (@ tptp.dvd_dvd_int _let_1) A)) (= (@ (@ tptp.modulo_modulo_int A) _let_1) tptp.one_one_int)))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (= (not (@ (@ tptp.dvd_dvd_Code_natural _let_1) A)) (= (@ (@ tptp.modulo8411746178871703098atural A) _let_1) tptp.one_one_Code_natural)))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger B) C)) (not (forall ((D3 tptp.code_integer)) (not (= B (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger C) D3)))))))))
% 2.52/3.51 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int B) C)) (not (forall ((D3 tptp.int)) (not (= B (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C) D3)))))))))
% 2.52/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.plus_plus_int tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ (@ tptp.modulo_modulo_int (@ _let_2 (@ _let_1 B))) (@ _let_1 A)) (@ _let_2 (@ _let_1 (@ (@ tptp.modulo_modulo_int B) A)))))))))
% 2.52/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 B))) (@ _let_1 A)) (@ (@ tptp.minus_minus_int (@ _let_1 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int B) tptp.one_one_int)) A))) tptp.one_one_int))))))
% 2.52/3.51 (assert (not (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) tptp.one_one_nat)))
% 2.52/3.51 (assert (not (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) tptp.one_one_int)))
% 2.52/3.51 (assert (not (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer)))
% 2.52/3.51 (assert (not (@ (@ tptp.dvd_dvd_Code_natural tptp.zero_z2226904508553997617atural) tptp.one_one_Code_natural)))
% 2.52/3.51 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (= (@ (@ tptp.times_times_nat B) A) (@ (@ tptp.times_times_nat C) A)) (= B C)))))
% 2.52/3.51 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (= (@ (@ tptp.times_times_int B) A) (@ (@ tptp.times_times_int C) A)) (= B C)))))
% 2.52/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (= (@ (@ tptp.times_3573771949741848930nteger B) A) (@ (@ tptp.times_3573771949741848930nteger C) A)) (= B C)))))
% 2.52/3.51 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural A) tptp.one_one_Code_natural) (= (= (@ (@ tptp.times_2397367101498566445atural B) A) (@ (@ tptp.times_2397367101498566445atural C) A)) (= B C)))))
% 2.52/3.51 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C))))))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C))))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C))))))
% 3.15/3.51 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural A))) (=> (@ (@ tptp.dvd_dvd_Code_natural A) tptp.one_one_Code_natural) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C))))))
% 3.15/3.51 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat B) C)))))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.dvd_dvd_int B) C)))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer B) C)))))
% 3.15/3.51 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural A) tptp.one_one_Code_natural) (= (@ (@ tptp.dvd_dvd_Code_natural (@ (@ tptp.times_2397367101498566445atural A) B)) C) (@ (@ tptp.dvd_dvd_Code_natural B) C)))))
% 3.15/3.51 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C)) (@ _let_1 C))))))
% 3.15/3.51 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ _let_1 C))))))
% 3.15/3.51 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ _let_1 C))))))
% 3.15/3.51 (assert (forall ((B tptp.code_natural) (A tptp.code_natural) (C tptp.code_natural)) (let ((_let_1 (@ tptp.dvd_dvd_Code_natural A))) (=> (@ (@ tptp.dvd_dvd_Code_natural B) tptp.one_one_Code_natural) (= (@ _let_1 (@ (@ tptp.times_2397367101498566445atural B) C)) (@ _let_1 C))))))
% 3.15/3.51 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat A) C)))))
% 3.15/3.51 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.dvd_dvd_int A) C)))))
% 3.15/3.51 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer A) C)))))
% 3.15/3.51 (assert (forall ((B tptp.code_natural) (A tptp.code_natural) (C tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural B) tptp.one_one_Code_natural) (= (@ (@ tptp.dvd_dvd_Code_natural (@ (@ tptp.times_2397367101498566445atural A) B)) C) (@ (@ tptp.dvd_dvd_Code_natural A) C)))))
% 3.15/3.51 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat C) B)) (@ _let_1 C))))))
% 3.15/3.51 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int C) B)) (@ _let_1 C))))))
% 3.15/3.51 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger C) B)) (@ _let_1 C))))))
% 3.15/3.51 (assert (forall ((B tptp.code_natural) (A tptp.code_natural) (C tptp.code_natural)) (let ((_let_1 (@ tptp.dvd_dvd_Code_natural A))) (=> (@ (@ tptp.dvd_dvd_Code_natural B) tptp.one_one_Code_natural) (= (@ _let_1 (@ (@ tptp.times_2397367101498566445atural C) B)) (@ _let_1 C))))))
% 3.15/3.51 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) tptp.one_one_nat) (and (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat)))))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) tptp.one_one_int) (and (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int)))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.one_one_Code_integer) (and (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer)))))
% 3.15/3.51 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.dvd_dvd_Code_natural (@ (@ tptp.times_2397367101498566445atural A) B)) tptp.one_one_Code_natural) (and (@ (@ tptp.dvd_dvd_Code_natural A) tptp.one_one_Code_natural) (@ (@ tptp.dvd_dvd_Code_natural B) tptp.one_one_Code_natural)))))
% 3.15/3.51 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger B) C)) A) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger B) A)) C)))))
% 3.15/3.51 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B) C)) A) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat B) A)) C)))))
% 3.15/3.51 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B) C)) A) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int B) A)) C)))))
% 3.15/3.51 (assert (forall ((C tptp.code_natural) (B tptp.code_natural) (A tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural C) B) (= (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural B) C)) A) (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.times_2397367101498566445atural B) A)) C)))))
% 3.15/3.51 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C))))))
% 3.15/3.51 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C))))))
% 3.15/3.51 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ _let_1 (@ (@ tptp.divide_divide_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C))))))
% 3.15/3.51 (assert (forall ((C tptp.code_natural) (B tptp.code_natural) (A tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural A))) (=> (@ (@ tptp.dvd_dvd_Code_natural C) B) (= (@ _let_1 (@ (@ tptp.divide5121882707175180666atural B) C)) (@ (@ tptp.divide5121882707175180666atural (@ _let_1 B)) C))))))
% 3.15/3.51 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B) C)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 B)) C)))))))
% 3.15/3.51 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) B) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B) C)) (@ (@ tptp.times_times_nat (@ _let_1 B)) C)))))))
% 3.15/3.51 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int C) B) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ _let_1 (@ (@ tptp.divide_divide_int B) C)) (@ (@ tptp.times_times_int (@ _let_1 B)) C)))))))
% 3.15/3.51 (assert (forall ((C tptp.code_natural) (B tptp.code_natural) (A tptp.code_natural)) (let ((_let_1 (@ tptp.divide5121882707175180666atural A))) (=> (@ (@ tptp.dvd_dvd_Code_natural C) B) (=> (@ (@ tptp.dvd_dvd_Code_natural B) A) (= (@ _let_1 (@ (@ tptp.divide5121882707175180666atural B) C)) (@ (@ tptp.times_2397367101498566445atural (@ _let_1 B)) C)))))))
% 3.15/3.51 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (let ((_let_2 (@ (@ tptp.times_3573771949741848930nteger B) C))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C)))))))
% 3.15/3.51 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (let ((_let_2 (@ (@ tptp.times_times_nat B) C))) (=> (@ (@ tptp.dvd_dvd_nat _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C)))))))
% 3.15/3.51 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ (@ tptp.times_times_int B) C))) (=> (@ (@ tptp.dvd_dvd_int _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C)))))))
% 3.15/3.51 (assert (forall ((B tptp.code_natural) (C tptp.code_natural) (A tptp.code_natural)) (let ((_let_1 (@ tptp.divide5121882707175180666atural A))) (let ((_let_2 (@ (@ tptp.times_2397367101498566445atural B) C))) (=> (@ (@ tptp.dvd_dvd_Code_natural _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide5121882707175180666atural (@ _let_1 B)) C)))))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) B) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.divide6298287555418463151nteger B) C)))))
% 3.15/3.51 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) B) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.divide_divide_nat B) C)))))
% 3.15/3.51 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) B) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.divide_divide_int B) C)))))
% 3.15/3.51 (assert (forall ((A tptp.code_natural) (C tptp.code_natural) (B tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural (@ (@ tptp.times_2397367101498566445atural A) C)) B) (@ (@ tptp.dvd_dvd_Code_natural A) (@ (@ tptp.divide5121882707175180666atural B) C)))))
% 3.15/3.51 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (D2 tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (=> (@ (@ tptp.dvd_dvd_Code_integer D2) C) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) (@ (@ tptp.divide6298287555418463151nteger C) D2)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D2)))))))
% 3.15/3.51 (assert (forall ((B tptp.nat) (A tptp.nat) (D2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (=> (@ (@ tptp.dvd_dvd_nat D2) C) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) (@ (@ tptp.divide_divide_nat C) D2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D2)))))))
% 3.15/3.51 (assert (forall ((B tptp.int) (A tptp.int) (D2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (=> (@ (@ tptp.dvd_dvd_int D2) C) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) (@ (@ tptp.divide_divide_int C) D2)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D2)))))))
% 3.15/3.51 (assert (forall ((B tptp.code_natural) (A tptp.code_natural) (D2 tptp.code_natural) (C tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural B) A) (=> (@ (@ tptp.dvd_dvd_Code_natural D2) C) (= (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural A) B)) (@ (@ tptp.divide5121882707175180666atural C) D2)) (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.times_2397367101498566445atural A) C)) (@ (@ tptp.times_2397367101498566445atural B) D2)))))))
% 3.15/3.51 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger C) B)) (@ _let_1 C))))))
% 3.15/3.51 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.divide_divide_nat C) B)) (@ _let_1 C))))))
% 3.15/3.51 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.divide_divide_int C) B)) (@ _let_1 C))))))
% 3.15/3.51 (assert (forall ((B tptp.code_natural) (A tptp.code_natural) (C tptp.code_natural)) (let ((_let_1 (@ tptp.dvd_dvd_Code_natural A))) (=> (@ (@ tptp.dvd_dvd_Code_natural B) tptp.one_one_Code_natural) (= (@ _let_1 (@ (@ tptp.divide5121882707175180666atural C) B)) (@ _let_1 C))))))
% 3.15/3.51 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer A) C)))))
% 3.15/3.51 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat A) C)))))
% 3.15/3.51 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A) B)) C) (@ (@ tptp.dvd_dvd_int A) C)))))
% 3.15/3.51 (assert (forall ((B tptp.code_natural) (A tptp.code_natural) (C tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural B) tptp.one_one_Code_natural) (= (@ (@ tptp.dvd_dvd_Code_natural (@ (@ tptp.divide5121882707175180666atural A) B)) C) (@ (@ tptp.dvd_dvd_Code_natural A) C)))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (= (@ (@ tptp.divide6298287555418463151nteger B) A) (@ (@ tptp.divide6298287555418463151nteger C) A)) (= B C)))))
% 3.15/3.51 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat B) A) (@ (@ tptp.divide_divide_nat C) A)) (= B C)))))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int B) A) (@ (@ tptp.divide_divide_int C) A)) (= B C)))))
% 3.15/3.51 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural A) tptp.one_one_Code_natural) (= (= (@ (@ tptp.divide5121882707175180666atural B) A) (@ (@ tptp.divide5121882707175180666atural C) A)) (= B C)))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo364778990260209775nteger A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (and (=> _let_3 (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not _let_3) (= _let_2 tptp.one_one_Code_integer))))))))
% 3.15/3.51 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat _let_1) A))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 tptp.one_one_nat))))))))
% 3.15/3.51 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_int _let_1) A))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 tptp.one_one_int))))))))
% 3.15/3.51 (assert (forall ((A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo8411746178871703098atural A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_Code_natural _let_1) A))) (and (=> _let_3 (= _let_2 tptp.zero_z2226904508553997617atural)) (=> (not _let_3) (= _let_2 tptp.one_one_Code_natural))))))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo364778990260209775nteger A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (=> (=> _let_3 (not (= _let_2 tptp.zero_z3403309356797280102nteger))) (not (=> (not _let_3) (not (= _let_2 tptp.one_one_Code_integer))))))))))
% 3.15/3.51 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat _let_1) A))) (=> (=> _let_3 (not (= _let_2 tptp.zero_zero_nat))) (not (=> (not _let_3) (not (= _let_2 tptp.one_one_nat))))))))))
% 3.15/3.51 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_int _let_1) A))) (=> (=> _let_3 (not (= _let_2 tptp.zero_zero_int))) (not (=> (not _let_3) (not (= _let_2 tptp.one_one_int))))))))))
% 3.15/3.51 (assert (forall ((A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo8411746178871703098atural A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_Code_natural _let_1) A))) (=> (=> _let_3 (not (= _let_2 tptp.zero_z2226904508553997617atural))) (not (=> (not _let_3) (not (= _let_2 tptp.one_one_Code_natural))))))))))
% 3.15/3.51 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B))) (@ (@ tptp.modulo364778990260209775nteger A) B))) C) (@ (@ tptp.plus_p5714425477246183910nteger A) C))))
% 3.15/3.51 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B))) (@ (@ tptp.modulo_modulo_nat A) B))) C) (@ (@ tptp.plus_plus_nat A) C))))
% 3.15/3.51 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B))) (@ (@ tptp.modulo_modulo_int A) B))) C) (@ (@ tptp.plus_plus_int A) C))))
% 3.15/3.51 (assert (forall ((B tptp.code_natural) (A tptp.code_natural) (C tptp.code_natural)) (= (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural B) (@ (@ tptp.divide5121882707175180666atural A) B))) (@ (@ tptp.modulo8411746178871703098atural A) B))) C) (@ (@ tptp.plus_p4538020629002901425atural A) C))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) (@ (@ tptp.modulo364778990260209775nteger A) B))) C) (@ (@ tptp.plus_p5714425477246183910nteger A) C))))
% 3.15/3.51 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) (@ (@ tptp.modulo_modulo_nat A) B))) C) (@ (@ tptp.plus_plus_nat A) C))))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) (@ (@ tptp.modulo_modulo_int A) B))) C) (@ (@ tptp.plus_plus_int A) C))))
% 3.15/3.51 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (= (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural A) B)) B)) (@ (@ tptp.modulo8411746178871703098atural A) B))) C) (@ (@ tptp.plus_p4538020629002901425atural A) C))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= A (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 3.15/3.51 (assert (forall ((A tptp.nat) (B tptp.nat)) (= A (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) (@ (@ tptp.modulo_modulo_nat A) B)))))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) (@ (@ tptp.modulo_modulo_int A) B)))))
% 3.15/3.51 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= A (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural A) B)) B)) (@ (@ tptp.modulo8411746178871703098atural A) B)))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) (@ (@ tptp.modulo364778990260209775nteger A) B)) A)))
% 3.15/3.51 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) (@ (@ tptp.modulo_modulo_nat A) B)) A)))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) (@ (@ tptp.modulo_modulo_int A) B)) A)))
% 3.15/3.51 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural A) B)) B)) (@ (@ tptp.modulo8411746178871703098atural A) B)) A)))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) A)))
% 3.15/3.51 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) A)))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) A)))
% 3.15/3.51 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.modulo8411746178871703098atural A) B)) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural A) B)) B)) A)))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B))) A)))
% 3.15/3.51 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B))) A)))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B))) A)))
% 3.15/3.51 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.modulo8411746178871703098atural A) B)) (@ (@ tptp.times_2397367101498566445atural B) (@ (@ tptp.divide5121882707175180666atural A) B))) A)))
% 3.15/3.51 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B))) (@ (@ tptp.modulo364778990260209775nteger A) B)) A)))
% 3.15/3.51 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B))) (@ (@ tptp.modulo_modulo_nat A) B)) A)))
% 3.15/3.51 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B))) (@ (@ tptp.modulo_modulo_int A) B)) A)))
% 3.15/3.51 (assert (forall ((B tptp.code_natural) (A tptp.code_natural)) (= (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural B) (@ (@ tptp.divide5121882707175180666atural A) B))) (@ (@ tptp.modulo8411746178871703098atural A) B)) A)))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B) C))) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger B) C))) C))))))
% 3.15/3.51 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.divide_divide_nat B) C))) (@ (@ tptp.divide_divide_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat B) C))) C))))))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.divide_divide_int (@ _let_1 B)) C) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.divide_divide_int B) C))) (@ (@ tptp.divide_divide_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B) C))) C))))))
% 3.15/3.51 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural A))) (= (@ (@ tptp.divide5121882707175180666atural (@ _let_1 B)) C) (@ (@ tptp.plus_p4538020629002901425atural (@ _let_1 (@ (@ tptp.divide5121882707175180666atural B) C))) (@ (@ tptp.divide5121882707175180666atural (@ _let_1 (@ (@ tptp.modulo8411746178871703098atural B) C))) C))))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 3.15/3.51 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) (@ (@ tptp.modulo_modulo_nat A) B))))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) (@ (@ tptp.modulo_modulo_int A) B))))
% 3.15/3.51 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.minus_7197305767214868737atural A) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural A) B)) B)) (@ (@ tptp.modulo8411746178871703098atural A) B))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B))))
% 3.15/3.51 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B))))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B))))
% 3.15/3.51 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.minus_7197305767214868737atural A) (@ (@ tptp.modulo8411746178871703098atural A) B)) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural A) B)) B))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B)))))
% 3.15/3.51 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B)))))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B)))))
% 3.15/3.51 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.minus_7197305767214868737atural A) (@ (@ tptp.modulo8411746178871703098atural A) B)) (@ (@ tptp.times_2397367101498566445atural B) (@ (@ tptp.divide5121882707175180666atural A) B)))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B))) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 3.15/3.51 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B))) (@ (@ tptp.modulo_modulo_nat A) B))))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B))) (@ (@ tptp.modulo_modulo_int A) B))))
% 3.15/3.51 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.minus_7197305767214868737atural A) (@ (@ tptp.times_2397367101498566445atural B) (@ (@ tptp.divide5121882707175180666atural A) B))) (@ (@ tptp.modulo8411746178871703098atural A) B))))
% 3.15/3.51 (assert (forall ((P2 (-> tptp.rat Bool)) (L tptp.rat)) (= (exists ((X2 tptp.rat)) (@ P2 (@ (@ tptp.times_times_rat L) X2))) (exists ((X2 tptp.rat)) (and (@ (@ tptp.dvd_dvd_rat L) (@ (@ tptp.plus_plus_rat X2) tptp.zero_zero_rat)) (@ P2 X2))))))
% 3.15/3.51 (assert (forall ((P2 (-> tptp.nat Bool)) (L tptp.nat)) (= (exists ((X2 tptp.nat)) (@ P2 (@ (@ tptp.times_times_nat L) X2))) (exists ((X2 tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat L) (@ (@ tptp.plus_plus_nat X2) tptp.zero_zero_nat)) (@ P2 X2))))))
% 3.15/3.51 (assert (forall ((P2 (-> tptp.int Bool)) (L tptp.int)) (= (exists ((X2 tptp.int)) (@ P2 (@ (@ tptp.times_times_int L) X2))) (exists ((X2 tptp.int)) (and (@ (@ tptp.dvd_dvd_int L) (@ (@ tptp.plus_plus_int X2) tptp.zero_zero_int)) (@ P2 X2))))))
% 3.15/3.51 (assert (forall ((P2 (-> tptp.code_integer Bool)) (L tptp.code_integer)) (= (exists ((X2 tptp.code_integer)) (@ P2 (@ (@ tptp.times_3573771949741848930nteger L) X2))) (exists ((X2 tptp.code_integer)) (and (@ (@ tptp.dvd_dvd_Code_integer L) (@ (@ tptp.plus_p5714425477246183910nteger X2) tptp.zero_z3403309356797280102nteger)) (@ P2 X2))))))
% 3.15/3.51 (assert (forall ((P2 (-> tptp.code_natural Bool)) (L tptp.code_natural)) (= (exists ((X2 tptp.code_natural)) (@ P2 (@ (@ tptp.times_2397367101498566445atural L) X2))) (exists ((X2 tptp.code_natural)) (and (@ (@ tptp.dvd_dvd_Code_natural L) (@ (@ tptp.plus_p4538020629002901425atural X2) tptp.zero_z2226904508553997617atural)) (@ P2 X2))))))
% 3.15/3.51 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (not (=> (not (= A tptp.zero_zero_nat)) (forall ((C3 tptp.nat)) (not (= B (@ (@ tptp.times_times_nat A) C3)))))))))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (not (=> (not (= A tptp.zero_zero_int)) (forall ((C3 tptp.int)) (not (= B (@ (@ tptp.times_times_int A) C3)))))))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (not (=> (not (= A tptp.zero_z3403309356797280102nteger)) (forall ((C3 tptp.code_integer)) (not (= B (@ (@ tptp.times_3573771949741848930nteger A) C3)))))))))
% 3.15/3.51 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural A) tptp.one_one_Code_natural) (not (=> (not (= A tptp.zero_z2226904508553997617atural)) (forall ((C3 tptp.code_natural)) (not (= B (@ (@ tptp.times_2397367101498566445atural A) C3)))))))))
% 3.15/3.51 (assert (forall ((D2 tptp.rat) (D tptp.rat) (T3 tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D2) D) (forall ((X4 tptp.rat) (K3 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D2))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat X4) T3)) (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.times_times_rat K3) D))) T3))))))))
% 3.15/3.51 (assert (forall ((D2 tptp.int) (D tptp.int) (T3 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D) (forall ((X4 tptp.int) (K3 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int X4) T3)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K3) D))) T3))))))))
% 3.15/3.51 (assert (forall ((D2 tptp.code_integer) (D tptp.code_integer) (T3 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer D2) D) (forall ((X4 tptp.code_integer) (K3 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer D2))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger X4) T3)) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger X4) (@ (@ tptp.times_3573771949741848930nteger K3) D))) T3))))))))
% 3.15/3.51 (assert (forall ((D2 tptp.rat) (D tptp.rat) (T3 tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D2) D) (forall ((X4 tptp.rat) (K3 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D2))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_rat X4) T3))) (not (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.times_times_rat K3) D))) T3)))))))))
% 3.15/3.51 (assert (forall ((D2 tptp.int) (D tptp.int) (T3 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D) (forall ((X4 tptp.int) (K3 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D2))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_int X4) T3))) (not (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K3) D))) T3)))))))))
% 3.15/3.51 (assert (forall ((D2 tptp.code_integer) (D tptp.code_integer) (T3 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer D2) D) (forall ((X4 tptp.code_integer) (K3 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer D2))) (= (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger X4) T3))) (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger X4) (@ (@ tptp.times_3573771949741848930nteger K3) D))) T3)))))))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (= (@ (@ tptp.divide6298287555418463151nteger B) A) C) (= B (@ (@ tptp.times_3573771949741848930nteger C) A)))))))
% 3.15/3.51 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (= (@ (@ tptp.divide_divide_nat B) A) C) (= B (@ (@ tptp.times_times_nat C) A)))))))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (= (@ (@ tptp.divide_divide_int B) A) C) (= B (@ (@ tptp.times_times_int C) A)))))))
% 3.15/3.51 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (=> (not (= A tptp.zero_z2226904508553997617atural)) (=> (@ (@ tptp.dvd_dvd_Code_natural A) B) (= (= (@ (@ tptp.divide5121882707175180666atural B) A) C) (= B (@ (@ tptp.times_2397367101498566445atural C) A)))))))
% 3.15/3.51 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger C) B)))))))
% 3.15/3.51 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat C) B)))))))
% 3.15/3.51 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A) B)) C) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int C) B)))))))
% 3.15/3.51 (assert (forall ((B tptp.code_natural) (A tptp.code_natural) (C tptp.code_natural)) (=> (not (= B tptp.zero_z2226904508553997617atural)) (=> (@ (@ tptp.dvd_dvd_Code_natural B) A) (= (@ (@ tptp.dvd_dvd_Code_natural (@ (@ tptp.divide5121882707175180666atural A) B)) C) (@ (@ tptp.dvd_dvd_Code_natural A) (@ (@ tptp.times_2397367101498566445atural C) B)))))))
% 3.15/3.51 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.divide6298287555418463151nteger B) C)) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) B))))))
% 3.15/3.51 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.divide_divide_nat B) C)) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) B))))))
% 3.15/3.51 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (not (= C tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.divide_divide_int B) C)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) B))))))
% 3.15/3.51 (assert (forall ((C tptp.code_natural) (B tptp.code_natural) (A tptp.code_natural)) (=> (not (= C tptp.zero_z2226904508553997617atural)) (=> (@ (@ tptp.dvd_dvd_Code_natural C) B) (= (@ (@ tptp.dvd_dvd_Code_natural A) (@ (@ tptp.divide5121882707175180666atural B) C)) (@ (@ tptp.dvd_dvd_Code_natural (@ (@ tptp.times_2397367101498566445atural A) C)) B))))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (=> (@ (@ tptp.dvd_dvd_Code_integer C) D2) (= (= (@ (@ tptp.divide6298287555418463151nteger B) A) (@ (@ tptp.divide6298287555418463151nteger D2) C)) (= (@ (@ tptp.times_3573771949741848930nteger B) C) (@ (@ tptp.times_3573771949741848930nteger A) D2)))))))))
% 3.15/3.51 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat) (D2 tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (not (= C tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (=> (@ (@ tptp.dvd_dvd_nat C) D2) (= (= (@ (@ tptp.divide_divide_nat B) A) (@ (@ tptp.divide_divide_nat D2) C)) (= (@ (@ tptp.times_times_nat B) C) (@ (@ tptp.times_times_nat A) D2)))))))))
% 3.15/3.51 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (not (= C tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (=> (@ (@ tptp.dvd_dvd_int C) D2) (= (= (@ (@ tptp.divide_divide_int B) A) (@ (@ tptp.divide_divide_int D2) C)) (= (@ (@ tptp.times_times_int B) C) (@ (@ tptp.times_times_int A) D2)))))))))
% 3.15/3.51 (assert (forall ((A tptp.code_natural) (C tptp.code_natural) (B tptp.code_natural) (D2 tptp.code_natural)) (=> (not (= A tptp.zero_z2226904508553997617atural)) (=> (not (= C tptp.zero_z2226904508553997617atural)) (=> (@ (@ tptp.dvd_dvd_Code_natural A) B) (=> (@ (@ tptp.dvd_dvd_Code_natural C) D2) (= (= (@ (@ tptp.divide5121882707175180666atural B) A) (@ (@ tptp.divide5121882707175180666atural D2) C)) (= (@ (@ tptp.times_2397367101498566445atural B) C) (@ (@ tptp.times_2397367101498566445atural A) D2)))))))))
% 3.15/3.51 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (= (@ (@ tptp.divide6298287555418463151nteger A) B) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger)))))
% 3.15/3.51 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat A) B) tptp.zero_zero_nat) (= A tptp.zero_zero_nat)))))
% 3.15/3.51 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int A) B) tptp.zero_zero_int) (= A tptp.zero_zero_int)))))
% 3.15/3.51 (assert (forall ((B tptp.code_natural) (A tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural B) tptp.one_one_Code_natural) (= (= (@ (@ tptp.divide5121882707175180666atural A) B) tptp.zero_z2226904508553997617atural) (= A tptp.zero_z2226904508553997617atural)))))
% 3.15/3.51 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer C) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C)))))))
% 3.15/3.51 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat C) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C)))))))
% 3.15/3.51 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int C) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C)))))))
% 3.15/3.51 (assert (forall ((B tptp.code_natural) (C tptp.code_natural) (A tptp.code_natural)) (let ((_let_1 (@ tptp.divide5121882707175180666atural A))) (=> (@ (@ tptp.dvd_dvd_Code_natural B) tptp.one_one_Code_natural) (=> (@ (@ tptp.dvd_dvd_Code_natural C) tptp.one_one_Code_natural) (= (@ _let_1 (@ (@ tptp.times_2397367101498566445atural B) C)) (@ (@ tptp.divide5121882707175180666atural (@ _let_1 B)) C)))))))
% 3.15/3.51 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C))))))
% 3.15/3.51 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C))))))
% 3.15/3.51 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int C) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.divide_divide_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C))))))
% 3.15/3.51 (assert (forall ((C tptp.code_natural) (A tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural A))) (=> (@ (@ tptp.dvd_dvd_Code_natural C) tptp.one_one_Code_natural) (= (@ _let_1 (@ (@ tptp.divide5121882707175180666atural B) C)) (@ (@ tptp.divide5121882707175180666atural (@ _let_1 B)) C))))))
% 3.15/3.51 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) C) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) B)))))
% 3.15/3.51 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) C) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C)) B)))))
% 3.15/3.51 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) C) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C)) B)))))
% 3.15/3.51 (assert (forall ((B tptp.code_natural) (A tptp.code_natural) (C tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural B) tptp.one_one_Code_natural) (= (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural A) B)) C) (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.times_2397367101498566445atural A) C)) B)))))
% 3.15/3.51 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C)))))))
% 3.15/3.51 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C)))))))
% 3.15/3.51 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int C) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C)))))))
% 3.15/3.51 (assert (forall ((C tptp.code_natural) (B tptp.code_natural) (A tptp.code_natural)) (let ((_let_1 (@ tptp.divide5121882707175180666atural A))) (=> (@ (@ tptp.dvd_dvd_Code_natural C) tptp.one_one_Code_natural) (=> (@ (@ tptp.dvd_dvd_Code_natural B) A) (= (@ _let_1 (@ (@ tptp.times_2397367101498566445atural B) C)) (@ (@ tptp.divide5121882707175180666atural (@ _let_1 B)) C)))))))
% 3.15/3.51 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (= A (@ (@ tptp.divide6298287555418463151nteger C) B)) (= (@ (@ tptp.times_3573771949741848930nteger A) B) C)))))
% 3.15/3.51 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (= A (@ (@ tptp.divide_divide_nat C) B)) (= (@ (@ tptp.times_times_nat A) B) C)))))
% 3.15/3.51 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (= A (@ (@ tptp.divide_divide_int C) B)) (= (@ (@ tptp.times_times_int A) B) C)))))
% 3.15/3.51 (assert (forall ((B tptp.code_natural) (A tptp.code_natural) (C tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural B) tptp.one_one_Code_natural) (= (= A (@ (@ tptp.divide5121882707175180666atural C) B)) (= (@ (@ tptp.times_2397367101498566445atural A) B) C)))))
% 3.15/3.51 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (= (@ (@ tptp.divide6298287555418463151nteger A) B) C) (= A (@ (@ tptp.times_3573771949741848930nteger C) B))))))
% 3.15/3.51 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat A) B) C) (= A (@ (@ tptp.times_times_nat C) B))))))
% 3.15/3.51 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int A) B) C) (= A (@ (@ tptp.times_times_int C) B))))))
% 3.15/3.51 (assert (forall ((B tptp.code_natural) (A tptp.code_natural) (C tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural B) tptp.one_one_Code_natural) (= (= (@ (@ tptp.divide5121882707175180666atural A) B) C) (= A (@ (@ tptp.times_2397367101498566445atural C) B))))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N)) tptp.one_one_Code_integer) (or (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= N tptp.zero_zero_nat)))))
% 3.15/3.51 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int A) N)) tptp.one_one_int) (or (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= N tptp.zero_zero_nat)))))
% 3.15/3.51 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat A) N)) tptp.one_one_nat) (or (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= N tptp.zero_zero_nat)))))
% 3.15/3.51 (assert (forall ((I2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I2))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M2)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) I2) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (not (=> (not (= A tptp.zero_z3403309356797280102nteger)) (forall ((B5 tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer))) (=> (not (= B5 tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B5) tptp.one_one_Code_integer) (=> (= (@ _let_1 A) B5) (=> (= (@ _let_1 B5) A) (=> (= (@ (@ tptp.times_3573771949741848930nteger A) B5) tptp.one_one_Code_integer) (not (= (@ (@ tptp.divide6298287555418463151nteger C) A) (@ (@ tptp.times_3573771949741848930nteger C) B5)))))))))))))))
% 3.15/3.51 (assert (forall ((A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (not (=> (not (= A tptp.zero_zero_nat)) (forall ((B5 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat tptp.one_one_nat))) (=> (not (= B5 tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B5) tptp.one_one_nat) (=> (= (@ _let_1 A) B5) (=> (= (@ _let_1 B5) A) (=> (= (@ (@ tptp.times_times_nat A) B5) tptp.one_one_nat) (not (= (@ (@ tptp.divide_divide_nat C) A) (@ (@ tptp.times_times_nat C) B5)))))))))))))))
% 3.15/3.51 (assert (forall ((A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (not (=> (not (= A tptp.zero_zero_int)) (forall ((B5 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int tptp.one_one_int))) (=> (not (= B5 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B5) tptp.one_one_int) (=> (= (@ _let_1 A) B5) (=> (= (@ _let_1 B5) A) (=> (= (@ (@ tptp.times_times_int A) B5) tptp.one_one_int) (not (= (@ (@ tptp.divide_divide_int C) A) (@ (@ tptp.times_times_int C) B5)))))))))))))))
% 3.15/3.51 (assert (forall ((A tptp.code_natural) (C tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural A) tptp.one_one_Code_natural) (not (=> (not (= A tptp.zero_z2226904508553997617atural)) (forall ((B5 tptp.code_natural)) (let ((_let_1 (@ tptp.divide5121882707175180666atural tptp.one_one_Code_natural))) (=> (not (= B5 tptp.zero_z2226904508553997617atural)) (=> (@ (@ tptp.dvd_dvd_Code_natural B5) tptp.one_one_Code_natural) (=> (= (@ _let_1 A) B5) (=> (= (@ _let_1 B5) A) (=> (= (@ (@ tptp.times_2397367101498566445atural A) B5) tptp.one_one_Code_natural) (not (= (@ (@ tptp.divide5121882707175180666atural C) A) (@ (@ tptp.times_2397367101498566445atural C) B5)))))))))))))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ (@ tptp.times_3573771949741848930nteger A) B)) (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) B))))))
% 3.15/3.51 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.divide_divide_nat A) (@ (@ tptp.times_times_nat A) B)) (@ (@ tptp.divide_divide_nat tptp.one_one_nat) B))))))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.divide_divide_int A) (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.divide_divide_int tptp.one_one_int) B))))))
% 3.15/3.51 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (not (= A tptp.zero_z2226904508553997617atural)) (=> (@ (@ tptp.dvd_dvd_Code_natural B) tptp.one_one_Code_natural) (= (@ (@ tptp.divide5121882707175180666atural A) (@ (@ tptp.times_2397367101498566445atural A) B)) (@ (@ tptp.divide5121882707175180666atural tptp.one_one_Code_natural) B))))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ (@ tptp.times_3573771949741848930nteger B) A)) (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) B))))))
% 3.15/3.51 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.divide_divide_nat A) (@ (@ tptp.times_times_nat B) A)) (@ (@ tptp.divide_divide_nat tptp.one_one_nat) B))))))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.divide_divide_int A) (@ (@ tptp.times_times_int B) A)) (@ (@ tptp.divide_divide_int tptp.one_one_int) B))))))
% 3.15/3.51 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (not (= A tptp.zero_z2226904508553997617atural)) (=> (@ (@ tptp.dvd_dvd_Code_natural B) tptp.one_one_Code_natural) (= (@ (@ tptp.divide5121882707175180666atural A) (@ (@ tptp.times_2397367101498566445atural B) A)) (@ (@ tptp.divide5121882707175180666atural tptp.one_one_Code_natural) B))))))
% 3.15/3.51 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A) (not (forall ((B5 tptp.nat)) (not (= A (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B5))))))))
% 3.15/3.51 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A) (not (forall ((B5 tptp.int)) (not (= A (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B5))))))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A) (not (forall ((B5 tptp.code_integer)) (not (= A (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B5))))))))
% 3.15/3.51 (assert (forall ((A tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) A) (not (forall ((B5 tptp.code_natural)) (not (= A (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) B5))))))))
% 3.15/3.51 (assert (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat)))
% 3.15/3.51 (assert (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int)))
% 3.15/3.51 (assert (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer)))
% 3.15/3.51 (assert (not (@ (@ tptp.dvd_dvd_Code_natural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) tptp.one_one_Code_natural)))
% 3.15/3.51 (assert (forall ((X tptp.code_integer) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X))) (=> (not (= X tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M2)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_Code_integer X) tptp.one_one_Code_integer) (@ (@ tptp.ord_less_eq_nat M2) N)))))))
% 3.15/3.51 (assert (forall ((X tptp.code_natural) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_7079662738309270450atural X))) (=> (not (= X tptp.zero_z2226904508553997617atural)) (= (@ (@ tptp.dvd_dvd_Code_natural (@ _let_1 M2)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_Code_natural X) tptp.one_one_Code_natural) (@ (@ tptp.ord_less_eq_nat M2) N)))))))
% 3.15/3.51 (assert (forall ((X tptp.int) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (=> (not (= X tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 M2)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_int X) tptp.one_one_int) (@ (@ tptp.ord_less_eq_nat M2) N)))))))
% 3.15/3.51 (assert (forall ((X tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat X))) (=> (not (= X tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M2)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_nat X) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat M2) N)))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (X tptp.code_integer)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X tptp.one_one_Code_integer)) (@ (@ tptp.dvd_dvd_Code_integer X) (@ (@ tptp.power_8256067586552552935nteger X) N)))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (X tptp.rat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X tptp.one_one_rat)) (@ (@ tptp.dvd_dvd_rat X) (@ (@ tptp.power_power_rat X) N)))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (X tptp.int)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X tptp.one_one_int)) (@ (@ tptp.dvd_dvd_int X) (@ (@ tptp.power_power_int X) N)))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (X tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X tptp.one_one_nat)) (@ (@ tptp.dvd_dvd_nat X) (@ (@ tptp.power_power_nat X) N)))))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat N) M2)) M2) (= N tptp.one_one_nat)))))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat M2) N)) M2) (= N tptp.one_one_nat)))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2793503036327961859nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se2793503036327961859nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1617098188084679374atural (@ tptp.suc N)) A) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.modulo8411746178871703098atural A) _let_1)) (@ (@ tptp.times_2397367101498566445atural _let_1) (@ (@ tptp.bit_se1617098188084679374atural N) (@ (@ tptp.divide5121882707175180666atural A) _let_1))))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7882103937844011126it_nat (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se7882103937844011126it_nat N) (@ (@ tptp.divide_divide_nat A) _let_1))))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7879613467334960850it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se7879613467334960850it_int N) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se8260200283734997820nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se8260200283734997820nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4205575877204974255it_nat (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se4205575877204974255it_nat N) (@ (@ tptp.divide_divide_nat A) _let_1))))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7083795435491715335atural (@ tptp.suc N)) A) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.modulo8411746178871703098atural A) _let_1)) (@ (@ tptp.times_2397367101498566445atural _let_1) (@ (@ tptp.bit_se7083795435491715335atural N) (@ (@ tptp.divide5121882707175180666atural A) _let_1))))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4203085406695923979it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se4203085406695923979it_int N) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 3.15/3.51 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger B))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) C))) (@ _let_1 B))))))))
% 3.15/3.51 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat A) B)) C))) (@ _let_1 B))))))))
% 3.15/3.51 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) B)) C))) (@ _let_1 B))))))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1)) A)))))
% 3.15/3.51 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1)) A)))))
% 3.15/3.51 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (= (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1)) A)))))
% 3.15/3.51 (assert (forall ((A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_Code_natural _let_1) A) (= (@ (@ tptp.times_2397367101498566445atural _let_1) (@ (@ tptp.divide5121882707175180666atural A) _let_1)) A)))))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M2) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.times_times_nat M2) N))) M2) tptp.one_one_nat))))
% 3.15/3.51 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger _let_2) B) (= _let_2 (@ _let_1 B))))))))
% 3.15/3.51 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat _let_2) B) (= _let_2 (@ _let_1 B))))))))
% 3.15/3.51 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int _let_2) B) (= _let_2 (@ _let_1 B))))))))
% 3.15/3.51 (assert (forall ((A tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) (not (forall ((B5 tptp.nat)) (not (= A (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B5)) tptp.one_one_nat))))))))
% 3.15/3.51 (assert (forall ((A tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) (not (forall ((B5 tptp.int)) (not (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B5)) tptp.one_one_int))))))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer)) (=> (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)) (not (forall ((B5 tptp.code_integer)) (not (= A (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B5)) tptp.one_one_Code_integer))))))))
% 3.15/3.51 (assert (forall ((A tptp.code_natural)) (=> (not (@ (@ tptp.dvd_dvd_Code_natural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) A)) (not (forall ((B5 tptp.code_natural)) (not (= A (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) B5)) tptp.one_one_Code_natural))))))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 tptp.one_one_int)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (let ((_let_2 (@ (@ tptp.power_power_rat _let_1) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 tptp.one_one_rat)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 tptp.one_one_Code_integer)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 3.15/3.51 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_3)) B) (= (@ _let_2 (@ _let_1 _let_3)) (@ _let_1 B)))))))))
% 3.15/3.51 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (let ((_let_2 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat A) _let_3)) B) (= (@ _let_2 (@ _let_1 _let_3)) (@ _let_1 B)))))))))
% 3.15/3.51 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int A) _let_3)) B) (= (@ _let_2 (@ _let_1 _let_3)) (@ _let_1 B)))))))))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) _let_2)) (@ _let_1 N)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M2)))) _let_2)))))))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) _let_2)) (@ _let_1 N)) (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M2)))) _let_2)))))))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) _let_2)) (@ _let_1 N)) (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M2)))) _let_2)))))))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N tptp.nat) (A tptp.code_natural)) (let ((_let_1 (@ tptp.power_7079662738309270450atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M2))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.times_2397367101498566445atural A) _let_2)) (@ _let_1 N)) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.modulo8411746178871703098atural A) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M2)))) _let_2)))))))
% 3.15/3.51 (assert (forall ((M2 tptp.code_integer) (X tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger X))) (let ((_let_2 (@ _let_1 M2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) M2)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) M2) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_p5714425477246183910nteger _let_2) M2))))))))))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat X))) (let ((_let_2 (@ _let_1 M2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_nat _let_2) M2))))))))))
% 3.15/3.51 (assert (forall ((M2 tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int X))) (let ((_let_2 (@ _let_1 M2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) M2)))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_int _let_2) M2))))))))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) _let_2) (= (@ (@ tptp.minus_8373710615458151222nteger _let_2) B) (@ _let_1 B)))))))))
% 3.15/3.51 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat B) _let_2) (= (@ (@ tptp.minus_minus_nat _let_2) B) (@ _let_1 B)))))))))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int B) _let_2) (= (@ (@ tptp.minus_minus_int _let_2) B) (@ _let_1 B)))))))))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger _let_1))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.minus_8373710615458151222nteger (@ _let_2 M2)) tptp.one_one_Code_integer)) (@ _let_2 N))) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (= (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ _let_2 M2)) tptp.one_one_nat)) (@ _let_2 N))) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int _let_1))) (= (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ _let_2 M2)) tptp.one_one_int)) (@ _let_2 N))) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_7079662738309270450atural _let_1))) (= (@ (@ tptp.dvd_dvd_Code_natural _let_1) (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.minus_7197305767214868737atural (@ _let_2 M2)) tptp.one_one_Code_natural)) (@ _let_2 N))) (@ (@ tptp.ord_less_eq_nat M2) N))))))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger _let_1))) (let ((_let_3 (@ _let_2 N))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.minus_8373710615458151222nteger (@ _let_2 M2)) tptp.one_one_Code_integer)) _let_3)) (or (= _let_3 tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_less_eq_nat M2) N))))))))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (let ((_let_3 (@ _let_2 N))) (= (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ _let_2 M2)) tptp.one_one_nat)) _let_3)) (or (= _let_3 tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M2) N))))))))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int _let_1))) (let ((_let_3 (@ _let_2 N))) (= (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ _let_2 M2)) tptp.one_one_int)) _let_3)) (or (= _let_3 tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_nat M2) N))))))))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_7079662738309270450atural _let_1))) (let ((_let_3 (@ _let_2 N))) (= (@ (@ tptp.dvd_dvd_Code_natural _let_1) (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.minus_7197305767214868737atural (@ _let_2 M2)) tptp.one_one_Code_natural)) _let_3)) (or (= _let_3 tptp.zero_z2226904508553997617atural) (@ (@ tptp.ord_less_eq_nat M2) N))))))))
% 3.15/3.51 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int W) (@ (@ tptp.plus_plus_int Z) tptp.one_one_int)) (@ (@ tptp.ord_less_eq_int W) Z))))
% 3.15/3.51 (assert (forall ((A3 tptp.nat) (B3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A3) B3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A3) N)) (@ (@ (@ tptp.if_nat (= (@ (@ tptp.modulo_modulo_nat B3) N) tptp.zero_zero_nat)) tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.divide_divide_nat B3) N))))))
% 3.15/3.51 (assert (forall ((A3 tptp.int) (B3 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int A3) B3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A3) N)) (@ (@ (@ tptp.if_int (= (@ (@ tptp.modulo_modulo_int B3) N) tptp.zero_zero_int)) tptp.one_one_int) tptp.zero_zero_int))) (@ (@ tptp.divide_divide_int B3) N))))))
% 3.15/3.51 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int W) (@ (@ tptp.minus_minus_int Z) tptp.one_one_int)) (@ (@ tptp.ord_less_int W) Z))))
% 3.15/3.51 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int tptp.one) N))))))
% 3.15/3.51 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int tptp.one) N))))))
% 3.15/3.51 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int tptp.one) N))))))))
% 3.15/3.51 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) _let_1) (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int tptp.one) N)))))))
% 3.15/3.51 (assert (forall ((I2 tptp.int) (K tptp.int) (P2 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int I2) K) (=> (@ P2 (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_int I3) K) (=> (@ P2 I3) (@ P2 (@ (@ tptp.minus_minus_int I3) tptp.one_one_int))))) (@ P2 I2))))))
% 3.15/3.51 (assert (forall ((I2 tptp.int) (K tptp.int) (P2 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int I2) K) (=> (@ P2 K) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I3) K) (=> (@ P2 I3) (@ P2 (@ (@ tptp.minus_minus_int I3) tptp.one_one_int))))) (@ P2 I2))))))
% 3.15/3.51 (assert (forall ((W tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int W))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z) tptp.one_one_int)) (or (@ _let_1 Z) (= W Z))))))
% 3.15/3.51 (assert (forall ((K tptp.int) (I2 tptp.int) (P2 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int K) I2) (=> (@ P2 (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_int K) I3) (=> (@ P2 I3) (@ P2 (@ (@ tptp.plus_plus_int I3) tptp.one_one_int))))) (@ P2 I2))))))
% 3.15/3.51 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 3.15/3.51 (assert (forall ((M2 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M2) (= (= (@ (@ tptp.times_times_int M2) N) tptp.one_one_int) (and (= M2 tptp.one_one_int) (= N tptp.one_one_int))))))
% 3.15/3.51 (assert (= tptp.sgn_sgn_int (lambda ((I4 tptp.int)) (@ (@ (@ tptp.if_int (= I4 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) I4)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 3.15/3.51 (assert (forall ((Z tptp.int)) (not (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)) Z) tptp.zero_zero_int))))
% 3.15/3.51 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)) Z)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Z) tptp.zero_zero_int))))
% 3.15/3.51 (assert (forall ((K tptp.int) (I2 tptp.int) (P2 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int K) I2) (=> (@ P2 K) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) I3) (=> (@ P2 I3) (@ P2 (@ (@ tptp.plus_plus_int I3) tptp.one_one_int))))) (@ P2 I2))))))
% 3.15/3.51 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W) tptp.one_one_int)) Z) (@ (@ tptp.ord_less_int W) Z))))
% 3.15/3.51 (assert (forall ((W tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_int W) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W) tptp.one_one_int)) Z))))
% 3.15/3.51 (assert (forall ((P2 (-> tptp.int Bool)) (K tptp.int) (I2 tptp.int)) (=> (@ P2 K) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) I3) (=> (@ P2 I3) (@ P2 (@ (@ tptp.plus_plus_int I3) tptp.one_one_int))))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I3) K) (=> (@ P2 I3) (@ P2 (@ (@ tptp.minus_minus_int I3) tptp.one_one_int))))) (@ P2 I2))))))
% 3.15/3.51 (assert (forall ((M2 tptp.int) (N tptp.int)) (=> (= (@ (@ tptp.times_times_int M2) N) tptp.one_one_int) (or (= M2 tptp.one_one_int) (= M2 (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 3.15/3.51 (assert (forall ((M2 tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (= (@ (@ tptp.times_times_int M2) N) tptp.one_one_int) (or (and (= M2 tptp.one_one_int) (= N tptp.one_one_int)) (and (= M2 _let_1) (= N _let_1)))))))
% 3.15/3.51 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1345352211410354436nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se1345352211410354436nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se168947363167071951atural (@ tptp.suc N)) A) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.modulo8411746178871703098atural A) _let_1)) (@ (@ tptp.times_2397367101498566445atural _let_1) (@ (@ tptp.bit_se168947363167071951atural N) (@ (@ tptp.divide5121882707175180666atural A) _let_1))))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2161824704523386999it_nat (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se2161824704523386999it_nat N) (@ (@ tptp.divide_divide_nat A) _let_1))))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2159334234014336723it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se2159334234014336723it_int N) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 3.15/3.51 (assert (= tptp.bit_ri6519982836138164636nteger (lambda ((N3 tptp.nat) (A2 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo364778990260209775nteger A2) _let_1))) (@ (@ (@ tptp.if_Code_integer (= N3 tptp.zero_zero_nat)) (@ tptp.uminus1351360451143612070nteger _let_2)) (@ (@ tptp.plus_p5714425477246183910nteger _let_2) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_ri6519982836138164636nteger (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) (@ (@ tptp.divide6298287555418463151nteger A2) _let_1))))))))))
% 3.15/3.51 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N3 tptp.nat) (A2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int A2) _let_1))) (@ (@ (@ tptp.if_int (= N3 tptp.zero_zero_nat)) (@ tptp.uminus_uminus_int _let_2)) (@ (@ tptp.plus_plus_int _let_2) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_ri631733984087533419it_int (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) (@ (@ tptp.divide_divide_int A2) _let_1))))))))))
% 3.15/3.51 (assert (forall ((B tptp.int) (A tptp.int) (Q4 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.product_Pair_int_int Q4))) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (=> (@ (@ (@ tptp.eucl_rel_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) B) (@ _let_2 R2)) (@ (@ (@ tptp.eucl_rel_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 A))) (@ _let_1 B)) (@ _let_2 (@ (@ tptp.minus_minus_int (@ _let_1 R2)) tptp.one_one_int)))))))))
% 3.15/3.51 (assert (forall ((B tptp.int) (A tptp.int) (Q4 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.plus_plus_int tptp.one_one_int))) (let ((_let_3 (@ tptp.product_Pair_int_int Q4))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (=> (@ (@ (@ tptp.eucl_rel_int A) B) (@ _let_3 R2)) (@ (@ (@ tptp.eucl_rel_int (@ _let_2 (@ _let_1 A))) (@ _let_1 B)) (@ _let_3 (@ _let_2 (@ _let_1 R2)))))))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_ri6519982836138164636nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_ri6519982836138164636nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_ri631733984087533419it_int N) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.bit_ri6519982836138164636nteger N) _let_1) _let_1))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_ri631733984087533419it_int N) _let_1) _let_1))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_ri6519982836138164636nteger (@ tptp.suc N)) tptp.one_one_Code_integer) tptp.one_one_Code_integer)))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) tptp.one_one_int) tptp.one_one_int)))
% 3.15/3.51 (assert (forall ((K tptp.num)) (= (@ (@ tptp.bit_ri6519982836138164636nteger (@ tptp.numeral_numeral_nat K)) tptp.one_one_Code_integer) tptp.one_one_Code_integer)))
% 3.15/3.51 (assert (forall ((K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat K)) tptp.one_one_int) tptp.one_one_int)))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int) (Q4 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.if_int (= R2 tptp.zero_zero_int)))) (let ((_let_2 (@ tptp.uminus_uminus_int Q4))) (=> (@ (@ (@ tptp.eucl_rel_int A) B) (@ (@ tptp.product_Pair_int_int Q4) R2)) (=> (not (= B tptp.zero_zero_int)) (@ (@ (@ tptp.eucl_rel_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.product_Pair_int_int (@ (@ _let_1 _let_2) (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int))) (@ (@ _let_1 tptp.zero_zero_int) (@ (@ tptp.minus_minus_int B) R2))))))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 3.15/3.51 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bitM M2)) (@ tptp.bit0 tptp.one)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M2)) tptp.one_one_int)) tptp.one_one_int))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1345352211410354436nteger tptp.zero_zero_nat) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1)))))))
% 3.15/3.51 (assert (forall ((A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se168947363167071951atural tptp.zero_zero_nat) A) (@ (@ tptp.plus_p4538020629002901425atural (@ tptp.zero_n8403883297036319079atural (@ (@ tptp.dvd_dvd_Code_natural _let_1) A))) (@ (@ tptp.times_2397367101498566445atural _let_1) (@ (@ tptp.divide5121882707175180666atural A) _let_1)))))))
% 3.15/3.51 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2161824704523386999it_nat tptp.zero_zero_nat) A) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat _let_1) A))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1)))))))
% 3.15/3.51 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2159334234014336723it_int tptp.zero_zero_nat) A) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.dvd_dvd_int _let_1) A))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1)))))))
% 3.15/3.51 (assert (= tptp.bit_se1745604003318907178nteger (lambda ((N3 tptp.nat) (A2 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_Code_integer (= N3 tptp.zero_zero_nat)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) (@ (@ tptp.divide6298287555418463151nteger A2) _let_1))) _let_1)) (@ (@ tptp.modulo364778990260209775nteger A2) _let_1)))))))
% 3.15/3.51 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N3 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= N3 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) (@ (@ tptp.divide_divide_nat A2) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_nat A2) _let_1)))))))
% 3.15/3.51 (assert (= tptp.bit_se569199155075624693atural (lambda ((N3 tptp.nat) (A2 tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_Code_natural (= N3 tptp.zero_zero_nat)) tptp.zero_z2226904508553997617atural) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.bit_se569199155075624693atural (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) (@ (@ tptp.divide5121882707175180666atural A2) _let_1))) _let_1)) (@ (@ tptp.modulo8411746178871703098atural A2) _let_1)))))))
% 3.15/3.51 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N3 tptp.nat) (A2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_int (= N3 tptp.zero_zero_nat)) tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) (@ (@ tptp.divide_divide_int A2) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_int A2) _let_1)))))))
% 3.15/3.51 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K4 tptp.int) (L3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (or (= K4 tptp.zero_zero_int) (= L3 tptp.zero_zero_int))) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (= K4 _let_2)) L3) (@ (@ (@ tptp.if_int (= L3 _let_2)) K4) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int K4) _let_1)) (@ (@ tptp.modulo_modulo_int L3) _let_1))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K4) _let_1)) (@ (@ tptp.divide_divide_int L3) _let_1))))))))))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.modulo8411746178871703098atural tptp.one_one_Code_natural) (@ (@ tptp.power_7079662738309270450atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n8403883297036319079atural (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 3.15/3.51 (assert (= tptp.upto_aux (lambda ((I4 tptp.int) (J2 tptp.int) (Js tptp.list_int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_int J2) I4)) Js) (@ (@ (@ tptp.upto_aux I4) (@ (@ tptp.minus_minus_int J2) tptp.one_one_int)) (@ (@ tptp.cons_int J2) Js))))))
% 3.15/3.51 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ (@ tptp.bit_se7788150548672797655nteger _let_1) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1))))))
% 3.15/3.51 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ (@ tptp.bit_se545348938243370406it_int _let_1) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1))))))
% 3.15/3.51 (assert (= (@ tptp.zero_n356916108424825756nteger true) tptp.one_one_Code_integer))
% 3.15/3.51 (assert (= (@ tptp.zero_n2052037380579107095ol_rat true) tptp.one_one_rat))
% 3.15/3.51 (assert (= (@ tptp.zero_n2687167440665602831ol_nat true) tptp.one_one_nat))
% 3.15/3.51 (assert (= (@ tptp.zero_n2684676970156552555ol_int true) tptp.one_one_int))
% 3.15/3.51 (assert (forall ((P2 Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P2) tptp.one_one_Code_integer) P2)))
% 3.15/3.51 (assert (forall ((P2 Bool)) (= (= (@ tptp.zero_n2052037380579107095ol_rat P2) tptp.one_one_rat) P2)))
% 3.15/3.51 (assert (forall ((P2 Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P2) tptp.one_one_nat) P2)))
% 3.15/3.51 (assert (forall ((P2 Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P2) tptp.one_one_int) P2)))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.suc N)) tptp.one_one_Code_integer) tptp.one_one_Code_integer)))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N)) tptp.one_one_nat) tptp.one_one_nat)))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) tptp.one_one_int) tptp.one_one_int)))
% 3.15/3.51 (assert (forall ((P2 Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P2)) tptp.one_one_Code_integer) (not P2))))
% 3.15/3.51 (assert (forall ((P2 Bool)) (= (@ (@ tptp.ord_less_rat (@ tptp.zero_n2052037380579107095ol_rat P2)) tptp.one_one_rat) (not P2))))
% 3.15/3.51 (assert (forall ((P2 Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P2)) tptp.one_one_nat) (not P2))))
% 3.15/3.51 (assert (forall ((P2 Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P2)) tptp.one_one_int) (not P2))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) A) A)))
% 3.15/3.51 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int tptp.one_one_int)) A) A)))
% 3.15/3.51 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) A)))
% 3.15/3.51 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) A)))
% 3.15/3.51 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger X) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X)))
% 3.15/3.51 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X) (@ tptp.uminus_uminus_int tptp.one_one_int)) X)))
% 3.15/3.51 (assert (forall ((P2 Bool)) (= (@ tptp.zero_n2052037380579107095ol_rat (not P2)) (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.zero_n2052037380579107095ol_rat P2)))))
% 3.15/3.51 (assert (forall ((P2 Bool)) (= (@ tptp.zero_n356916108424825756nteger (not P2)) (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.zero_n356916108424825756nteger P2)))))
% 3.15/3.51 (assert (forall ((P2 Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (not P2)) (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.zero_n2684676970156552555ol_int P2)))))
% 3.15/3.51 (assert (forall ((L tptp.num)) (= (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.numeral_numeral_nat L)) tptp.one_one_Code_integer) tptp.one_one_Code_integer)))
% 3.15/3.51 (assert (forall ((L tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L)) tptp.one_one_nat) tptp.one_one_nat)))
% 3.15/3.51 (assert (forall ((L tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) tptp.one_one_int) tptp.one_one_int)))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N) tptp.one_one_nat) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (= (@ (@ tptp.bit_se1745604003318907178nteger N) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger) (= N tptp.zero_zero_nat))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (= (@ (@ tptp.bit_se569199155075624693atural N) tptp.one_one_Code_natural) tptp.zero_z2226904508553997617atural) (= N tptp.zero_zero_nat))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N) tptp.one_one_int) tptp.zero_zero_int) (= N tptp.zero_zero_nat))))
% 3.15/3.51 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 X))) tptp.one_one_Code_integer) tptp.one_one_Code_integer)))
% 3.15/3.51 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se2773287842338716102atural (@ tptp.numera5444537566228673987atural (@ tptp.bit1 X))) tptp.one_one_Code_natural) tptp.one_one_Code_natural)))
% 3.15/3.51 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) tptp.one_one_int) tptp.one_one_int)))
% 3.15/3.51 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) tptp.one_one_nat) tptp.one_one_nat)))
% 3.15/3.51 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se3949692690581998587nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 Y))) tptp.one_one_Code_integer)))
% 3.15/3.51 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se2773287842338716102atural tptp.one_one_Code_natural) (@ tptp.numera5444537566228673987atural (@ tptp.bit1 Y))) tptp.one_one_Code_natural)))
% 3.15/3.51 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) tptp.one_one_int)))
% 3.15/3.51 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) tptp.one_one_nat)))
% 3.15/3.51 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat A))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) (@ tptp.zero_n2052037380579107095ol_rat (not (= A tptp.zero_zero_rat)))))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.sgn_sgn_Code_integer A))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) (@ tptp.zero_n356916108424825756nteger (not (= A tptp.zero_z3403309356797280102nteger)))))))
% 3.15/3.51 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.sgn_sgn_int A))) (= (@ (@ tptp.times_times_int _let_1) _let_1) (@ tptp.zero_n2684676970156552555ol_int (not (= A tptp.zero_zero_int)))))))
% 3.15/3.51 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se3949692690581998587nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Y))) tptp.zero_z3403309356797280102nteger)))
% 3.15/3.51 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se2773287842338716102atural tptp.one_one_Code_natural) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 Y))) tptp.zero_z2226904508553997617atural)))
% 3.15/3.51 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) tptp.zero_zero_int)))
% 3.15/3.51 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) tptp.zero_zero_nat)))
% 3.15/3.51 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 X))) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 3.15/3.51 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se2773287842338716102atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 X))) tptp.one_one_Code_natural) tptp.zero_z2226904508553997617atural)))
% 3.15/3.51 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) tptp.one_one_int) tptp.zero_zero_int)))
% 3.15/3.51 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) tptp.one_one_nat) tptp.zero_zero_nat)))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 X))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Y))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.numera6620942414471956472nteger X)) (@ tptp.numera6620942414471956472nteger Y))))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se2773287842338716102atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 X))) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 Y))) (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se2773287842338716102atural (@ tptp.numera5444537566228673987atural X)) (@ tptp.numera5444537566228673987atural Y))))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y))))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y))))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1745604003318907178nteger N) tptp.one_one_Code_integer) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) tptp.one_one_nat) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) tptp.one_one_int) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 3.15/3.51 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) tptp.one_one_int) tptp.one_one_int)))
% 3.15/3.51 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) tptp.one_one_int)))
% 3.15/3.51 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 tptp.one))))
% 3.15/3.51 (assert (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit1 tptp.one))))
% 3.15/3.51 (assert (= (@ tptp.neg_nu5831290666863070958nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 tptp.one))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 X))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Y))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.numera6620942414471956472nteger X)) (@ tptp.numera6620942414471956472nteger Y))))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se2773287842338716102atural (@ tptp.numera5444537566228673987atural (@ tptp.bit1 X))) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 Y))) (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se2773287842338716102atural (@ tptp.numera5444537566228673987atural X)) (@ tptp.numera5444537566228673987atural Y))))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y))))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y))))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 X))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 Y))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.numera6620942414471956472nteger X)) (@ tptp.numera6620942414471956472nteger Y))))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se2773287842338716102atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 X))) (@ tptp.numera5444537566228673987atural (@ tptp.bit1 Y))) (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se2773287842338716102atural (@ tptp.numera5444537566228673987atural X)) (@ tptp.numera5444537566228673987atural Y))))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y))))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (= (@ (@ tptp.bit_se7788150548672797655nteger (@ tptp.suc N)) A) (@ (@ tptp.bit_se7788150548672797655nteger N) (@ (@ tptp.times_3573771949741848930nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (A tptp.code_natural)) (= (@ (@ tptp.bit_se6611745700429515170atural (@ tptp.suc N)) A) (@ (@ tptp.bit_se6611745700429515170atural N) (@ (@ tptp.times_2397367101498566445atural A) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (A tptp.int)) (= (@ (@ tptp.bit_se545348938243370406it_int (@ tptp.suc N)) A) (@ (@ tptp.bit_se545348938243370406it_int N) (@ (@ tptp.times_times_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (A tptp.nat)) (= (@ (@ tptp.bit_se547839408752420682it_nat (@ tptp.suc N)) A) (@ (@ tptp.bit_se547839408752420682it_nat N) (@ (@ tptp.times_times_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se7788150548672797655nteger N) tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se6611745700429515170atural N) tptp.one_one_Code_natural) (@ (@ tptp.power_7079662738309270450atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) N))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int N) tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se547839408752420682it_nat N) tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 3.15/3.51 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) tptp.one_one_int) tptp.zero_zero_int)))
% 3.15/3.51 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) tptp.zero_zero_int)))
% 3.15/3.51 (assert (= (@ tptp.neg_nu3811975205180677377ec_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 tptp.one)))))
% 3.15/3.51 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.bit1 tptp.one)))))
% 3.15/3.51 (assert (= (@ tptp.neg_nu7757733837767384882nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 tptp.one)))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 X))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 Y))) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.numera6620942414471956472nteger X)) (@ tptp.numera6620942414471956472nteger Y)))))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se2773287842338716102atural (@ tptp.numera5444537566228673987atural (@ tptp.bit1 X))) (@ tptp.numera5444537566228673987atural (@ tptp.bit1 Y))) (@ (@ tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural) (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se2773287842338716102atural (@ tptp.numera5444537566228673987atural X)) (@ tptp.numera5444537566228673987atural Y)))))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y)))))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y)))))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n356916108424825756nteger (= N tptp.zero_zero_nat)))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2687167440665602831ol_nat (= N tptp.zero_zero_nat)))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide5121882707175180666atural tptp.one_one_Code_natural) (@ (@ tptp.power_7079662738309270450atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n8403883297036319079atural (= N tptp.zero_zero_nat)))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2684676970156552555ol_int (= N tptp.zero_zero_nat)))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n356916108424825756nteger (= N tptp.zero_zero_nat)))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2687167440665602831ol_nat (= N tptp.zero_zero_nat)))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide5121882707175180666atural tptp.one_one_Code_natural) (@ (@ tptp.power_7079662738309270450atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n8403883297036319079atural (= N tptp.zero_zero_nat)))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2684676970156552555ol_int (= N tptp.zero_zero_nat)))))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se2925701944663578781it_nat M2) _let_1) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat N) M2))) _let_1)))))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se1745604003318907178nteger M2) _let_1) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat N) M2))) _let_1)))))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_7079662738309270450atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se569199155075624693atural M2) _let_1) (@ (@ tptp.times_2397367101498566445atural (@ tptp.zero_n8403883297036319079atural (@ (@ tptp.ord_less_nat N) M2))) _let_1)))))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se2923211474154528505it_int M2) _let_1) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat N) M2))) _let_1)))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) _let_1) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_eq_nat _let_1) N))) _let_1)))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger _let_1))) (= (@ (@ tptp.bit_se1745604003318907178nteger N) _let_2) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat _let_1)) N))) _let_2))))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera5444537566228673987atural _let_1))) (= (@ (@ tptp.bit_se569199155075624693atural N) _let_2) (@ (@ tptp.times_2397367101498566445atural (@ tptp.zero_n8403883297036319079atural (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat _let_1)) N))) _let_2))))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (= (@ (@ tptp.bit_se2923211474154528505it_int N) _let_2) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat _let_1)) N))) _let_2))))))
% 3.15/3.51 (assert (forall ((V2 tptp.num) (W tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 V2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int V2)) (@ tptp.numeral_numeral_int W)))) tptp.one_one_int))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 3.15/3.51 (assert (forall ((P2 Bool) (Q2 Bool)) (= (@ tptp.zero_n2687167440665602831ol_nat (and P2 Q2)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat P2)) (@ tptp.zero_n2687167440665602831ol_nat Q2)))))
% 3.15/3.51 (assert (forall ((P2 Bool) (Q2 Bool)) (= (@ tptp.zero_n356916108424825756nteger (and P2 Q2)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger P2)) (@ tptp.zero_n356916108424825756nteger Q2)))))
% 3.15/3.51 (assert (forall ((P2 Bool) (Q2 Bool)) (= (@ tptp.zero_n8403883297036319079atural (and P2 Q2)) (@ (@ tptp.times_2397367101498566445atural (@ tptp.zero_n8403883297036319079atural P2)) (@ tptp.zero_n8403883297036319079atural Q2)))))
% 3.15/3.51 (assert (forall ((P2 Bool) (Q2 Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (and P2 Q2)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int P2)) (@ tptp.zero_n2684676970156552555ol_int Q2)))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (= (@ (@ tptp.bit_se3949692690581998587nteger A) B) _let_1) (and (= A _let_1) (= B _let_1))))))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (= (@ (@ tptp.bit_se725231765392027082nd_int A) B) _let_1) (and (= A _let_1) (= B _let_1))))))
% 3.15/3.51 (assert (forall ((P2 Bool)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P2)) tptp.one_one_Code_integer)))
% 3.15/3.51 (assert (forall ((P2 Bool)) (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P2)) tptp.one_one_rat)))
% 3.15/3.51 (assert (forall ((P2 Bool)) (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P2)) tptp.one_one_nat)))
% 3.15/3.51 (assert (forall ((P2 Bool)) (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P2)) tptp.one_one_int)))
% 3.15/3.51 (assert (= tptp.zero_n2687167440665602831ol_nat (lambda ((P6 Bool)) (@ (@ (@ tptp.if_nat P6) tptp.one_one_nat) tptp.zero_zero_nat))))
% 3.15/3.51 (assert (= tptp.zero_n2052037380579107095ol_rat (lambda ((P6 Bool)) (@ (@ (@ tptp.if_rat P6) tptp.one_one_rat) tptp.zero_zero_rat))))
% 3.15/3.51 (assert (= tptp.zero_n356916108424825756nteger (lambda ((P6 Bool)) (@ (@ (@ tptp.if_Code_integer P6) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))))
% 3.15/3.51 (assert (= tptp.zero_n8403883297036319079atural (lambda ((P6 Bool)) (@ (@ (@ tptp.if_Code_natural P6) tptp.one_one_Code_natural) tptp.zero_z2226904508553997617atural))))
% 3.15/3.51 (assert (= tptp.zero_n2684676970156552555ol_int (lambda ((P6 Bool)) (@ (@ (@ tptp.if_int P6) tptp.one_one_int) tptp.zero_zero_int))))
% 3.15/3.51 (assert (forall ((P2 (-> tptp.nat Bool)) (P5 Bool)) (= (@ P2 (@ tptp.zero_n2687167440665602831ol_nat P5)) (and (=> P5 (@ P2 tptp.one_one_nat)) (=> (not P5) (@ P2 tptp.zero_zero_nat))))))
% 3.15/3.51 (assert (forall ((P2 (-> tptp.rat Bool)) (P5 Bool)) (= (@ P2 (@ tptp.zero_n2052037380579107095ol_rat P5)) (and (=> P5 (@ P2 tptp.one_one_rat)) (=> (not P5) (@ P2 tptp.zero_zero_rat))))))
% 3.15/3.51 (assert (forall ((P2 (-> tptp.code_integer Bool)) (P5 Bool)) (= (@ P2 (@ tptp.zero_n356916108424825756nteger P5)) (and (=> P5 (@ P2 tptp.one_one_Code_integer)) (=> (not P5) (@ P2 tptp.zero_z3403309356797280102nteger))))))
% 3.15/3.51 (assert (forall ((P2 (-> tptp.code_natural Bool)) (P5 Bool)) (= (@ P2 (@ tptp.zero_n8403883297036319079atural P5)) (and (=> P5 (@ P2 tptp.one_one_Code_natural)) (=> (not P5) (@ P2 tptp.zero_z2226904508553997617atural))))))
% 3.15/3.51 (assert (forall ((P2 (-> tptp.int Bool)) (P5 Bool)) (= (@ P2 (@ tptp.zero_n2684676970156552555ol_int P5)) (and (=> P5 (@ P2 tptp.one_one_int)) (=> (not P5) (@ P2 tptp.zero_zero_int))))))
% 3.15/3.51 (assert (forall ((P2 (-> tptp.nat Bool)) (P5 Bool)) (= (@ P2 (@ tptp.zero_n2687167440665602831ol_nat P5)) (not (or (and P5 (not (@ P2 tptp.one_one_nat))) (and (not P5) (not (@ P2 tptp.zero_zero_nat))))))))
% 3.15/3.51 (assert (forall ((P2 (-> tptp.rat Bool)) (P5 Bool)) (= (@ P2 (@ tptp.zero_n2052037380579107095ol_rat P5)) (not (or (and P5 (not (@ P2 tptp.one_one_rat))) (and (not P5) (not (@ P2 tptp.zero_zero_rat))))))))
% 3.15/3.51 (assert (forall ((P2 (-> tptp.code_integer Bool)) (P5 Bool)) (= (@ P2 (@ tptp.zero_n356916108424825756nteger P5)) (not (or (and P5 (not (@ P2 tptp.one_one_Code_integer))) (and (not P5) (not (@ P2 tptp.zero_z3403309356797280102nteger))))))))
% 3.15/3.51 (assert (forall ((P2 (-> tptp.code_natural Bool)) (P5 Bool)) (= (@ P2 (@ tptp.zero_n8403883297036319079atural P5)) (not (or (and P5 (not (@ P2 tptp.one_one_Code_natural))) (and (not P5) (not (@ P2 tptp.zero_z2226904508553997617atural))))))))
% 3.15/3.51 (assert (forall ((P2 (-> tptp.int Bool)) (P5 Bool)) (= (@ P2 (@ tptp.zero_n2684676970156552555ol_int P5)) (not (or (and P5 (not (@ P2 tptp.one_one_int))) (and (not P5) (not (@ P2 tptp.zero_zero_int))))))))
% 3.15/3.51 (assert (@ (@ tptp.comm_m1654649897431166824nteger tptp.bit_se3949692690581998587nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 3.15/3.51 (assert (@ (@ tptp.comm_monoid_int tptp.bit_se725231765392027082nd_int) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 3.15/3.51 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 K))) (=> (not (= _let_2 tptp.zero_zero_int)) (= (@ _let_1 (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)))))))
% 3.15/3.51 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat _let_1) _let_1)) tptp.one_one_nat)))))
% 3.15/3.51 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.numeral_numeral_int (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int _let_1) _let_1)) tptp.one_one_int)))))
% 3.15/3.51 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat _let_1) _let_1)) tptp.one_one_rat)))))
% 3.15/3.51 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (= (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1)) tptp.one_one_Code_integer)))))
% 3.15/3.51 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera5444537566228673987atural N))) (= (@ tptp.numera5444537566228673987atural (@ tptp.bit1 N)) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.plus_p4538020629002901425atural _let_1) _let_1)) tptp.one_one_Code_natural)))))
% 3.15/3.51 (assert (@ (@ tptp.monoid_Code_integer tptp.bit_se3949692690581998587nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 3.15/3.51 (assert (@ (@ tptp.monoid_int tptp.bit_se725231765392027082nd_int) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 3.15/3.51 (assert (@ (@ tptp.semila6106414119144251899nteger tptp.bit_se3949692690581998587nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 3.15/3.51 (assert (@ (@ tptp.semila9079005292280841162tr_int tptp.bit_se725231765392027082nd_int) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 3.15/3.51 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.suc N)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 K))) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger N) (@ tptp.numera6620942414471956472nteger K))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se569199155075624693atural (@ tptp.suc N)) (@ tptp.numera5444537566228673987atural (@ tptp.bit1 K))) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.bit_se569199155075624693atural N) (@ tptp.numera5444537566228673987atural K))) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_natural))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 3.15/3.51 (assert (forall ((A tptp.assn)) (= (@ (@ tptp.power_power_assn A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn A) A)) A))))
% 3.15/3.51 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat A) A)) A))))
% 3.15/3.51 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int A) A)) A))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger A) A)) A))))
% 3.15/3.51 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.power_7079662738309270450atural A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.times_2397367101498566445atural A) A)) A))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.bit_se7788150548672797655nteger N))) (= (@ _let_2 (@ (@ tptp.times_3573771949741848930nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_2 A)) _let_1))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.bit_se6611745700429515170atural N))) (= (@ _let_2 (@ (@ tptp.times_2397367101498566445atural A) _let_1)) (@ (@ tptp.times_2397367101498566445atural (@ _let_2 A)) _let_1))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.bit_se545348938243370406it_int N))) (= (@ _let_2 (@ (@ tptp.times_times_int A) _let_1)) (@ (@ tptp.times_times_int (@ _let_2 A)) _let_1))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.bit_se547839408752420682it_nat N))) (= (@ _let_2 (@ (@ tptp.times_times_nat A) _let_1)) (@ (@ tptp.times_times_nat (@ _let_2 A)) _let_1))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K))))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K))) (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.suc N)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 K))) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger N) (@ tptp.numera6620942414471956472nteger K))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se569199155075624693atural (@ tptp.suc N)) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 K))) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.bit_se569199155075624693atural N) (@ tptp.numera5444537566228673987atural K))) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger A) tptp.one_one_Code_integer) (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 3.15/3.51 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.bit_se2773287842338716102atural A) tptp.one_one_Code_natural) (@ (@ tptp.modulo8411746178871703098atural A) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))))
% 3.15/3.51 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) tptp.one_one_int) (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 3.15/3.51 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat A) tptp.one_one_nat) (@ (@ tptp.modulo_modulo_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger tptp.one_one_Code_integer) A) (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 3.15/3.51 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.bit_se2773287842338716102atural tptp.one_one_Code_natural) A) (@ (@ tptp.modulo8411746178871703098atural A) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))))
% 3.15/3.51 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) A) (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 3.15/3.51 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) A) (@ (@ tptp.modulo_modulo_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 3.15/3.51 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_int (@ tptp.bitM N)) (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) tptp.one_one_int))))
% 3.15/3.51 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_rat (@ tptp.bitM N)) (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 N))) tptp.one_one_rat))))
% 3.15/3.51 (assert (forall ((N tptp.num)) (= (@ tptp.numera6620942414471956472nteger (@ tptp.bitM N)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N))) tptp.one_one_Code_integer))))
% 3.15/3.51 (assert (= tptp.bit_se7788150548672797655nteger (lambda ((N3 tptp.nat) (A2 tptp.code_integer)) (@ (@ tptp.times_3573771949741848930nteger A2) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N3)))))
% 3.15/3.51 (assert (= tptp.bit_se6611745700429515170atural (lambda ((N3 tptp.nat) (A2 tptp.code_natural)) (@ (@ tptp.times_2397367101498566445atural A2) (@ (@ tptp.power_7079662738309270450atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) N3)))))
% 3.15/3.51 (assert (= tptp.bit_se545348938243370406it_int (lambda ((N3 tptp.nat) (A2 tptp.int)) (@ (@ tptp.times_times_int A2) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N3)))))
% 3.15/3.51 (assert (= tptp.bit_se547839408752420682it_nat (lambda ((N3 tptp.nat) (A2 tptp.nat)) (@ (@ tptp.times_times_nat A2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)))))
% 3.15/3.51 (assert (forall ((P2 (-> tptp.code_integer Bool)) (A tptp.code_integer)) (=> (forall ((A6 tptp.code_integer)) (=> (= (@ (@ tptp.divide6298287555418463151nteger A6) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A6) (@ P2 A6))) (=> (forall ((A6 tptp.code_integer) (B5 Bool)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.zero_n356916108424825756nteger B5)) (@ (@ tptp.times_3573771949741848930nteger _let_1) A6)))) (=> (@ P2 A6) (=> (= (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1) A6) (@ P2 _let_2)))))) (@ P2 A)))))
% 3.15/3.51 (assert (forall ((P2 (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((A6 tptp.nat)) (=> (= (@ (@ tptp.divide_divide_nat A6) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A6) (@ P2 A6))) (=> (forall ((A6 tptp.nat) (B5 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat B5)) (@ (@ tptp.times_times_nat _let_1) A6)))) (=> (@ P2 A6) (=> (= (@ (@ tptp.divide_divide_nat _let_2) _let_1) A6) (@ P2 _let_2)))))) (@ P2 A)))))
% 3.15/3.51 (assert (forall ((P2 (-> tptp.code_natural Bool)) (A tptp.code_natural)) (=> (forall ((A6 tptp.code_natural)) (=> (= (@ (@ tptp.divide5121882707175180666atural A6) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) A6) (@ P2 A6))) (=> (forall ((A6 tptp.code_natural) (B5 Bool)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_p4538020629002901425atural (@ tptp.zero_n8403883297036319079atural B5)) (@ (@ tptp.times_2397367101498566445atural _let_1) A6)))) (=> (@ P2 A6) (=> (= (@ (@ tptp.divide5121882707175180666atural _let_2) _let_1) A6) (@ P2 _let_2)))))) (@ P2 A)))))
% 3.15/3.51 (assert (forall ((P2 (-> tptp.int Bool)) (A tptp.int)) (=> (forall ((A6 tptp.int)) (=> (= (@ (@ tptp.divide_divide_int A6) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A6) (@ P2 A6))) (=> (forall ((A6 tptp.int) (B5 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int B5)) (@ (@ tptp.times_times_int _let_1) A6)))) (=> (@ P2 A6) (=> (= (@ (@ tptp.divide_divide_int _let_2) _let_1) A6) (@ P2 _let_2)))))) (@ P2 A)))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M2))) (= (@ (@ tptp.modulo364778990260209775nteger _let_2) (@ _let_1 N)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat M2) N))) _let_2))))))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M2))) (= (@ (@ tptp.modulo_modulo_nat _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat M2) N))) _let_2))))))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_7079662738309270450atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M2))) (= (@ (@ tptp.modulo8411746178871703098atural _let_2) (@ _let_1 N)) (@ (@ tptp.times_2397367101498566445atural (@ tptp.zero_n8403883297036319079atural (@ (@ tptp.ord_less_nat M2) N))) _let_2))))))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M2))) (= (@ (@ tptp.modulo_modulo_int _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat M2) N))) _let_2))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 K))) (=> (not (= _let_2 (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) tptp.one_one_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_2)))))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.bit_se1745604003318907178nteger _let_1) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1)) tptp.one_one_Code_integer)))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) tptp.one_one_int)))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))) _let_1)) (@ (@ tptp.modulo364778990260209775nteger A) _let_1))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ (@ tptp.divide_divide_nat A) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_nat A) _let_1))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se569199155075624693atural (@ tptp.suc N)) A) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.bit_se569199155075624693atural N) (@ (@ tptp.divide5121882707175180666atural A) _let_1))) _let_1)) (@ (@ tptp.modulo8411746178871703098atural A) _let_1))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ (@ tptp.divide_divide_int A) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_int A) _let_1))))))
% 3.15/3.51 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (= (@ (@ tptp.bit_se1745604003318907178nteger _let_1) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1)) tptp.one_one_Code_integer)))))
% 3.15/3.51 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (= (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) tptp.one_one_int)))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se1745604003318907178nteger N) A))) (let ((_let_3 (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (=> (= (@ (@ tptp.divide6298287555418463151nteger A) _let_1) A) (and (=> _let_3 (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger _let_1) N)) tptp.one_one_Code_integer))))))))))
% 3.15/3.51 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se2925701944663578781it_nat N) A))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat _let_1) A))) (=> (= (@ (@ tptp.divide_divide_nat A) _let_1) A) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat _let_1) N)) tptp.one_one_nat))))))))))
% 3.15/3.51 (assert (forall ((A tptp.code_natural) (N tptp.nat)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se569199155075624693atural N) A))) (let ((_let_3 (@ (@ tptp.dvd_dvd_Code_natural _let_1) A))) (=> (= (@ (@ tptp.divide5121882707175180666atural A) _let_1) A) (and (=> _let_3 (= _let_2 tptp.zero_z2226904508553997617atural)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_7197305767214868737atural (@ (@ tptp.power_7079662738309270450atural _let_1) N)) tptp.one_one_Code_natural))))))))))
% 3.15/3.51 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se2923211474154528505it_int N) A))) (let ((_let_3 (@ (@ tptp.dvd_dvd_int _let_1) A))) (=> (= (@ (@ tptp.divide_divide_int A) _let_1) A) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int _let_1) N)) tptp.one_one_int))))))))))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M2))) (= (@ (@ tptp.divide6298287555418463151nteger _let_2) (@ _let_1 N)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (and (not (= _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.ord_less_eq_nat N) M2)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N))))))))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M2))) (= (@ (@ tptp.divide_divide_nat _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (and (not (= _let_2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_nat N) M2)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N))))))))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_7079662738309270450atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M2))) (= (@ (@ tptp.divide5121882707175180666atural _let_2) (@ _let_1 N)) (@ (@ tptp.times_2397367101498566445atural (@ tptp.zero_n8403883297036319079atural (and (not (= _let_2 tptp.zero_z2226904508553997617atural)) (@ (@ tptp.ord_less_eq_nat N) M2)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N))))))))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M2))) (= (@ (@ tptp.divide_divide_int _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (and (not (= _let_2 tptp.zero_zero_int)) (@ (@ tptp.ord_less_eq_nat N) M2)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M2) N))))))))
% 3.15/3.51 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 3.15/3.51 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 3.15/3.51 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K))))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 3.15/3.51 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K4 tptp.int) (L3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K4)) (not (@ _let_2 L3)))))) (let ((_let_4 (@ (@ tptp.insert_int2 tptp.zero_zero_int) (@ (@ tptp.insert_int2 (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (@ (@ (@ tptp.if_int (and (@ (@ tptp.member_int2 K4) _let_4) (@ (@ tptp.member_int2 L3) _let_4))) (@ tptp.uminus_uminus_int _let_3)) (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K4) _let_1)) (@ (@ tptp.divide_divide_int L3) _let_1))))))))))))
% 3.15/3.51 (assert (forall ((X tptp.int) (Xa tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 X)) (not (@ _let_2 Xa)))))) (let ((_let_4 (@ (@ tptp.insert_int2 tptp.zero_zero_int) (@ (@ tptp.insert_int2 (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_5 (and (@ (@ tptp.member_int2 X) _let_4) (@ (@ tptp.member_int2 Xa) _let_4)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X) Xa) Y) (and (=> _let_5 (= Y (@ tptp.uminus_uminus_int _let_3))) (=> (not _let_5) (= Y (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X) _let_1)) (@ (@ tptp.divide_divide_int Xa) _let_1)))))))))))))))
% 3.15/3.51 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))))
% 3.15/3.51 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.numeral_numeral_nat L)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 K))) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.pred_numeral L)) (@ tptp.numera6620942414471956472nteger K))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer))))
% 3.15/3.51 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se569199155075624693atural (@ tptp.numeral_numeral_nat L)) (@ tptp.numera5444537566228673987atural (@ tptp.bit1 K))) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.bit_se569199155075624693atural (@ tptp.pred_numeral L)) (@ tptp.numera5444537566228673987atural K))) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_natural))))
% 3.15/3.51 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 3.15/3.51 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2)))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 3.15/3.51 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M2)))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 3.15/3.51 (assert (forall ((A (-> tptp.produc3658429121746597890et_nat Bool)) (A3 tptp.set_Pr4532377907799695533_nat_o) (B3 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.inf_in1906310914598751387_nat_o A3))) (let ((_let_2 (@ tptp.insert5175938949040314269_nat_o A))) (=> (@ (@ tptp.member6576561426505652726_nat_o A) A3) (= (@ _let_1 (@ _let_2 B3)) (@ _let_2 (@ _let_1 B3))))))))
% 3.15/3.51 (assert (forall ((A tptp.int) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.inf_inf_set_int A3))) (let ((_let_2 (@ tptp.insert_int2 A))) (=> (@ (@ tptp.member_int2 A) A3) (= (@ _let_1 (@ _let_2 B3)) (@ _let_2 (@ _let_1 B3))))))))
% 3.15/3.51 (assert (forall ((A tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A3))) (let ((_let_2 (@ tptp.insert8211810215607154385at_nat A))) (=> (@ (@ tptp.member8440522571783428010at_nat A) A3) (= (@ _let_1 (@ _let_2 B3)) (@ _let_2 (@ _let_1 B3))))))))
% 3.15/3.51 (assert (forall ((A tptp.nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A3))) (let ((_let_2 (@ tptp.insert_nat2 A))) (=> (@ (@ tptp.member_nat2 A) A3) (= (@ _let_1 (@ _let_2 B3)) (@ _let_2 (@ _let_1 B3))))))))
% 3.15/3.51 (assert (forall ((A (-> tptp.produc3658429121746597890et_nat Bool)) (A3 tptp.set_Pr4532377907799695533_nat_o) (B3 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.inf_in1906310914598751387_nat_o A3))) (=> (not (@ (@ tptp.member6576561426505652726_nat_o A) A3)) (= (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o A) B3)) (@ _let_1 B3))))))
% 3.15/3.51 (assert (forall ((A tptp.int) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.inf_inf_set_int A3))) (=> (not (@ (@ tptp.member_int2 A) A3)) (= (@ _let_1 (@ (@ tptp.insert_int2 A) B3)) (@ _let_1 B3))))))
% 3.15/3.51 (assert (forall ((A tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A3))) (=> (not (@ (@ tptp.member8440522571783428010at_nat A) A3)) (= (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat A) B3)) (@ _let_1 B3))))))
% 3.15/3.51 (assert (forall ((A tptp.nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A3))) (=> (not (@ (@ tptp.member_nat2 A) A3)) (= (@ _let_1 (@ (@ tptp.insert_nat2 A) B3)) (@ _let_1 B3))))))
% 3.15/3.51 (assert (forall ((A tptp.int) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int2 A))) (= (@ (@ tptp.inf_inf_set_int (@ _let_1 A3)) (@ _let_1 B3)) (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3))))))
% 3.15/3.51 (assert (forall ((A tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A))) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 A3)) (@ _let_1 B3)) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3))))))
% 3.15/3.51 (assert (forall ((A tptp.nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat2 A))) (= (@ (@ tptp.inf_inf_set_nat (@ _let_1 A3)) (@ _let_1 B3)) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3))))))
% 3.15/3.51 (assert (forall ((A (-> tptp.produc3658429121746597890et_nat Bool)) (C2 tptp.set_Pr4532377907799695533_nat_o) (B3 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.insert5175938949040314269_nat_o A))) (=> (@ (@ tptp.member6576561426505652726_nat_o A) C2) (= (@ (@ tptp.inf_in1906310914598751387_nat_o (@ _let_1 B3)) C2) (@ _let_1 (@ (@ tptp.inf_in1906310914598751387_nat_o B3) C2)))))))
% 3.15/3.51 (assert (forall ((A tptp.int) (C2 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int2 A))) (=> (@ (@ tptp.member_int2 A) C2) (= (@ (@ tptp.inf_inf_set_int (@ _let_1 B3)) C2) (@ _let_1 (@ (@ tptp.inf_inf_set_int B3) C2)))))))
% 3.15/3.51 (assert (forall ((A tptp.product_prod_nat_nat) (C2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.insert8211810215607154385at_nat A))) (=> (@ (@ tptp.member8440522571783428010at_nat A) C2) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 B3)) C2) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B3) C2)))))))
% 3.15/3.51 (assert (forall ((A tptp.nat) (C2 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat2 A))) (=> (@ (@ tptp.member_nat2 A) C2) (= (@ (@ tptp.inf_inf_set_nat (@ _let_1 B3)) C2) (@ _let_1 (@ (@ tptp.inf_inf_set_nat B3) C2)))))))
% 3.15/3.51 (assert (forall ((A (-> tptp.produc3658429121746597890et_nat Bool)) (C2 tptp.set_Pr4532377907799695533_nat_o) (B3 tptp.set_Pr4532377907799695533_nat_o)) (=> (not (@ (@ tptp.member6576561426505652726_nat_o A) C2)) (= (@ (@ tptp.inf_in1906310914598751387_nat_o (@ (@ tptp.insert5175938949040314269_nat_o A) B3)) C2) (@ (@ tptp.inf_in1906310914598751387_nat_o B3) C2)))))
% 3.15/3.51 (assert (forall ((A tptp.int) (C2 tptp.set_int) (B3 tptp.set_int)) (=> (not (@ (@ tptp.member_int2 A) C2)) (= (@ (@ tptp.inf_inf_set_int (@ (@ tptp.insert_int2 A) B3)) C2) (@ (@ tptp.inf_inf_set_int B3) C2)))))
% 3.15/3.51 (assert (forall ((A tptp.product_prod_nat_nat) (C2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (=> (not (@ (@ tptp.member8440522571783428010at_nat A) C2)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.insert8211810215607154385at_nat A) B3)) C2) (@ (@ tptp.inf_in2572325071724192079at_nat B3) C2)))))
% 3.15/3.51 (assert (forall ((A tptp.nat) (C2 tptp.set_nat) (B3 tptp.set_nat)) (=> (not (@ (@ tptp.member_nat2 A) C2)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.insert_nat2 A) B3)) C2) (@ (@ tptp.inf_inf_set_nat B3) C2)))))
% 3.15/3.51 (assert (forall ((A (-> tptp.produc3658429121746597890et_nat Bool)) (A3 tptp.set_Pr4532377907799695533_nat_o) (B3 tptp.set_Pr4532377907799695533_nat_o)) (= (= (@ (@ tptp.inf_in1906310914598751387_nat_o (@ (@ tptp.insert5175938949040314269_nat_o A) A3)) B3) tptp.bot_bo7824918357723582233_nat_o) (and (not (@ (@ tptp.member6576561426505652726_nat_o A) B3)) (= (@ (@ tptp.inf_in1906310914598751387_nat_o A3) B3) tptp.bot_bo7824918357723582233_nat_o)))))
% 3.15/3.51 (assert (forall ((A tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.insert8211810215607154385at_nat A) A3)) B3) tptp.bot_bo2099793752762293965at_nat) (and (not (@ (@ tptp.member8440522571783428010at_nat A) B3)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3) tptp.bot_bo2099793752762293965at_nat)))))
% 3.15/3.51 (assert (forall ((A tptp.nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.insert_nat2 A) A3)) B3) tptp.bot_bot_set_nat) (and (not (@ (@ tptp.member_nat2 A) B3)) (= (@ (@ tptp.inf_inf_set_nat A3) B3) tptp.bot_bot_set_nat)))))
% 3.15/3.51 (assert (forall ((A tptp.int) (A3 tptp.set_int) (B3 tptp.set_int)) (= (= (@ (@ tptp.inf_inf_set_int (@ (@ tptp.insert_int2 A) A3)) B3) tptp.bot_bot_set_int) (and (not (@ (@ tptp.member_int2 A) B3)) (= (@ (@ tptp.inf_inf_set_int A3) B3) tptp.bot_bot_set_int)))))
% 3.15/3.51 (assert (forall ((A (-> tptp.produc3658429121746597890et_nat Bool)) (A3 tptp.set_Pr4532377907799695533_nat_o) (B3 tptp.set_Pr4532377907799695533_nat_o)) (= (= tptp.bot_bo7824918357723582233_nat_o (@ (@ tptp.inf_in1906310914598751387_nat_o (@ (@ tptp.insert5175938949040314269_nat_o A) A3)) B3)) (and (not (@ (@ tptp.member6576561426505652726_nat_o A) B3)) (= tptp.bot_bo7824918357723582233_nat_o (@ (@ tptp.inf_in1906310914598751387_nat_o A3) B3))))))
% 3.15/3.51 (assert (forall ((A tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (= tptp.bot_bo2099793752762293965at_nat (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.insert8211810215607154385at_nat A) A3)) B3)) (and (not (@ (@ tptp.member8440522571783428010at_nat A) B3)) (= tptp.bot_bo2099793752762293965at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3))))))
% 3.15/3.51 (assert (forall ((A tptp.nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (= (= tptp.bot_bot_set_nat (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.insert_nat2 A) A3)) B3)) (and (not (@ (@ tptp.member_nat2 A) B3)) (= tptp.bot_bot_set_nat (@ (@ tptp.inf_inf_set_nat A3) B3))))))
% 3.15/3.51 (assert (forall ((A tptp.int) (A3 tptp.set_int) (B3 tptp.set_int)) (= (= tptp.bot_bot_set_int (@ (@ tptp.inf_inf_set_int (@ (@ tptp.insert_int2 A) A3)) B3)) (and (not (@ (@ tptp.member_int2 A) B3)) (= tptp.bot_bot_set_int (@ (@ tptp.inf_inf_set_int A3) B3))))))
% 3.15/3.51 (assert (forall ((B3 tptp.set_Pr4532377907799695533_nat_o) (A (-> tptp.produc3658429121746597890et_nat Bool)) (A3 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.inf_in1906310914598751387_nat_o B3))) (= (= (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o A) A3)) tptp.bot_bo7824918357723582233_nat_o) (and (not (@ (@ tptp.member6576561426505652726_nat_o A) B3)) (= (@ _let_1 A3) tptp.bot_bo7824918357723582233_nat_o))))))
% 3.15/3.51 (assert (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (A tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat B3))) (= (= (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat A) A3)) tptp.bot_bo2099793752762293965at_nat) (and (not (@ (@ tptp.member8440522571783428010at_nat A) B3)) (= (@ _let_1 A3) tptp.bot_bo2099793752762293965at_nat))))))
% 3.15/3.51 (assert (forall ((B3 tptp.set_nat) (A tptp.nat) (A3 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat B3))) (= (= (@ _let_1 (@ (@ tptp.insert_nat2 A) A3)) tptp.bot_bot_set_nat) (and (not (@ (@ tptp.member_nat2 A) B3)) (= (@ _let_1 A3) tptp.bot_bot_set_nat))))))
% 3.15/3.51 (assert (forall ((B3 tptp.set_int) (A tptp.int) (A3 tptp.set_int)) (let ((_let_1 (@ tptp.inf_inf_set_int B3))) (= (= (@ _let_1 (@ (@ tptp.insert_int2 A) A3)) tptp.bot_bot_set_int) (and (not (@ (@ tptp.member_int2 A) B3)) (= (@ _let_1 A3) tptp.bot_bot_set_int))))))
% 3.15/3.51 (assert (forall ((A3 tptp.set_Pr4532377907799695533_nat_o) (B (-> tptp.produc3658429121746597890et_nat Bool)) (B3 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.inf_in1906310914598751387_nat_o A3))) (= (= tptp.bot_bo7824918357723582233_nat_o (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o B) B3))) (and (not (@ (@ tptp.member6576561426505652726_nat_o B) A3)) (= tptp.bot_bo7824918357723582233_nat_o (@ _let_1 B3)))))))
% 3.15/3.51 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B tptp.product_prod_nat_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A3))) (= (= tptp.bot_bo2099793752762293965at_nat (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat B) B3))) (and (not (@ (@ tptp.member8440522571783428010at_nat B) A3)) (= tptp.bot_bo2099793752762293965at_nat (@ _let_1 B3)))))))
% 3.15/3.51 (assert (forall ((A3 tptp.set_nat) (B tptp.nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A3))) (= (= tptp.bot_bot_set_nat (@ _let_1 (@ (@ tptp.insert_nat2 B) B3))) (and (not (@ (@ tptp.member_nat2 B) A3)) (= tptp.bot_bot_set_nat (@ _let_1 B3)))))))
% 3.15/3.51 (assert (forall ((A3 tptp.set_int) (B tptp.int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.inf_inf_set_int A3))) (= (= tptp.bot_bot_set_int (@ _let_1 (@ (@ tptp.insert_int2 B) B3))) (and (not (@ (@ tptp.member_int2 B) A3)) (= tptp.bot_bot_set_int (@ _let_1 B3)))))))
% 3.15/3.51 (assert (forall ((I2 tptp.int) (J tptp.int)) (= (= (@ (@ tptp.upto I2) J) tptp.nil_int) (@ (@ tptp.ord_less_int J) I2))))
% 3.15/3.51 (assert (forall ((I2 tptp.int) (J tptp.int)) (= (= tptp.nil_int (@ (@ tptp.upto I2) J)) (@ (@ tptp.ord_less_int J) I2))))
% 3.15/3.51 (assert (forall ((J tptp.int) (I2 tptp.int)) (=> (@ (@ tptp.ord_less_int J) I2) (= (@ (@ tptp.upto I2) J) tptp.nil_int))))
% 3.15/3.51 (assert (forall ((I2 tptp.int)) (= (@ (@ tptp.upto I2) I2) (@ (@ tptp.cons_int I2) tptp.nil_int))))
% 3.15/3.51 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) tptp.one_one_nat)))
% 3.15/3.51 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat)))
% 3.15/3.51 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M2))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 3.15/3.51 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))) (let ((_let_2 (@ tptp.numeral_numeral_int M2))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 3.15/3.51 (assert (forall ((A (-> tptp.produc3658429121746597890et_nat Bool)) (A3 tptp.set_Pr4532377907799695533_nat_o) (B3 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.inf_in1906310914598751387_nat_o A3))) (let ((_let_2 (@ _let_1 B3))) (let ((_let_3 (@ tptp.insert5175938949040314269_nat_o A))) (let ((_let_4 (@ _let_1 (@ _let_3 B3)))) (let ((_let_5 (@ (@ tptp.member6576561426505652726_nat_o A) A3))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))))
% 3.15/3.51 (assert (forall ((A tptp.int) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.inf_inf_set_int A3))) (let ((_let_2 (@ _let_1 B3))) (let ((_let_3 (@ tptp.insert_int2 A))) (let ((_let_4 (@ _let_1 (@ _let_3 B3)))) (let ((_let_5 (@ (@ tptp.member_int2 A) A3))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))))
% 3.15/3.51 (assert (forall ((A tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A3))) (let ((_let_2 (@ _let_1 B3))) (let ((_let_3 (@ tptp.insert8211810215607154385at_nat A))) (let ((_let_4 (@ _let_1 (@ _let_3 B3)))) (let ((_let_5 (@ (@ tptp.member8440522571783428010at_nat A) A3))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))))
% 3.15/3.51 (assert (forall ((A tptp.nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A3))) (let ((_let_2 (@ _let_1 B3))) (let ((_let_3 (@ tptp.insert_nat2 A))) (let ((_let_4 (@ _let_1 (@ _let_3 B3)))) (let ((_let_5 (@ (@ tptp.member_nat2 A) A3))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))))
% 3.15/3.51 (assert (forall ((A (-> tptp.produc3658429121746597890et_nat Bool)) (C2 tptp.set_Pr4532377907799695533_nat_o) (B3 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ (@ tptp.inf_in1906310914598751387_nat_o B3) C2))) (let ((_let_2 (@ tptp.insert5175938949040314269_nat_o A))) (let ((_let_3 (@ (@ tptp.inf_in1906310914598751387_nat_o (@ _let_2 B3)) C2))) (let ((_let_4 (@ (@ tptp.member6576561426505652726_nat_o A) C2))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 3.15/3.51 (assert (forall ((A tptp.int) (C2 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ (@ tptp.inf_inf_set_int B3) C2))) (let ((_let_2 (@ tptp.insert_int2 A))) (let ((_let_3 (@ (@ tptp.inf_inf_set_int (@ _let_2 B3)) C2))) (let ((_let_4 (@ (@ tptp.member_int2 A) C2))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 3.15/3.51 (assert (forall ((A tptp.product_prod_nat_nat) (C2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B3) C2))) (let ((_let_2 (@ tptp.insert8211810215607154385at_nat A))) (let ((_let_3 (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_2 B3)) C2))) (let ((_let_4 (@ (@ tptp.member8440522571783428010at_nat A) C2))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 3.15/3.51 (assert (forall ((A tptp.nat) (C2 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.inf_inf_set_nat B3) C2))) (let ((_let_2 (@ tptp.insert_nat2 A))) (let ((_let_3 (@ (@ tptp.inf_inf_set_nat (@ _let_2 B3)) C2))) (let ((_let_4 (@ (@ tptp.member_nat2 A) C2))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 3.15/3.51 (assert (= tptp.upto (lambda ((I4 tptp.int) (J2 tptp.int)) (@ (@ (@ tptp.upto_aux I4) J2) tptp.nil_int))))
% 3.15/3.51 (assert (= tptp.pred_numeral (lambda ((K4 tptp.num)) (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K4)) tptp.one_one_nat))))
% 3.15/3.51 (assert (forall ((X tptp.int) (Xa tptp.int) (Y tptp.list_int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int X) Xa))) (=> (= (@ (@ tptp.upto X) Xa) Y) (and (=> _let_1 (= Y (@ (@ tptp.cons_int X) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) Xa)))) (=> (not _let_1) (= Y tptp.nil_int)))))))
% 3.15/3.51 (assert (= tptp.upto (lambda ((I4 tptp.int) (J2 tptp.int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_eq_int I4) J2)) (@ (@ tptp.cons_int I4) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) J2))) tptp.nil_int))))
% 3.15/3.51 (assert (forall ((I2 tptp.int) (J tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I2) J) (= (@ (@ tptp.upto I2) J) (@ (@ tptp.cons_int I2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I2) tptp.one_one_int)) J))))))
% 3.15/3.51 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K))) (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 3.15/3.51 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.numeral_numeral_nat L)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 K))) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.pred_numeral L)) (@ tptp.numera6620942414471956472nteger K))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 3.15/3.51 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se569199155075624693atural (@ tptp.numeral_numeral_nat L)) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 K))) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.bit_se569199155075624693atural (@ tptp.pred_numeral L)) (@ tptp.numera5444537566228673987atural K))) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))))
% 3.15/3.51 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 3.15/3.51 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K)) (not (@ _let_2 L)))))) (let ((_let_4 (@ (@ tptp.bit_se725231765392027082nd_int K) L))) (let ((_let_5 (@ (@ tptp.insert_int2 tptp.zero_zero_int) (@ (@ tptp.insert_int2 (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_6 (and (@ (@ tptp.member_int2 K) _let_5) (@ (@ tptp.member_int2 L) _let_5)))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int K) L)) (and (=> _let_6 (= _let_4 (@ tptp.uminus_uminus_int _let_3))) (=> (not _let_6) (= _let_4 (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1))))))))))))))))
% 3.15/3.51 (assert (forall ((X tptp.int) (Xa tptp.int) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int X) Xa)))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ tptp.dvd_dvd_int _let_2))) (let ((_let_4 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_3 X)) (not (@ _let_3 Xa)))))) (let ((_let_5 (@ (@ tptp.insert_int2 tptp.zero_zero_int) (@ (@ tptp.insert_int2 (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_6 (and (@ (@ tptp.member_int2 X) _let_5) (@ (@ tptp.member_int2 Xa) _let_5)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X) Xa) Y) (=> _let_1 (not (=> (and (=> _let_6 (= Y (@ tptp.uminus_uminus_int _let_4))) (=> (not _let_6) (= Y (@ (@ tptp.plus_plus_int _let_4) (@ (@ tptp.times_times_int _let_2) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X) _let_2)) (@ (@ tptp.divide_divide_int Xa) _let_2))))))) (not _let_1)))))))))))))
% 3.15/3.51 (assert (forall ((N tptp.num)) (= (@ tptp.bit_se2119862282449309892nteger (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2119862282449309892nteger (@ tptp.pred_numeral N)))))))
% 3.15/3.51 (assert (forall ((N tptp.num)) (= (@ tptp.bit_se943457434206027407atural (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural) (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) (@ tptp.bit_se943457434206027407atural (@ tptp.pred_numeral N)))))))
% 3.15/3.51 (assert (forall ((N tptp.num)) (= (@ tptp.bit_se2000444600071755411sk_int (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int (@ tptp.pred_numeral N)))))))
% 3.15/3.51 (assert (forall ((N tptp.num)) (= (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.pred_numeral N)))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (K tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N) K) (@ tptp.bit_se2000444600071755411sk_int N)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.plus_plus_int K) tptp.one_one_int)))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se3222712562003087583nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 X))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 Y))) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se3222712562003087583nteger (@ tptp.numera6620942414471956472nteger X)) (@ tptp.numera6620942414471956472nteger Y)))))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se2046307713759805098atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 X))) (@ tptp.numera5444537566228673987atural (@ tptp.bit1 Y))) (@ (@ tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural) (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se2046307713759805098atural (@ tptp.numera5444537566228673987atural X)) (@ tptp.numera5444537566228673987atural Y)))))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y)))))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y)))))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se3222712562003087583nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 X))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Y))) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se3222712562003087583nteger (@ tptp.numera6620942414471956472nteger X)) (@ tptp.numera6620942414471956472nteger Y)))))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se2046307713759805098atural (@ tptp.numera5444537566228673987atural (@ tptp.bit1 X))) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 Y))) (@ (@ tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural) (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se2046307713759805098atural (@ tptp.numera5444537566228673987atural X)) (@ tptp.numera5444537566228673987atural Y)))))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y)))))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y)))))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se3222712562003087583nteger A) tptp.one_one_Code_integer) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.zero_n356916108424825756nteger _let_1))) (@ tptp.zero_n356916108424825756nteger (not _let_1)))))))
% 3.15/3.51 (assert (forall ((A tptp.code_natural)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_natural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se2046307713759805098atural A) tptp.one_one_Code_natural) (@ (@ tptp.minus_7197305767214868737atural (@ (@ tptp.plus_p4538020629002901425atural A) (@ tptp.zero_n8403883297036319079atural _let_1))) (@ tptp.zero_n8403883297036319079atural (not _let_1)))))))
% 3.15/3.51 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se6528837805403552850or_nat A) tptp.one_one_nat) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))))
% 3.15/3.51 (assert (forall ((A tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se6526347334894502574or_int A) tptp.one_one_int) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) (@ tptp.zero_n2684676970156552555ol_int _let_1))) (@ tptp.zero_n2684676970156552555ol_int (not _let_1)))))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se3222712562003087583nteger tptp.one_one_Code_integer) A) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.zero_n356916108424825756nteger _let_1))) (@ tptp.zero_n356916108424825756nteger (not _let_1)))))))
% 3.15/3.51 (assert (forall ((A tptp.code_natural)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_natural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se2046307713759805098atural tptp.one_one_Code_natural) A) (@ (@ tptp.minus_7197305767214868737atural (@ (@ tptp.plus_p4538020629002901425atural A) (@ tptp.zero_n8403883297036319079atural _let_1))) (@ tptp.zero_n8403883297036319079atural (not _let_1)))))))
% 3.15/3.51 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se6528837805403552850or_nat tptp.one_one_nat) A) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))))
% 3.15/3.51 (assert (forall ((A tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se6526347334894502574or_int tptp.one_one_int) A) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) (@ tptp.zero_n2684676970156552555ol_int _let_1))) (@ tptp.zero_n2684676970156552555ol_int (not _let_1)))))))
% 3.15/3.51 (assert (= (@ tptp.bit_se2119862282449309892nteger (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_Code_integer))
% 3.15/3.51 (assert (= (@ tptp.bit_se2000444600071755411sk_int (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_int))
% 3.15/3.51 (assert (= (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1745604003318907178nteger N) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.bit_se2119862282449309892nteger N))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.bit_se2000444600071755411sk_int N))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se3222712562003087583nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 X))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Y))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se3222712562003087583nteger (@ tptp.numera6620942414471956472nteger X)) (@ tptp.numera6620942414471956472nteger Y))))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se2046307713759805098atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 X))) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 Y))) (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se2046307713759805098atural (@ tptp.numera5444537566228673987atural X)) (@ tptp.numera5444537566228673987atural Y))))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y))))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y))))))
% 3.15/3.51 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se3222712562003087583nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Y))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 Y)))))
% 3.15/3.51 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se2046307713759805098atural tptp.one_one_Code_natural) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 Y))) (@ tptp.numera5444537566228673987atural (@ tptp.bit1 Y)))))
% 3.15/3.51 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y)))))
% 3.15/3.51 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y)))))
% 3.15/3.51 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se3222712562003087583nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 Y))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Y)))))
% 3.15/3.51 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se2046307713759805098atural tptp.one_one_Code_natural) (@ tptp.numera5444537566228673987atural (@ tptp.bit1 Y))) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 Y)))))
% 3.15/3.51 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y)))))
% 3.15/3.51 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y)))))
% 3.15/3.51 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se3222712562003087583nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 X))) tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 X)))))
% 3.15/3.51 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se2046307713759805098atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 X))) tptp.one_one_Code_natural) (@ tptp.numera5444537566228673987atural (@ tptp.bit1 X)))))
% 3.15/3.51 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))))
% 3.15/3.51 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 X)))))
% 3.15/3.51 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se3222712562003087583nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 X))) tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 X)))))
% 3.15/3.51 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se2046307713759805098atural (@ tptp.numera5444537566228673987atural (@ tptp.bit1 X))) tptp.one_one_Code_natural) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 X)))))
% 3.15/3.51 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 X)))))
% 3.15/3.51 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 X)))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se3222712562003087583nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 X))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 Y))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se3222712562003087583nteger (@ tptp.numera6620942414471956472nteger X)) (@ tptp.numera6620942414471956472nteger Y))))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se2046307713759805098atural (@ tptp.numera5444537566228673987atural (@ tptp.bit1 X))) (@ tptp.numera5444537566228673987atural (@ tptp.bit1 Y))) (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se2046307713759805098atural (@ tptp.numera5444537566228673987atural X)) (@ tptp.numera5444537566228673987atural Y))))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y))))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y))))))
% 3.15/3.51 (assert (= tptp.bit_se2161824704523386999it_nat (lambda ((M3 tptp.nat) (N3 tptp.nat)) (@ (@ tptp.bit_se6528837805403552850or_nat N3) (@ (@ tptp.bit_se547839408752420682it_nat M3) tptp.one_one_nat)))))
% 3.15/3.51 (assert (= tptp.bit_se2159334234014336723it_int (lambda ((N3 tptp.nat) (K4 tptp.int)) (@ (@ tptp.bit_se6526347334894502574or_int K4) (@ (@ tptp.bit_se545348938243370406it_int N3) tptp.one_one_int)))))
% 3.15/3.51 (assert (= tptp.bit_se1345352211410354436nteger (lambda ((N3 tptp.nat) (A2 tptp.code_integer)) (@ (@ tptp.bit_se3222712562003087583nteger A2) (@ (@ tptp.bit_se7788150548672797655nteger N3) tptp.one_one_Code_integer)))))
% 3.15/3.51 (assert (= tptp.bit_se2159334234014336723it_int (lambda ((N3 tptp.nat) (A2 tptp.int)) (@ (@ tptp.bit_se6526347334894502574or_int A2) (@ (@ tptp.bit_se545348938243370406it_int N3) tptp.one_one_int)))))
% 3.15/3.51 (assert (= tptp.bit_se2161824704523386999it_nat (lambda ((N3 tptp.nat) (A2 tptp.nat)) (@ (@ tptp.bit_se6528837805403552850or_nat A2) (@ (@ tptp.bit_se547839408752420682it_nat N3) tptp.one_one_nat)))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (= (@ _let_1 K) (@ tptp.bit_se2000444600071755411sk_int N)) (= (@ _let_1 (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) tptp.zero_zero_int)))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_int (@ tptp.bit_se2000444600071755411sk_int N)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))
% 3.15/3.51 (assert (= tptp.bit_se2002935070580805687sk_nat (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)) tptp.one_one_nat))))
% 3.15/3.51 (assert (= tptp.bit_se2000444600071755411sk_int (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N3)) tptp.one_one_int))))
% 3.15/3.51 (assert (= tptp.bit_se2119862282449309892nteger (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N3)) tptp.one_one_Code_integer))))
% 3.15/3.51 (assert (= tptp.bit_se943457434206027407atural (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_7197305767214868737atural (@ (@ tptp.power_7079662738309270450atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) N3)) tptp.one_one_Code_natural))))
% 3.15/3.51 (assert (= tptp.bit_se2000444600071755411sk_int (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N3)) tptp.one_one_int))))
% 3.15/3.51 (assert (= tptp.bit_se2002935070580805687sk_nat (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)) tptp.one_one_nat))))
% 3.15/3.51 (assert (forall ((A0 tptp.int) (A1 tptp.int) (P2 (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int A0) A1)) (=> (forall ((K2 tptp.int) (L4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.insert_int2 tptp.zero_zero_int) (@ (@ tptp.insert_int2 (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int K2) L4)) (=> (=> (not (and (@ (@ tptp.member_int2 K2) _let_2) (@ (@ tptp.member_int2 L4) _let_2))) (@ (@ P2 (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L4) _let_1))) (@ (@ P2 K2) L4)))))) (@ (@ P2 A0) A1)))))
% 3.15/3.51 (assert (forall ((I2 tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.upto I2) J))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int I2) J))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I2) J)) (and (=> _let_2 (= _let_1 (@ (@ tptp.cons_int I2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I2) tptp.one_one_int)) J)))) (=> (not _let_2) (= _let_1 tptp.nil_int))))))))
% 3.15/3.51 (assert (forall ((X tptp.int) (Xa tptp.int) (Y tptp.list_int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int X) Xa)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int X) Xa))) (=> (= (@ (@ tptp.upto X) Xa) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y (@ (@ tptp.cons_int X) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) Xa)))) (=> (not _let_2) (= Y tptp.nil_int))) (not _let_1)))))))))
% 3.15/3.51 (assert (forall ((A0 tptp.int) (A1 tptp.int) (P2 (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int A0) A1)) (=> (forall ((I3 tptp.int) (J3 tptp.int)) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I3) J3)) (=> (=> (@ (@ tptp.ord_less_eq_int I3) J3) (@ (@ P2 (@ (@ tptp.plus_plus_int I3) tptp.one_one_int)) J3)) (@ (@ P2 I3) J3)))) (@ (@ P2 A0) A1)))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (F2 (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F2 (@ (@ tptp.plus_plus_nat I3) tptp.one_one_nat))) (@ F2 I3)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F2 tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F2 N)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I3) N) (= (@ F2 I3) K))))))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1080825931792720795nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 X))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 Y))) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1080825931792720795nteger (@ tptp.numera6620942414471956472nteger X)) (@ tptp.numera6620942414471956472nteger Y)))))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se9127793120404214118atural (@ tptp.numera5444537566228673987atural (@ tptp.bit1 X))) (@ tptp.numera5444537566228673987atural (@ tptp.bit1 Y))) (@ (@ tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural) (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se9127793120404214118atural (@ tptp.numera5444537566228673987atural X)) (@ tptp.numera5444537566228673987atural Y)))))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y)))))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y)))))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1080825931792720795nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 X))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Y))) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1080825931792720795nteger (@ tptp.numera6620942414471956472nteger X)) (@ tptp.numera6620942414471956472nteger Y)))))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se9127793120404214118atural (@ tptp.numera5444537566228673987atural (@ tptp.bit1 X))) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 Y))) (@ (@ tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural) (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se9127793120404214118atural (@ tptp.numera5444537566228673987atural X)) (@ tptp.numera5444537566228673987atural Y)))))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y)))))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y)))))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1080825931792720795nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 X))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 Y))) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1080825931792720795nteger (@ tptp.numera6620942414471956472nteger X)) (@ tptp.numera6620942414471956472nteger Y)))))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se9127793120404214118atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 X))) (@ tptp.numera5444537566228673987atural (@ tptp.bit1 Y))) (@ (@ tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural) (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se9127793120404214118atural (@ tptp.numera5444537566228673987atural X)) (@ tptp.numera5444537566228673987atural Y)))))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y)))))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y)))))))
% 3.15/3.51 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M2))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M2)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))))
% 3.15/3.51 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 3.15/3.51 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.abs_abs_int A)) (= A tptp.zero_zero_int))))
% 3.15/3.51 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ tptp.abs_abs_rat A)) (= A tptp.zero_zero_rat))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.abs_abs_Code_integer A)) (= A tptp.zero_z3403309356797280102nteger))))
% 3.15/3.51 (assert (forall ((A tptp.int)) (= (= (@ tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 3.15/3.51 (assert (forall ((A tptp.rat)) (= (= (@ tptp.abs_abs_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 3.15/3.51 (assert (= (@ tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))
% 3.15/3.51 (assert (= (@ tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 3.15/3.51 (assert (= (@ tptp.abs_abs_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 3.15/3.51 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 3.15/3.51 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ (@ tptp.times_times_int _let_1) _let_1) (@ (@ tptp.times_times_int A) A)))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) (@ (@ tptp.times_3573771949741848930nteger A) A)))))
% 3.15/3.51 (assert (= (@ tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 3.15/3.51 (assert (= (@ tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))
% 3.15/3.51 (assert (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))
% 3.15/3.51 (assert (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 3.15/3.51 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))))
% 3.15/3.51 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 3.15/3.51 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 3.15/3.51 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) A) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A))))
% 3.15/3.51 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) A) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 3.15/3.51 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 3.15/3.51 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A)) (not (= A tptp.zero_z3403309356797280102nteger)))))
% 3.15/3.51 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A)) (not (= A tptp.zero_zero_rat)))))
% 3.15/3.51 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.abs_abs_int A)) (not (= A tptp.zero_zero_int)))))
% 3.15/3.51 (assert (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 3.15/3.51 (assert (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 3.15/3.51 (assert (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 3.15/3.51 (assert (forall ((X tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.bit_se1080825931792720795nteger X) _let_1) _let_1))))
% 3.15/3.51 (assert (forall ((X tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_se1409905431419307370or_int X) _let_1) _let_1))))
% 3.15/3.51 (assert (forall ((X tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.bit_se1080825931792720795nteger _let_1) X) _let_1))))
% 3.15/3.51 (assert (forall ((X tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_se1409905431419307370or_int _let_1) X) _let_1))))
% 3.15/3.51 (assert (forall ((X tptp.int)) (= (@ (@ tptp.dvd_dvd_int X) tptp.one_one_int) (= (@ tptp.abs_abs_int X) tptp.one_one_int))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 3.15/3.51 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (= (@ tptp.abs_abs_rat A) (@ tptp.uminus_uminus_rat A)))))
% 3.15/3.51 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (= (@ tptp.abs_abs_int A) (@ tptp.uminus_uminus_int A)))))
% 3.15/3.51 (assert (= (@ tptp.bit_ri7632146776885996613nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 3.15/3.51 (assert (= (@ tptp.bit_ri7919022796975470100ot_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 3.15/3.51 (assert (= (@ tptp.bit_ri7632146776885996613nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 3.15/3.51 (assert (= (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 3.15/3.51 (assert (forall ((Y tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 Y)))) (= (@ (@ tptp.bit_se1080825931792720795nteger tptp.one_one_Code_integer) _let_1) _let_1))))
% 3.15/3.51 (assert (forall ((Y tptp.num)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit1 Y)))) (= (@ (@ tptp.bit_se9127793120404214118atural tptp.one_one_Code_natural) _let_1) _let_1))))
% 3.15/3.51 (assert (forall ((Y tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit1 Y)))) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))))
% 3.15/3.51 (assert (forall ((Y tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat tptp.one_one_nat) _let_1) _let_1))))
% 3.15/3.51 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 X)))) (= (@ (@ tptp.bit_se1080825931792720795nteger _let_1) tptp.one_one_Code_integer) _let_1))))
% 3.15/3.51 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit1 X)))) (= (@ (@ tptp.bit_se9127793120404214118atural _let_1) tptp.one_one_Code_natural) _let_1))))
% 3.15/3.51 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit1 X)))) (= (@ (@ tptp.bit_se1409905431419307370or_int _let_1) tptp.one_one_int) _let_1))))
% 3.15/3.51 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat _let_1) tptp.one_one_nat) _let_1))))
% 3.15/3.51 (assert (forall ((A tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ tptp.abs_abs_int (@ tptp.sgn_sgn_int A)) tptp.one_one_int))))
% 3.15/3.51 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ tptp.abs_abs_rat (@ tptp.sgn_sgn_rat A)) tptp.one_one_rat))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (@ tptp.abs_abs_Code_integer (@ tptp.sgn_sgn_Code_integer A)) tptp.one_one_Code_integer))))
% 3.15/3.51 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))))) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))))
% 3.15/3.51 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))))) (= (@ (@ tptp.bit_se1409905431419307370or_int _let_1) tptp.one_one_int) _let_1))))
% 3.15/3.51 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.bit_se1080825931792720795nteger X) (@ tptp.bit_ri7632146776885996613nteger X)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 3.15/3.51 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int X) (@ tptp.bit_ri7919022796975470100ot_int X)) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 3.15/3.51 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.bit_se1080825931792720795nteger (@ tptp.bit_ri7632146776885996613nteger X)) X) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 3.15/3.51 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.bit_ri7919022796975470100ot_int X)) X) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 3.15/3.51 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.bit_se3222712562003087583nteger X) (@ tptp.bit_ri7632146776885996613nteger X)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 3.15/3.51 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int X) (@ tptp.bit_ri7919022796975470100ot_int X)) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 3.15/3.51 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.bit_se3222712562003087583nteger (@ tptp.bit_ri7632146776885996613nteger X)) X) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 3.15/3.51 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.bit_ri7919022796975470100ot_int X)) X) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 3.15/3.51 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.bit_se3222712562003087583nteger X) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.bit_ri7632146776885996613nteger X))))
% 3.15/3.51 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int X) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.bit_ri7919022796975470100ot_int X))))
% 3.15/3.51 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.bit_se3222712562003087583nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X) (@ tptp.bit_ri7632146776885996613nteger X))))
% 3.15/3.51 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.uminus_uminus_int tptp.one_one_int)) X) (@ tptp.bit_ri7919022796975470100ot_int X))))
% 3.15/3.51 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int Z)) tptp.one_one_int) (= Z tptp.zero_zero_int))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1080825931792720795nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 X))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Y))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1080825931792720795nteger (@ tptp.numera6620942414471956472nteger X)) (@ tptp.numera6620942414471956472nteger Y))))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se9127793120404214118atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 X))) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 Y))) (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se9127793120404214118atural (@ tptp.numera5444537566228673987atural X)) (@ tptp.numera5444537566228673987atural Y))))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y))))))
% 3.15/3.51 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y))))))
% 3.15/3.51 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se1080825931792720795nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 X))) tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 X)))))
% 3.15/3.51 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se9127793120404214118atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 X))) tptp.one_one_Code_natural) (@ tptp.numera5444537566228673987atural (@ tptp.bit1 X)))))
% 3.15/3.51 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 X)))))
% 3.15/3.51 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))))
% 3.15/3.51 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se1080825931792720795nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Y))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 Y)))))
% 3.15/3.51 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se9127793120404214118atural tptp.one_one_Code_natural) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 Y))) (@ tptp.numera5444537566228673987atural (@ tptp.bit1 Y)))))
% 3.15/3.51 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y)))))
% 3.15/3.51 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y)))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se7788150548672797655nteger N) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.bit_ri7632146776885996613nteger (@ tptp.bit_se2119862282449309892nteger N)))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.bit_se2000444600071755411sk_int N)))))
% 3.15/3.51 (assert (= (@ tptp.bit_ri7632146776885996613nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 3.15/3.51 (assert (= (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))
% 3.15/3.51 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M2))) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int _let_2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)) (@ (@ tptp.minus_minus_int _let_1) tptp.one_one_int))))))))
% 3.15/3.51 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M2))) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int _let_2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)) (@ (@ tptp.minus_minus_int _let_1) tptp.one_one_int))))))))
% 3.15/3.51 (assert (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) (@ tptp.bit_ri7919022796975470100ot_int tptp.zero_zero_int)))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) B) (@ (@ tptp.ord_le3102999989581377725nteger A) B))))
% 3.15/3.51 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B) (@ (@ tptp.ord_less_eq_rat A) B))))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B) (@ (@ tptp.ord_less_eq_int A) B))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.abs_abs_Code_integer A))))
% 3.15/3.51 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ tptp.abs_abs_rat A))))
% 3.15/3.51 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ tptp.abs_abs_int A))))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))))
% 3.15/3.51 (assert (= (@ tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 3.15/3.51 (assert (= (@ tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))
% 3.15/3.51 (assert (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B)) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B) A)))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) B)) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger B) A)))))
% 3.15/3.51 (assert (= tptp.bit_se7882103937844011126it_nat (lambda ((M3 tptp.nat) (N3 tptp.nat)) (@ (@ tptp.bit_se1412395901928357646or_nat N3) (@ (@ tptp.bit_se547839408752420682it_nat M3) tptp.one_one_nat)))))
% 3.15/3.51 (assert (forall ((M2 tptp.num)) (let ((_let_1 (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int))) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M2))) _let_1) _let_1))))
% 3.15/3.51 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))))) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))))
% 3.15/3.51 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))))))
% 3.15/3.51 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M2))) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) (@ tptp.bit_ri7919022796975470100ot_int tptp.zero_zero_int))))
% 3.15/3.51 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (= (@ (@ tptp.bit_se3949692690581998587nteger X) Y) tptp.zero_z3403309356797280102nteger) (=> (= (@ (@ tptp.bit_se1080825931792720795nteger X) Y) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (= (@ tptp.bit_ri7632146776885996613nteger X) Y)))))
% 3.15/3.51 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X) Y) tptp.zero_zero_int) (=> (= (@ (@ tptp.bit_se1409905431419307370or_int X) Y) (@ tptp.uminus_uminus_int tptp.one_one_int)) (= (@ tptp.bit_ri7919022796975470100ot_int X) Y)))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A))))
% 3.15/3.51 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A))))
% 3.15/3.51 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.abs_abs_int A))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger))))
% 3.15/3.51 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat))))
% 3.15/3.51 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))))
% 3.15/3.51 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 3.15/3.51 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.plus_p5714425477246183910nteger A) B))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))))
% 3.15/3.51 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.plus_plus_rat A) B))) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.plus_plus_int A) B))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger B) A)))))
% 3.15/3.51 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat B) A)))))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B) A)))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) B)))))
% 3.15/3.51 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B)))))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B)))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) B)))))
% 3.15/3.51 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B)))))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B)))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer B))) (let ((_let_2 (@ tptp.abs_abs_Code_integer A))) (=> (@ (@ tptp.ord_le6747313008572928689nteger _let_2) C) (=> (@ (@ tptp.ord_le6747313008572928689nteger _let_1) D2) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger _let_2) _let_1)) (@ (@ tptp.times_3573771949741848930nteger C) D2))))))))
% 3.15/3.51 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat B))) (let ((_let_2 (@ tptp.abs_abs_rat A))) (=> (@ (@ tptp.ord_less_rat _let_2) C) (=> (@ (@ tptp.ord_less_rat _let_1) D2) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat _let_2) _let_1)) (@ (@ tptp.times_times_rat C) D2))))))))
% 3.15/3.51 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int B))) (let ((_let_2 (@ tptp.abs_abs_int A))) (=> (@ (@ tptp.ord_less_int _let_2) C) (=> (@ (@ tptp.ord_less_int _let_1) D2) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int _let_2) _let_1)) (@ (@ tptp.times_times_int C) D2))))))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) B)))))
% 3.15/3.51 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B)))))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B)))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 3.15/3.51 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B))))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) B) (and (@ (@ tptp.ord_le3102999989581377725nteger A) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B)))))
% 3.15/3.51 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B) (and (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B)))))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B) (and (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B)))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 3.15/3.51 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 3.15/3.51 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 3.15/3.51 (assert (= tptp.abs_abs_rat (lambda ((K4 tptp.rat)) (@ (@ tptp.times_times_rat K4) (@ tptp.sgn_sgn_rat K4)))))
% 3.15/3.51 (assert (= tptp.abs_abs_int (lambda ((K4 tptp.int)) (@ (@ tptp.times_times_int K4) (@ tptp.sgn_sgn_int K4)))))
% 3.15/3.51 (assert (= tptp.abs_abs_Code_integer (lambda ((K4 tptp.code_integer)) (@ (@ tptp.times_3573771949741848930nteger K4) (@ tptp.sgn_sgn_Code_integer K4)))))
% 3.15/3.51 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat A)) (@ tptp.sgn_sgn_rat A)) A)))
% 3.15/3.51 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A)) (@ tptp.sgn_sgn_int A)) A)))
% 3.15/3.51 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.sgn_sgn_Code_integer A)) A)))
% 3.15/3.51 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.sgn_sgn_rat A)) (@ tptp.abs_abs_rat A)) A)))
% 3.15/3.51 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A)) (@ tptp.abs_abs_int A)) A)))
% 3.15/3.51 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.sgn_sgn_Code_integer A)) (@ tptp.abs_abs_Code_integer A)) A)))
% 3.15/3.51 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.sgn_sgn_rat X)) (@ tptp.abs_abs_rat X)) X)))
% 3.15/3.51 (assert (forall ((X tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int X)) (@ tptp.abs_abs_int X)) X)))
% 3.15/3.51 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.sgn_sgn_Code_integer X)) (@ tptp.abs_abs_Code_integer X)) X)))
% 3.15/3.51 (assert (forall ((M2 tptp.int) (N tptp.int)) (=> (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int M2) N)) tptp.one_one_int) (= (@ tptp.abs_abs_int M2) tptp.one_one_int))))
% 3.15/3.51 (assert (= tptp.bit_se7879613467334960850it_int (lambda ((N3 tptp.nat) (K4 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int K4) (@ (@ tptp.bit_se545348938243370406it_int N3) tptp.one_one_int)))))
% 3.15/3.51 (assert (@ (@ (@ (@ (@ tptp.boolea5643492148547655015nteger tptp.bit_se3949692690581998587nteger) tptp.bit_se1080825931792720795nteger) tptp.bit_ri7632146776885996613nteger) tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 3.15/3.51 (assert (@ (@ (@ (@ (@ tptp.boolea5469654029284665142ra_int tptp.bit_se725231765392027082nd_int) tptp.bit_se1409905431419307370or_int) tptp.bit_ri7919022796975470100ot_int) tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 3.15/3.51 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M2))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M2)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))))
% 3.15/3.51 (assert (forall ((X tptp.rat)) (=> (forall ((E tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X)) E))) (= X tptp.zero_zero_rat))))
% 3.15/3.51 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer Y)) X) (@ tptp.abs_abs_Code_integer (@ (@ tptp.times_3573771949741848930nteger Y) X))))))
% 3.15/3.51 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X) (= (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat Y)) X) (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat Y) X))))))
% 3.15/3.51 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int Y)) X) (@ tptp.abs_abs_int (@ (@ tptp.times_times_int Y) X))))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (and (or (@ _let_1 A) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger)) (or (@ _let_1 B) (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger))) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))))))
% 3.15/3.51 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (and (or (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (or (@ _let_1 B) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat))) (= (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))))))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (and (or (@ _let_1 A) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)) (or (@ _let_1 B) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int))) (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.abs_abs_Code_integer A))) tptp.zero_z3403309356797280102nteger)))
% 3.15/3.51 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.abs_abs_rat A))) tptp.zero_zero_rat)))
% 3.15/3.51 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.abs_abs_int A))) tptp.zero_zero_int)))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) B))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))))
% 3.15/3.51 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B))) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger C) D2)))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) C))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger B) D2))))))
% 3.15/3.51 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat C) D2)))) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) C))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat B) D2))))))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int C) D2)))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) C))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B) D2))))))
% 3.15/3.51 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (= (@ tptp.abs_abs_int A) (@ tptp.uminus_uminus_int A)))))
% 3.15/3.51 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ tptp.abs_abs_rat A) (@ tptp.uminus_uminus_rat A)))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 3.15/3.51 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int (@ tptp.sgn_sgn_int A)))) (let ((_let_2 (= A tptp.zero_zero_int))) (and (=> _let_2 (= _let_1 tptp.zero_zero_int)) (=> (not _let_2) (= _let_1 tptp.one_one_int)))))))
% 3.15/3.51 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat (@ tptp.sgn_sgn_rat A)))) (let ((_let_2 (= A tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_rat)) (=> (not _let_2) (= _let_1 tptp.one_one_rat)))))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer (@ tptp.sgn_sgn_Code_integer A)))) (let ((_let_2 (= A tptp.zero_z3403309356797280102nteger))) (and (=> _let_2 (= _let_1 tptp.zero_z3403309356797280102nteger)) (=> (not _let_2) (= _let_1 tptp.one_one_Code_integer)))))))
% 3.15/3.51 (assert (= tptp.uminus1351360451143612070nteger (lambda ((A2 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.bit_ri7632146776885996613nteger A2)) tptp.one_one_Code_integer))))
% 3.15/3.51 (assert (= tptp.uminus_uminus_int (lambda ((A2 tptp.int)) (@ (@ tptp.plus_plus_int (@ tptp.bit_ri7919022796975470100ot_int A2)) tptp.one_one_int))))
% 3.15/3.51 (assert (= tptp.uminus1351360451143612070nteger (lambda ((A2 tptp.code_integer)) (@ tptp.bit_ri7632146776885996613nteger (@ (@ tptp.minus_8373710615458151222nteger A2) tptp.one_one_Code_integer)))))
% 3.15/3.51 (assert (= tptp.uminus_uminus_int (lambda ((A2 tptp.int)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.minus_minus_int A2) tptp.one_one_int)))))
% 3.15/3.51 (assert (= tptp.bit_ri7632146776885996613nteger (lambda ((A2 tptp.code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger A2)) tptp.one_one_Code_integer))))
% 3.15/3.51 (assert (= tptp.bit_ri7919022796975470100ot_int (lambda ((A2 tptp.int)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int A2)) tptp.one_one_int))))
% 3.15/3.51 (assert (= tptp.bit_ri7919022796975470100ot_int (lambda ((K4 tptp.int)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int K4)) tptp.one_one_int))))
% 3.15/3.51 (assert (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) tptp.zero_zero_int))
% 3.15/3.51 (assert (= tptp.bit_se2793503036327961859nteger (lambda ((N3 tptp.nat) (A2 tptp.code_integer)) (@ (@ tptp.bit_se1080825931792720795nteger A2) (@ (@ tptp.bit_se7788150548672797655nteger N3) tptp.one_one_Code_integer)))))
% 3.15/3.51 (assert (= tptp.bit_se7879613467334960850it_int (lambda ((N3 tptp.nat) (A2 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int A2) (@ (@ tptp.bit_se545348938243370406it_int N3) tptp.one_one_int)))))
% 3.15/3.51 (assert (= tptp.bit_se7882103937844011126it_nat (lambda ((N3 tptp.nat) (A2 tptp.nat)) (@ (@ tptp.bit_se1412395901928357646or_nat A2) (@ (@ tptp.bit_se547839408752420682it_nat N3) tptp.one_one_nat)))))
% 3.15/3.51 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M2))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M2)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))))
% 3.15/3.51 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M2))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M2)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))))
% 3.15/3.51 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N3 tptp.nat) (K4 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int K4) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se545348938243370406it_int N3) tptp.one_one_int))))))
% 3.15/3.51 (assert (forall ((X tptp.code_integer)) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.abs_abs_Code_integer X)))))
% 3.15/3.51 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.abs_abs_rat X)))))
% 3.15/3.51 (assert (forall ((X tptp.int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.abs_abs_int X)))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (let ((_let_2 (@ tptp.bit_se1080825931792720795nteger A))) (let ((_let_3 (@ tptp.bit_se3949692690581998587nteger A))) (=> (= (@ _let_3 X) tptp.zero_z3403309356797280102nteger) (=> (= (@ _let_2 X) _let_1) (=> (= (@ _let_3 Y) tptp.zero_z3403309356797280102nteger) (=> (= (@ _let_2 Y) _let_1) (= X Y))))))))))
% 3.15/3.51 (assert (forall ((A tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (let ((_let_2 (@ tptp.bit_se1409905431419307370or_int A))) (let ((_let_3 (@ tptp.bit_se725231765392027082nd_int A))) (=> (= (@ _let_3 X) tptp.zero_zero_int) (=> (= (@ _let_2 X) _let_1) (=> (= (@ _let_3 Y) tptp.zero_zero_int) (=> (= (@ _let_2 Y) _let_1) (= X Y))))))))))
% 3.15/3.51 (assert (forall ((M2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 M2)))) (= (@ (@ tptp.bit_se725231765392027082nd_int _let_1) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) _let_1))))
% 3.15/3.51 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) tptp.one_one_int)))
% 3.15/3.51 (assert (forall ((M2 tptp.int) (N tptp.int)) (=> (not (= M2 tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int M2) N)) M2) (= (@ tptp.abs_abs_int N) tptp.one_one_int)))))
% 3.15/3.51 (assert (= tptp.bit_se8260200283734997820nteger (lambda ((N3 tptp.nat) (A2 tptp.code_integer)) (@ (@ tptp.bit_se3949692690581998587nteger A2) (@ tptp.bit_ri7632146776885996613nteger (@ (@ tptp.bit_se7788150548672797655nteger N3) tptp.one_one_Code_integer))))))
% 3.15/3.51 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N3 tptp.nat) (A2 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int A2) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se545348938243370406it_int N3) tptp.one_one_int))))))
% 3.15/3.51 (assert (forall ((X tptp.code_integer)) (= (= (@ (@ tptp.power_8256067586552552935nteger X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer) (= (@ tptp.abs_abs_Code_integer X) tptp.one_one_Code_integer))))
% 3.15/3.51 (assert (forall ((X tptp.rat)) (= (= (@ (@ tptp.power_power_rat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat) (= (@ tptp.abs_abs_rat X) tptp.one_one_rat))))
% 3.15/3.51 (assert (forall ((X tptp.int)) (= (= (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int) (= (@ tptp.abs_abs_int X) tptp.one_one_int))))
% 3.15/3.51 (assert (forall ((M2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M2))) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.bit0 M2)))))
% 3.15/3.51 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) tptp.zero_zero_int)))
% 3.15/3.51 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K4 tptp.int) (L3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (= K4 _let_2)) (@ tptp.bit_ri7919022796975470100ot_int L3)) (@ (@ (@ tptp.if_int (= L3 _let_2)) (@ tptp.bit_ri7919022796975470100ot_int K4)) (@ (@ (@ tptp.if_int (= K4 tptp.zero_zero_int)) L3) (@ (@ (@ tptp.if_int (= L3 tptp.zero_zero_int)) K4) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.modulo_modulo_int K4) _let_1)) (@ (@ tptp.modulo_modulo_int L3) _let_1)))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.divide_divide_int K4) _let_1)) (@ (@ tptp.divide_divide_int L3) _let_1)))))))))))))
% 3.15/3.51 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X)) tptp.one_one_Code_integer))))
% 3.15/3.51 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X)) tptp.one_one_rat))))
% 3.15/3.51 (assert (forall ((X tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X)) tptp.one_one_int))))
% 3.15/3.51 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer X)) tptp.one_one_Code_integer))))
% 3.15/3.51 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat X)) tptp.one_one_rat))))
% 3.15/3.51 (assert (forall ((X tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int X)) tptp.one_one_int))))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N tptp.nat) (F2 (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat M2) I3) (@ (@ tptp.ord_less_nat I3) N)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F2 (@ tptp.suc I3))) (@ F2 I3)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (=> (@ (@ tptp.ord_less_eq_int (@ F2 M2)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F2 N)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M2) I3) (@ (@ tptp.ord_less_eq_nat I3) N) (= (@ F2 I3) K)))))))))
% 3.15/3.51 (assert (forall ((D2 tptp.int) (X tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int X))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (@ (@ tptp.ord_less_int (@ _let_1 (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ _let_1 Z))) tptp.one_one_int)) D2))) Z)))))
% 3.15/3.51 (assert (forall ((D2 tptp.int) (Z tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (@ (@ tptp.ord_less_int Z) (@ (@ tptp.plus_plus_int X) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) Z))) tptp.one_one_int)) D2))))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se1080825931792720795nteger A) tptp.one_one_Code_integer) (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A))))))
% 3.15/3.51 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.bit_se9127793120404214118atural A) tptp.one_one_Code_natural) (@ (@ tptp.plus_p4538020629002901425atural A) (@ tptp.zero_n8403883297036319079atural (@ (@ tptp.dvd_dvd_Code_natural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) A))))))
% 3.15/3.51 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int A) tptp.one_one_int) (@ (@ tptp.plus_plus_int A) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A))))))
% 3.15/3.51 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat A) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat A) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A))))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se1080825931792720795nteger tptp.one_one_Code_integer) A) (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A))))))
% 3.15/3.51 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.bit_se9127793120404214118atural tptp.one_one_Code_natural) A) (@ (@ tptp.plus_p4538020629002901425atural A) (@ tptp.zero_n8403883297036319079atural (@ (@ tptp.dvd_dvd_Code_natural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) A))))))
% 3.15/3.51 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) A) (@ (@ tptp.plus_plus_int A) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A))))))
% 3.15/3.51 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat tptp.one_one_nat) A) (@ (@ tptp.plus_plus_nat A) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A))))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ tptp.bit_se2119862282449309892nteger (@ tptp.suc N)) (@ (@ tptp.bit_se1080825931792720795nteger tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2119862282449309892nteger N))))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ tptp.bit_se943457434206027407atural (@ tptp.suc N)) (@ (@ tptp.bit_se9127793120404214118atural tptp.one_one_Code_natural) (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) (@ tptp.bit_se943457434206027407atural N))))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ tptp.bit_se2000444600071755411sk_int (@ tptp.suc N)) (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int N))))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.suc N)) (@ (@ tptp.bit_se1412395901928357646or_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2002935070580805687sk_nat N))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (F2 (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F2 (@ tptp.suc I3))) (@ F2 I3)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F2 tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F2 N)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I3) N) (= (@ F2 I3) K))))))))
% 3.15/3.51 (assert (@ (@ (@ (@ (@ (@ tptp.boolea2445317508997433345nteger tptp.bit_se3949692690581998587nteger) tptp.bit_se1080825931792720795nteger) tptp.bit_ri7632146776885996613nteger) tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.bit_se3222712562003087583nteger))
% 3.15/3.51 (assert (@ (@ (@ (@ (@ (@ tptp.boolea8527374999097803216ff_int tptp.bit_se725231765392027082nd_int) tptp.bit_se1409905431419307370or_int) tptp.bit_ri7919022796975470100ot_int) tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bit_se6526347334894502574or_int))
% 3.15/3.51 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K4 tptp.int) (L3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (or (= K4 _let_2) (= L3 _let_2))) _let_2) (@ (@ (@ tptp.if_int (= K4 tptp.zero_zero_int)) L3) (@ (@ (@ tptp.if_int (= L3 tptp.zero_zero_int)) K4) (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int (@ (@ tptp.modulo_modulo_int K4) _let_1)) (@ (@ tptp.modulo_modulo_int L3) _let_1))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.divide_divide_int K4) _let_1)) (@ (@ tptp.divide_divide_int L3) _let_1))))))))))))
% 3.15/3.51 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bitM N)))))))
% 3.15/3.51 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bitM N)))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (Xs tptp.list_h2745205591237434579t_unit) (Ys tptp.list_set_nat)) (let ((_let_1 (@ tptp.size_s3254054031482475050et_nat Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s7011499401410611007t_unit Xs)) _let_1)) (= (@ (@ tptp.nth_Pr7683458668995092411et_nat (@ (@ tptp.produc7481864959766642638et_nat Xs) Ys)) N) (@ (@ tptp.produc7507926704131184380et_nat (@ (@ tptp.nth_he7452997726511547988t_unit Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_set_nat Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (Xs tptp.list_P7985473006766602707_nat_o) (Ys tptp.list_P9062070895058802706et_nat)) (let ((_let_1 (@ tptp.size_s2864271983995610790et_nat Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s8908918004648414271_nat_o Xs)) _let_1)) (= (@ (@ tptp.nth_Pr3610913089060847927et_nat (@ (@ tptp.produc2866688925348378442et_nat Xs) Ys)) N) (@ (@ tptp.produc5001842942810119800et_nat (@ (@ tptp.nth_Pr6840583978799713108_nat_o Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_Pr7683458668995092411et_nat Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (Xs tptp.list_P7985473006766602707_nat_o) (Ys tptp.list_P2321686559999237006et_nat)) (let ((_let_1 (@ tptp.size_s6841928198497307170et_nat Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s8908918004648414271_nat_o Xs)) _let_1)) (= (@ (@ tptp.nth_Pr7590663101126261939et_nat (@ (@ tptp.produc7119410244218060998et_nat Xs) Ys)) N) (@ (@ tptp.produc2245416461498447860et_nat (@ (@ tptp.nth_Pr6840583978799713108_nat_o Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_Pr3610913089060847927et_nat Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (Xs tptp.list_int) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_int Xs)) _let_1)) (= (@ (@ tptp.nth_Pr4439495888332055232nt_int (@ (@ tptp.product_int_int Xs) Ys)) N) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.nth_int Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_int Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (Xs tptp.list_int) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_int Xs)) _let_1)) (= (@ (@ tptp.nth_Pr8617346907841251940nt_nat (@ (@ tptp.product_int_nat Xs) Ys)) N) (@ (@ tptp.product_Pair_int_nat (@ (@ tptp.nth_int Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_nat Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (Xs tptp.list_nat) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs)) _let_1)) (= (@ (@ tptp.nth_Pr3440142176431000676at_int (@ (@ tptp.product_nat_int Xs) Ys)) N) (@ (@ tptp.product_Pair_nat_int (@ (@ tptp.nth_nat Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_int Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (Xs tptp.list_nat) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs)) _let_1)) (= (@ (@ tptp.nth_Pr7617993195940197384at_nat (@ (@ tptp.product_nat_nat Xs) Ys)) N) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.nth_nat Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_nat Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 3.15/3.51 (assert (= tptp.bit_se3928097537394005634nteger (lambda ((N3 tptp.nat) (A2 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (= N3 tptp.zero_zero_nat)) A2) (@ (@ tptp.bit_se3928097537394005634nteger (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) (@ (@ tptp.divide6298287555418463151nteger A2) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 3.15/3.51 (assert (= tptp.bit_se8570568707652914677it_nat (lambda ((N3 tptp.nat) (A2 tptp.nat)) (@ (@ (@ tptp.if_nat (= N3 tptp.zero_zero_nat)) A2) (@ (@ tptp.bit_se8570568707652914677it_nat (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) (@ (@ tptp.divide_divide_nat A2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 3.15/3.51 (assert (= tptp.bit_se2751692689150723149atural (lambda ((N3 tptp.nat) (A2 tptp.code_natural)) (@ (@ (@ tptp.if_Code_natural (= N3 tptp.zero_zero_nat)) A2) (@ (@ tptp.bit_se2751692689150723149atural (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) (@ (@ tptp.divide5121882707175180666atural A2) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))))))
% 3.15/3.51 (assert (= tptp.bit_se8568078237143864401it_int (lambda ((N3 tptp.nat) (A2 tptp.int)) (@ (@ (@ tptp.if_int (= N3 tptp.zero_zero_nat)) A2) (@ (@ tptp.bit_se8568078237143864401it_int (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) (@ (@ tptp.divide_divide_int A2) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))))
% 3.15/3.51 (assert (= tptp.bit_se9216721137139052372nteger (lambda ((A2 tptp.code_integer) (N3 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= N3 tptp.zero_zero_nat))) (and (=> _let_2 (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A2))) (=> (not _let_2) (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.divide6298287555418463151nteger A2) _let_1)) (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)))))))))
% 3.15/3.51 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((A2 tptp.nat) (N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= N3 tptp.zero_zero_nat))) (and (=> _let_2 (not (@ (@ tptp.dvd_dvd_nat _let_1) A2))) (=> (not _let_2) (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.divide_divide_nat A2) _let_1)) (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)))))))))
% 3.15/3.51 (assert (= tptp.bit_se8040316288895769887atural (lambda ((A2 tptp.code_natural) (N3 tptp.nat)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= N3 tptp.zero_zero_nat))) (and (=> _let_2 (not (@ (@ tptp.dvd_dvd_Code_natural _let_1) A2))) (=> (not _let_2) (@ (@ tptp.bit_se8040316288895769887atural (@ (@ tptp.divide5121882707175180666atural A2) _let_1)) (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)))))))))
% 3.15/3.51 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((A2 tptp.int) (N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= N3 tptp.zero_zero_nat))) (and (=> _let_2 (not (@ (@ tptp.dvd_dvd_int _let_1) A2))) (=> (not _let_2) (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.divide_divide_int A2) _let_1)) (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)))))))))
% 3.15/3.51 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_nat _let_1) B))) (let ((_let_3 (= N tptp.zero_zero_nat))) (=> (forall ((J3 tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat A) (@ tptp.suc J3)))) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.plus_plus_nat A) _let_2)) N) (and (=> _let_3 (not (@ (@ tptp.dvd_dvd_nat _let_1) A))) (=> (not _let_3) (@ (@ tptp.bit_se1148574629649215175it_nat _let_2) N))))))))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_3573771949741848930nteger _let_1) B))) (let ((_let_3 (= N tptp.zero_zero_nat))) (=> (forall ((J3 tptp.nat)) (not (@ (@ tptp.bit_se9216721137139052372nteger A) (@ tptp.suc J3)))) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.plus_p5714425477246183910nteger A) _let_2)) N) (and (=> _let_3 (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (=> (not _let_3) (@ (@ tptp.bit_se9216721137139052372nteger _let_2) N))))))))))
% 3.15/3.51 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (N tptp.nat)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_2397367101498566445atural _let_1) B))) (let ((_let_3 (= N tptp.zero_zero_nat))) (=> (forall ((J3 tptp.nat)) (not (@ (@ tptp.bit_se8040316288895769887atural A) (@ tptp.suc J3)))) (= (@ (@ tptp.bit_se8040316288895769887atural (@ (@ tptp.plus_p4538020629002901425atural A) _let_2)) N) (and (=> _let_3 (not (@ (@ tptp.dvd_dvd_Code_natural _let_1) A))) (=> (not _let_3) (@ (@ tptp.bit_se8040316288895769887atural _let_2) N))))))))))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_int _let_1) B))) (let ((_let_3 (= N tptp.zero_zero_nat))) (=> (forall ((J3 tptp.nat)) (not (@ (@ tptp.bit_se1146084159140164899it_int A) (@ tptp.suc J3)))) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.plus_plus_int A) _let_2)) N) (and (=> _let_3 (not (@ (@ tptp.dvd_dvd_int _let_1) A))) (=> (not _let_3) (@ (@ tptp.bit_se1146084159140164899it_int _let_2) N))))))))))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.ord_max_int A) B))) (= (@ (@ tptp.ord_max_int _let_1) B) _let_1))))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_max_int A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 3.15/3.51 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_max_int A) A) A)))
% 3.15/3.51 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B) C)) A) (and (@ (@ tptp.ord_less_eq_rat B) A) (@ (@ tptp.ord_less_eq_rat C) A)))))
% 3.15/3.51 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B) C)) A) (and (@ (@ tptp.ord_less_eq_nat B) A) (@ (@ tptp.ord_less_eq_nat C) A)))))
% 3.15/3.51 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B) C)) A) (and (@ (@ tptp.ord_less_eq_int B) A) (@ (@ tptp.ord_less_eq_int C) A)))))
% 3.15/3.51 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= (@ (@ tptp.ord_max_rat A) B) B))))
% 3.15/3.51 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.ord_max_nat A) B) B))))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (= (@ (@ tptp.ord_max_int A) B) B))))
% 3.15/3.51 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.ord_max_rat A) B) A))))
% 3.15/3.51 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.ord_max_nat A) B) A))))
% 3.15/3.51 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.ord_max_int A) B) A))))
% 3.15/3.51 (assert (forall ((F2 (-> tptp.produc6575502325842934193n_assn tptp.assn)) (Xs tptp.list_P8527749157015355191n_assn)) (= (@ tptp.size_size_list_assn (@ (@ tptp.map_Pr8991440229025900053n_assn F2) Xs)) (@ tptp.size_s6829681357464350627n_assn Xs))))
% 3.15/3.51 (assert (forall ((F2 (-> tptp.int tptp.int)) (Xs tptp.list_int)) (= (@ tptp.size_size_list_int (@ (@ tptp.map_int_int F2) Xs)) (@ tptp.size_size_list_int Xs))))
% 3.15/3.51 (assert (forall ((F2 (-> tptp.nat tptp.int)) (Xs tptp.list_nat)) (= (@ tptp.size_size_list_int (@ (@ tptp.map_nat_int F2) Xs)) (@ tptp.size_size_list_nat Xs))))
% 3.15/3.51 (assert (forall ((F2 (-> tptp.int tptp.nat)) (Xs tptp.list_int)) (= (@ tptp.size_size_list_nat (@ (@ tptp.map_int_nat F2) Xs)) (@ tptp.size_size_list_int Xs))))
% 3.15/3.51 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (Xs tptp.list_nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.map_nat_nat F2) Xs)) (@ tptp.size_size_list_nat Xs))))
% 3.15/3.51 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.ord_max_Code_integer X) Y)) Z) (and (@ (@ tptp.ord_le6747313008572928689nteger X) Z) (@ (@ tptp.ord_le6747313008572928689nteger Y) Z)))))
% 3.15/3.51 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.ord_max_rat X) Y)) Z) (and (@ (@ tptp.ord_less_rat X) Z) (@ (@ tptp.ord_less_rat Y) Z)))))
% 3.15/3.51 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_max_nat X) Y)) Z) (and (@ (@ tptp.ord_less_nat X) Z) (@ (@ tptp.ord_less_nat Y) Z)))))
% 3.15/3.51 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.ord_max_int X) Y)) Z) (and (@ (@ tptp.ord_less_int X) Z) (@ (@ tptp.ord_less_int Y) Z)))))
% 3.15/3.51 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (= (@ (@ tptp.ord_max_Code_integer A) B) B))))
% 3.15/3.51 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (= (@ (@ tptp.ord_max_rat A) B) B))))
% 3.15/3.51 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.ord_max_nat A) B) B))))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (= (@ (@ tptp.ord_max_int A) B) B))))
% 3.15/3.51 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) A) (= (@ (@ tptp.ord_max_Code_integer A) B) A))))
% 3.15/3.51 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (= (@ (@ tptp.ord_max_rat A) B) A))))
% 3.15/3.51 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (= (@ (@ tptp.ord_max_nat A) B) A))))
% 3.15/3.51 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (= (@ (@ tptp.ord_max_int A) B) A))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_se8568078237143864401it_int N) _let_1) _let_1))))
% 3.15/3.51 (assert (forall ((A tptp.list_int) (B tptp.list_int) (A5 tptp.list_int) (B6 tptp.list_int)) (=> (= (@ tptp.size_size_list_int A) (@ tptp.size_size_list_int B)) (=> (= (@ tptp.size_size_list_int A5) (@ tptp.size_size_list_int B6)) (= (= (@ (@ tptp.zip_int_int A) B) (@ (@ tptp.zip_int_int A5) B6)) (and (= A A5) (= B B6)))))))
% 3.15/3.51 (assert (forall ((A tptp.list_int) (B tptp.list_nat) (A5 tptp.list_int) (B6 tptp.list_nat)) (=> (= (@ tptp.size_size_list_int A) (@ tptp.size_size_list_nat B)) (=> (= (@ tptp.size_size_list_int A5) (@ tptp.size_size_list_nat B6)) (= (= (@ (@ tptp.zip_int_nat A) B) (@ (@ tptp.zip_int_nat A5) B6)) (and (= A A5) (= B B6)))))))
% 3.15/3.51 (assert (forall ((A tptp.list_nat) (B tptp.list_int) (A5 tptp.list_nat) (B6 tptp.list_int)) (=> (= (@ tptp.size_size_list_nat A) (@ tptp.size_size_list_int B)) (=> (= (@ tptp.size_size_list_nat A5) (@ tptp.size_size_list_int B6)) (= (= (@ (@ tptp.zip_nat_int A) B) (@ (@ tptp.zip_nat_int A5) B6)) (and (= A A5) (= B B6)))))))
% 3.15/3.51 (assert (forall ((A tptp.list_nat) (B tptp.list_nat) (A5 tptp.list_nat) (B6 tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat A) (@ tptp.size_size_list_nat B)) (=> (= (@ tptp.size_size_list_nat A5) (@ tptp.size_size_list_nat B6)) (= (= (@ (@ tptp.zip_nat_nat A) B) (@ (@ tptp.zip_nat_nat A5) B6)) (and (= A A5) (= B B6)))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (Xs tptp.list_int)) (= (@ tptp.size_s2970893825323803983at_int (@ (@ tptp.enumerate_int N) Xs)) (@ tptp.size_size_list_int Xs))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (Xs tptp.list_nat)) (= (@ tptp.size_s5460976970255530739at_nat (@ (@ tptp.enumerate_nat N) Xs)) (@ tptp.size_size_list_nat Xs))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_int)) (= (@ tptp.size_size_list_int (@ tptp.rotate1_int Xs)) (@ tptp.size_size_list_int Xs))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_nat)) (= (@ tptp.size_size_list_nat (@ tptp.rotate1_nat Xs)) (@ tptp.size_size_list_nat Xs))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn)) (= (= (@ tptp.size_s6829681357464350627n_assn Xs) tptp.zero_zero_nat) (= Xs tptp.nil_Pr5671120429643327159n_assn))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_int)) (= (= (@ tptp.size_size_list_int Xs) tptp.zero_zero_nat) (= Xs tptp.nil_int))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_nat)) (= (= (@ tptp.size_size_list_nat Xs) tptp.zero_zero_nat) (= Xs tptp.nil_nat))))
% 3.15/3.51 (assert (= (@ (@ tptp.ord_max_nat tptp.one_one_nat) tptp.zero_zero_nat) tptp.one_one_nat))
% 3.15/3.51 (assert (= (@ (@ tptp.ord_max_rat tptp.one_one_rat) tptp.zero_zero_rat) tptp.one_one_rat))
% 3.15/3.51 (assert (= (@ (@ tptp.ord_max_Code_integer tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer))
% 3.15/3.51 (assert (= (@ (@ tptp.ord_max_Code_natural tptp.one_one_Code_natural) tptp.zero_z2226904508553997617atural) tptp.one_one_Code_natural))
% 3.15/3.51 (assert (= (@ (@ tptp.ord_max_int tptp.one_one_int) tptp.zero_zero_int) tptp.one_one_int))
% 3.15/3.51 (assert (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) tptp.one_one_nat) tptp.one_one_nat))
% 3.15/3.51 (assert (= (@ (@ tptp.ord_max_rat tptp.zero_zero_rat) tptp.one_one_rat) tptp.one_one_rat))
% 3.15/3.51 (assert (= (@ (@ tptp.ord_max_Code_integer tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 3.15/3.51 (assert (= (@ (@ tptp.ord_max_Code_natural tptp.zero_z2226904508553997617atural) tptp.one_one_Code_natural) tptp.one_one_Code_natural))
% 3.15/3.51 (assert (= (@ (@ tptp.ord_max_int tptp.zero_zero_int) tptp.one_one_int) tptp.one_one_int))
% 3.15/3.51 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.ord_max_nat _let_1) tptp.one_one_nat) _let_1))))
% 3.15/3.51 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.ord_max_int _let_1) tptp.one_one_int) _let_1))))
% 3.15/3.51 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X))) (= (@ (@ tptp.ord_max_rat _let_1) tptp.one_one_rat) _let_1))))
% 3.15/3.51 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger X))) (= (@ (@ tptp.ord_max_Code_integer _let_1) tptp.one_one_Code_integer) _let_1))))
% 3.15/3.51 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera5444537566228673987atural X))) (= (@ (@ tptp.ord_max_Code_natural _let_1) tptp.one_one_Code_natural) _let_1))))
% 3.15/3.51 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.ord_max_nat tptp.one_one_nat) _let_1) _let_1))))
% 3.15/3.51 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.ord_max_int tptp.one_one_int) _let_1) _let_1))))
% 3.15/3.51 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X))) (= (@ (@ tptp.ord_max_rat tptp.one_one_rat) _let_1) _let_1))))
% 3.15/3.51 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger X))) (= (@ (@ tptp.ord_max_Code_integer tptp.one_one_Code_integer) _let_1) _let_1))))
% 3.15/3.51 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera5444537566228673987atural X))) (= (@ (@ tptp.ord_max_Code_natural tptp.one_one_Code_natural) _let_1) _let_1))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (= (@ tptp.size_size_list_int (@ (@ tptp.splice_int Xs) Ys)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_list_int Xs)) (@ tptp.size_size_list_int Ys)))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.splice_nat Xs) Ys)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_list_nat Xs)) (@ tptp.size_size_list_nat Ys)))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (= (@ tptp.size_s5157815400016825771nt_int (@ (@ tptp.product_int_int Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_int Xs)) (@ tptp.size_size_list_int Ys)))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_nat)) (= (@ tptp.size_s7647898544948552527nt_nat (@ (@ tptp.product_int_nat Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_int Xs)) (@ tptp.size_size_list_nat Ys)))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_int)) (= (@ tptp.size_s2970893825323803983at_int (@ (@ tptp.product_nat_int Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs)) (@ tptp.size_size_list_int Ys)))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (= (@ tptp.size_s5460976970255530739at_nat (@ (@ tptp.product_nat_nat Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs)) (@ tptp.size_size_list_nat Ys)))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_P8527749157015355191n_assn)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s6829681357464350627n_assn Xs)) (not (= Xs tptp.nil_Pr5671120429643327159n_assn)))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_int)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_int Xs)) (not (= Xs tptp.nil_int)))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_nat Xs)) (not (= Xs tptp.nil_nat)))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (Xs tptp.list_P8527749157015355191n_assn) (F2 (-> tptp.produc6575502325842934193n_assn tptp.assn))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6829681357464350627n_assn Xs)) (= (@ (@ tptp.nth_assn (@ (@ tptp.map_Pr8991440229025900053n_assn F2) Xs)) N) (@ F2 (@ (@ tptp.nth_Pr1769885009046257848n_assn Xs) N))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (Xs tptp.list_int) (F2 (-> tptp.int tptp.nat))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_nat (@ (@ tptp.map_int_nat F2) Xs)) N) (@ F2 (@ (@ tptp.nth_int Xs) N))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (Xs tptp.list_int) (F2 (-> tptp.int tptp.int))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int (@ (@ tptp.map_int_int F2) Xs)) N) (@ F2 (@ (@ tptp.nth_int Xs) N))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (Xs tptp.list_nat) (F2 (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_int (@ (@ tptp.map_nat_int F2) Xs)) N) (@ F2 (@ (@ tptp.nth_nat Xs) N))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (Xs tptp.list_nat) (F2 (-> tptp.nat tptp.nat))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat (@ (@ tptp.map_nat_nat F2) Xs)) N) (@ F2 (@ (@ tptp.nth_nat Xs) N))))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se3928097537394005634nteger N) tptp.one_one_Code_integer) (@ tptp.zero_n356916108424825756nteger (= N tptp.zero_zero_nat)))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se8570568707652914677it_nat N) tptp.one_one_nat) (@ tptp.zero_n2687167440665602831ol_nat (= N tptp.zero_zero_nat)))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se8568078237143864401it_int N) tptp.one_one_int) (@ tptp.zero_n2684676970156552555ol_int (= N tptp.zero_zero_nat)))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_nat)) (=> (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_nat Ys)) (= (@ (@ tptp.map_Pr4307537318738222789at_int tptp.product_fst_int_nat) (@ (@ tptp.zip_int_nat Xs) Ys)) Xs))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_int)) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_int Ys)) (= (@ (@ tptp.map_Pr6125295803703450217nt_nat tptp.product_fst_nat_int) (@ (@ tptp.zip_nat_int Xs) Ys)) Xs))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys)) (= (@ (@ tptp.map_Pr3938374229010428429at_nat tptp.product_fst_nat_nat) (@ (@ tptp.zip_nat_nat Xs) Ys)) Xs))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_h2745205591237434579t_unit) (Ys tptp.list_set_nat)) (=> (= (@ tptp.size_s7011499401410611007t_unit Xs) (@ tptp.size_s3254054031482475050et_nat Ys)) (= (@ (@ tptp.map_Pr7042224834074979589t_unit tptp.produc1824681642469235216et_nat) (@ (@ tptp.zip_he6711929980790699996et_nat Xs) Ys)) Xs))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (=> (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys)) (= (@ (@ tptp.map_Pr6494458893431244577nt_int tptp.product_fst_int_int) (@ (@ tptp.zip_int_int Xs) Ys)) Xs))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_assn) (Ys tptp.list_assn)) (=> (= (@ tptp.size_size_list_assn Xs) (@ tptp.size_size_list_assn Ys)) (= (@ (@ tptp.map_Pr8991440229025900053n_assn tptp.produc9167289414957590229n_assn) (@ (@ tptp.zip_assn_assn Xs) Ys)) Xs))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_nat)) (=> (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_nat Ys)) (= (@ (@ tptp.map_Pr4310027789247273065at_nat tptp.product_snd_int_nat) (@ (@ tptp.zip_int_nat Xs) Ys)) Ys))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_int)) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_int Ys)) (= (@ (@ tptp.map_Pr6122805333194399941nt_int tptp.product_snd_nat_int) (@ (@ tptp.zip_nat_int Xs) Ys)) Ys))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys)) (= (@ (@ tptp.map_Pr3938374229010428429at_nat tptp.product_snd_nat_nat) (@ (@ tptp.zip_nat_nat Xs) Ys)) Ys))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_h2745205591237434579t_unit) (Ys tptp.list_set_nat)) (=> (= (@ tptp.size_s7011499401410611007t_unit Xs) (@ tptp.size_s3254054031482475050et_nat Ys)) (= (@ (@ tptp.map_Pr4871828589360411470et_nat tptp.produc8586169260539613262et_nat) (@ (@ tptp.zip_he6711929980790699996et_nat Xs) Ys)) Ys))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (=> (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys)) (= (@ (@ tptp.map_Pr6494458893431244577nt_int tptp.product_snd_int_int) (@ (@ tptp.zip_int_int Xs) Ys)) Ys))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_assn) (Ys tptp.list_assn)) (=> (= (@ tptp.size_size_list_assn Xs) (@ tptp.size_size_list_assn Ys)) (= (@ (@ tptp.map_Pr8991440229025900053n_assn tptp.produc2051961928117032727n_assn) (@ (@ tptp.zip_assn_assn Xs) Ys)) Ys))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_int)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs)) tptp.one_one_nat) (= (@ tptp.rotate1_int Xs) Xs))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) tptp.one_one_nat) (= (@ tptp.rotate1_nat Xs) Xs))))
% 3.15/3.51 (assert (forall ((L tptp.list_P8527749157015355191n_assn)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.size_s6829681357464350627n_assn L)) (not (= L tptp.nil_Pr5671120429643327159n_assn)))))
% 3.15/3.51 (assert (forall ((L tptp.list_int)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.size_size_list_int L)) (not (= L tptp.nil_int)))))
% 3.15/3.51 (assert (forall ((L tptp.list_nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.size_size_list_nat L)) (not (= L tptp.nil_nat)))))
% 3.15/3.51 (assert (forall ((I2 tptp.nat) (Xs tptp.list_h2745205591237434579t_unit) (Ys tptp.list_set_nat)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 (@ tptp.size_s7011499401410611007t_unit Xs)) (=> (@ _let_1 (@ tptp.size_s3254054031482475050et_nat Ys)) (= (@ (@ tptp.nth_Pr7683458668995092411et_nat (@ (@ tptp.zip_he6711929980790699996et_nat Xs) Ys)) I2) (@ (@ tptp.produc7507926704131184380et_nat (@ (@ tptp.nth_he7452997726511547988t_unit Xs) I2)) (@ (@ tptp.nth_set_nat Ys) I2))))))))
% 3.15/3.51 (assert (forall ((I2 tptp.nat) (Xs tptp.list_P7985473006766602707_nat_o) (Ys tptp.list_P9062070895058802706et_nat)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 (@ tptp.size_s8908918004648414271_nat_o Xs)) (=> (@ _let_1 (@ tptp.size_s2864271983995610790et_nat Ys)) (= (@ (@ tptp.nth_Pr3610913089060847927et_nat (@ (@ tptp.zip_Pr7134870689397686104et_nat Xs) Ys)) I2) (@ (@ tptp.produc5001842942810119800et_nat (@ (@ tptp.nth_Pr6840583978799713108_nat_o Xs) I2)) (@ (@ tptp.nth_Pr7683458668995092411et_nat Ys) I2))))))))
% 3.15/3.51 (assert (forall ((I2 tptp.nat) (Xs tptp.list_P7985473006766602707_nat_o) (Ys tptp.list_P2321686559999237006et_nat)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 (@ tptp.size_s8908918004648414271_nat_o Xs)) (=> (@ _let_1 (@ tptp.size_s6841928198497307170et_nat Ys)) (= (@ (@ tptp.nth_Pr7590663101126261939et_nat (@ (@ tptp.zip_Pr8136144321567152340et_nat Xs) Ys)) I2) (@ (@ tptp.produc2245416461498447860et_nat (@ (@ tptp.nth_Pr6840583978799713108_nat_o Xs) I2)) (@ (@ tptp.nth_Pr3610913089060847927et_nat Ys) I2))))))))
% 3.15/3.51 (assert (forall ((I2 tptp.nat) (Xs tptp.list_int) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 (@ tptp.size_size_list_int Xs)) (=> (@ _let_1 (@ tptp.size_size_list_int Ys)) (= (@ (@ tptp.nth_Pr4439495888332055232nt_int (@ (@ tptp.zip_int_int Xs) Ys)) I2) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.nth_int Xs) I2)) (@ (@ tptp.nth_int Ys) I2))))))))
% 3.15/3.51 (assert (forall ((I2 tptp.nat) (Xs tptp.list_int) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 (@ tptp.size_size_list_int Xs)) (=> (@ _let_1 (@ tptp.size_size_list_nat Ys)) (= (@ (@ tptp.nth_Pr8617346907841251940nt_nat (@ (@ tptp.zip_int_nat Xs) Ys)) I2) (@ (@ tptp.product_Pair_int_nat (@ (@ tptp.nth_int Xs) I2)) (@ (@ tptp.nth_nat Ys) I2))))))))
% 3.15/3.51 (assert (forall ((I2 tptp.nat) (Xs tptp.list_nat) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 (@ tptp.size_size_list_nat Xs)) (=> (@ _let_1 (@ tptp.size_size_list_int Ys)) (= (@ (@ tptp.nth_Pr3440142176431000676at_int (@ (@ tptp.zip_nat_int Xs) Ys)) I2) (@ (@ tptp.product_Pair_nat_int (@ (@ tptp.nth_nat Xs) I2)) (@ (@ tptp.nth_int Ys) I2))))))))
% 3.15/3.51 (assert (forall ((I2 tptp.nat) (Xs tptp.list_nat) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 (@ tptp.size_size_list_nat Xs)) (=> (@ _let_1 (@ tptp.size_size_list_nat Ys)) (= (@ (@ tptp.nth_Pr7617993195940197384at_nat (@ (@ tptp.zip_nat_nat Xs) Ys)) I2) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.nth_nat Xs) I2)) (@ (@ tptp.nth_nat Ys) I2))))))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys))) (not (= Xs Ys)))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys))) (not (= Xs Ys)))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (exists ((Xs2 tptp.list_int)) (= (@ tptp.size_size_list_int Xs2) N))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (exists ((Xs2 tptp.list_nat)) (= (@ tptp.size_size_list_nat Xs2) N))))
% 3.15/3.51 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_max_int B))) (let ((_let_2 (@ tptp.ord_max_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 3.15/3.51 (assert (= tptp.ord_max_int (lambda ((A2 tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_max_int B2) A2))))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_max_int A))) (= (@ (@ tptp.ord_max_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.ord_max_int B) C))))))
% 3.15/3.51 (assert (forall ((L tptp.list_P5707943133018811711nt_int)) (not (forall ((L1 tptp.list_int) (L2 tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int L2))) (=> (= L (@ (@ tptp.zip_int_int L1) L2)) (=> (= (@ tptp.size_size_list_int L1) _let_1) (not (= (@ tptp.size_s5157815400016825771nt_int L) _let_1)))))))))
% 3.15/3.51 (assert (forall ((L tptp.list_P8198026277950538467nt_nat)) (not (forall ((L1 tptp.list_int) (L2 tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat L2))) (=> (= L (@ (@ tptp.zip_int_nat L1) L2)) (=> (= (@ tptp.size_size_list_int L1) _let_1) (not (= (@ tptp.size_s7647898544948552527nt_nat L) _let_1)))))))))
% 3.15/3.51 (assert (forall ((L tptp.list_P3521021558325789923at_int)) (not (forall ((L1 tptp.list_nat) (L2 tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int L2))) (=> (= L (@ (@ tptp.zip_nat_int L1) L2)) (=> (= (@ tptp.size_size_list_nat L1) _let_1) (not (= (@ tptp.size_s2970893825323803983at_int L) _let_1)))))))))
% 3.15/3.51 (assert (forall ((L tptp.list_P6011104703257516679at_nat)) (not (forall ((L1 tptp.list_nat) (L2 tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat L2))) (=> (= L (@ (@ tptp.zip_nat_nat L1) L2)) (=> (= (@ tptp.size_size_list_nat L1) _let_1) (not (= (@ tptp.size_s5460976970255530739at_nat L) _let_1)))))))))
% 3.15/3.51 (assert (= tptp.bit_se9216721137139052372nteger (lambda ((A2 tptp.code_integer) (N3 tptp.nat)) (= (@ (@ tptp.bit_se3949692690581998587nteger (@ (@ tptp.bit_se3928097537394005634nteger N3) A2)) tptp.one_one_Code_integer) tptp.one_one_Code_integer))))
% 3.15/3.51 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((A2 tptp.nat) (N3 tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.bit_se8570568707652914677it_nat N3) A2)) tptp.one_one_nat) tptp.one_one_nat))))
% 3.15/3.51 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((A2 tptp.int) (N3 tptp.nat)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.bit_se8568078237143864401it_int N3) A2)) tptp.one_one_int) tptp.one_one_int))))
% 3.15/3.51 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 3.15/3.51 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 3.15/3.51 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 3.15/3.51 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 3.15/3.51 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 3.15/3.51 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 3.15/3.51 (assert (= tptp.ord_less_eq_rat (lambda ((A2 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_max_rat A2) B2) B2))))
% 3.15/3.51 (assert (= tptp.ord_less_eq_nat (lambda ((A2 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_max_nat A2) B2) B2))))
% 3.15/3.51 (assert (= tptp.ord_less_eq_int (lambda ((A2 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_max_int A2) B2) B2))))
% 3.15/3.51 (assert (= tptp.ord_less_eq_rat (lambda ((B2 tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.ord_max_rat A2) B2) A2))))
% 3.15/3.51 (assert (= tptp.ord_less_eq_nat (lambda ((B2 tptp.nat) (A2 tptp.nat)) (= (@ (@ tptp.ord_max_nat A2) B2) A2))))
% 3.15/3.51 (assert (= tptp.ord_less_eq_int (lambda ((B2 tptp.int) (A2 tptp.int)) (= (@ (@ tptp.ord_max_int A2) B2) A2))))
% 3.15/3.51 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_rat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 3.15/3.51 (assert (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 3.15/3.51 (assert (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int Z))) (= (@ _let_1 (@ (@ tptp.ord_max_int X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 3.15/3.51 (assert (forall ((B tptp.rat) (A tptp.rat)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.ord_max_rat A) B))))
% 3.15/3.51 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_nat B) (@ (@ tptp.ord_max_nat A) B))))
% 3.15/3.51 (assert (forall ((B tptp.int) (A tptp.int)) (@ (@ tptp.ord_less_eq_int B) (@ (@ tptp.ord_max_int A) B))))
% 3.15/3.51 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.ord_max_rat A) B))))
% 3.15/3.51 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.ord_max_nat A) B))))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.ord_max_int A) B))))
% 3.15/3.51 (assert (= tptp.ord_less_eq_rat (lambda ((B2 tptp.rat) (A2 tptp.rat)) (= A2 (@ (@ tptp.ord_max_rat A2) B2)))))
% 3.15/3.51 (assert (= tptp.ord_less_eq_nat (lambda ((B2 tptp.nat) (A2 tptp.nat)) (= A2 (@ (@ tptp.ord_max_nat A2) B2)))))
% 3.15/3.51 (assert (= tptp.ord_less_eq_int (lambda ((B2 tptp.int) (A2 tptp.int)) (= A2 (@ (@ tptp.ord_max_int A2) B2)))))
% 3.15/3.51 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B) C)) A)))))
% 3.15/3.51 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B) C)) A)))))
% 3.15/3.51 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int C) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B) C)) A)))))
% 3.15/3.51 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_rat B) A) (not (@ (@ tptp.ord_less_eq_rat C) A)))))))
% 3.15/3.51 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_nat B) A) (not (@ (@ tptp.ord_less_eq_nat C) A)))))))
% 3.15/3.51 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_int B) A) (not (@ (@ tptp.ord_less_eq_int C) A)))))))
% 3.15/3.51 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= A (@ (@ tptp.ord_max_rat A) B)) (@ (@ tptp.ord_less_eq_rat B) A))))
% 3.15/3.51 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= A (@ (@ tptp.ord_max_nat A) B)) (@ (@ tptp.ord_less_eq_nat B) A))))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= A (@ (@ tptp.ord_max_int A) B)) (@ (@ tptp.ord_less_eq_int B) A))))
% 3.15/3.51 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= A (@ (@ tptp.ord_max_rat A) B)))))
% 3.15/3.51 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A (@ (@ tptp.ord_max_nat A) B)))))
% 3.15/3.51 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A (@ (@ tptp.ord_max_int A) B)))))
% 3.15/3.51 (assert (forall ((C tptp.rat) (A tptp.rat) (D2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) A) (=> (@ (@ tptp.ord_less_eq_rat D2) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat C) D2)) (@ (@ tptp.ord_max_rat A) B))))))
% 3.15/3.51 (assert (forall ((C tptp.nat) (A tptp.nat) (D2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) A) (=> (@ (@ tptp.ord_less_eq_nat D2) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat C) D2)) (@ (@ tptp.ord_max_nat A) B))))))
% 3.15/3.51 (assert (forall ((C tptp.int) (A tptp.int) (D2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) A) (=> (@ (@ tptp.ord_less_eq_int D2) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int C) D2)) (@ (@ tptp.ord_max_int A) B))))))
% 3.15/3.51 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_Code_integer A) B))))))
% 3.15/3.51 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 3.15/3.51 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 3.15/3.51 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 3.15/3.51 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_Code_integer A) B))))))
% 3.15/3.51 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 3.15/3.51 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 3.15/3.51 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 3.15/3.51 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((B2 tptp.code_integer) (A2 tptp.code_integer)) (and (= A2 (@ (@ tptp.ord_max_Code_integer A2) B2)) (not (= A2 B2))))))
% 3.15/3.51 (assert (= tptp.ord_less_rat (lambda ((B2 tptp.rat) (A2 tptp.rat)) (and (= A2 (@ (@ tptp.ord_max_rat A2) B2)) (not (= A2 B2))))))
% 3.15/3.51 (assert (= tptp.ord_less_nat (lambda ((B2 tptp.nat) (A2 tptp.nat)) (and (= A2 (@ (@ tptp.ord_max_nat A2) B2)) (not (= A2 B2))))))
% 3.15/3.51 (assert (= tptp.ord_less_int (lambda ((B2 tptp.int) (A2 tptp.int)) (and (= A2 (@ (@ tptp.ord_max_int A2) B2)) (not (= A2 B2))))))
% 3.15/3.51 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.ord_max_Code_integer B) C)) A) (not (=> (@ (@ tptp.ord_le6747313008572928689nteger B) A) (not (@ (@ tptp.ord_le6747313008572928689nteger C) A)))))))
% 3.15/3.51 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.ord_max_rat B) C)) A) (not (=> (@ (@ tptp.ord_less_rat B) A) (not (@ (@ tptp.ord_less_rat C) A)))))))
% 3.15/3.51 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_max_nat B) C)) A) (not (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat C) A)))))))
% 3.15/3.51 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.ord_max_int B) C)) A) (not (=> (@ (@ tptp.ord_less_int B) A) (not (@ (@ tptp.ord_less_int C) A)))))))
% 3.15/3.51 (assert (forall ((Z tptp.code_integer) (X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger Z))) (= (@ _let_1 (@ (@ tptp.ord_max_Code_integer X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 3.15/3.51 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_rat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 3.15/3.51 (assert (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 3.15/3.51 (assert (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_int Z))) (= (@ _let_1 (@ (@ tptp.ord_max_int X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 3.15/3.51 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger X))) (= (@ _let_1 (@ (@ tptp.ord_max_Code_integer Y) Z)) (@ (@ tptp.ord_max_Code_integer (@ _let_1 Y)) (@ _let_1 Z))))))
% 3.15/3.51 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat X))) (= (@ _let_1 (@ (@ tptp.ord_max_rat Y) Z)) (@ (@ tptp.ord_max_rat (@ _let_1 Y)) (@ _let_1 Z))))))
% 3.15/3.51 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat X))) (= (@ _let_1 (@ (@ tptp.ord_max_nat Y) Z)) (@ (@ tptp.ord_max_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 3.15/3.51 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X))) (= (@ _let_1 (@ (@ tptp.ord_max_int Y) Z)) (@ (@ tptp.ord_max_int (@ _let_1 Y)) (@ _let_1 Z))))))
% 3.15/3.51 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.ord_max_Code_integer X) Y)) Z) (@ (@ tptp.ord_max_Code_integer (@ (@ tptp.plus_p5714425477246183910nteger X) Z)) (@ (@ tptp.plus_p5714425477246183910nteger Y) Z)))))
% 3.15/3.51 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.ord_max_rat X) Y)) Z) (@ (@ tptp.ord_max_rat (@ (@ tptp.plus_plus_rat X) Z)) (@ (@ tptp.plus_plus_rat Y) Z)))))
% 3.15/3.51 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat X) Y)) Z) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat X) Z)) (@ (@ tptp.plus_plus_nat Y) Z)))))
% 3.15/3.51 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int X) Y)) Z) (@ (@ tptp.ord_max_int (@ (@ tptp.plus_plus_int X) Z)) (@ (@ tptp.plus_plus_int Y) Z)))))
% 3.15/3.51 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.ord_max_int X) Y)) Z) (@ (@ tptp.ord_max_int (@ (@ tptp.minus_minus_int X) Z)) (@ (@ tptp.minus_minus_int Y) Z)))))
% 3.15/3.51 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.ord_max_Code_integer X) Y)) Z) (@ (@ tptp.ord_max_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X) Z)) (@ (@ tptp.minus_8373710615458151222nteger Y) Z)))))
% 3.15/3.51 (assert (= tptp.sup_sup_int tptp.ord_max_int))
% 3.15/3.51 (assert (forall ((P2 (-> tptp.list_int Bool)) (Xs tptp.list_int)) (=> (forall ((Xs2 tptp.list_int)) (=> (forall ((Ys5 tptp.list_int)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_int Ys5)) (@ tptp.size_size_list_int Xs2)) (@ P2 Ys5))) (@ P2 Xs2))) (@ P2 Xs))))
% 3.15/3.51 (assert (forall ((P2 (-> tptp.list_nat Bool)) (Xs tptp.list_nat)) (=> (forall ((Xs2 tptp.list_nat)) (=> (forall ((Ys5 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat Ys5)) (@ tptp.size_size_list_nat Xs2)) (@ P2 Ys5))) (@ P2 Xs2))) (@ P2 Xs))))
% 3.15/3.51 (assert (forall ((M tptp.set_list_int)) (=> (@ tptp.finite3922522038869484883st_int M) (exists ((N4 tptp.nat)) (forall ((X4 tptp.list_int)) (=> (@ (@ tptp.member_list_int X4) M) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_int X4)) N4)))))))
% 3.15/3.51 (assert (forall ((M tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat M) (exists ((N4 tptp.nat)) (forall ((X4 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X4) M) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat X4)) N4)))))))
% 3.15/3.51 (assert (forall ((F2 (-> tptp.produc6575502325842934193n_assn tptp.assn)) (Xs tptp.list_P8527749157015355191n_assn) (G3 (-> tptp.produc6575502325842934193n_assn tptp.assn)) (Ys tptp.list_P8527749157015355191n_assn)) (=> (= (@ (@ tptp.map_Pr8991440229025900053n_assn F2) Xs) (@ (@ tptp.map_Pr8991440229025900053n_assn G3) Ys)) (= (@ tptp.size_s6829681357464350627n_assn Xs) (@ tptp.size_s6829681357464350627n_assn Ys)))))
% 3.15/3.51 (assert (forall ((F2 (-> tptp.produc6575502325842934193n_assn tptp.assn)) (Xs tptp.list_P8527749157015355191n_assn) (G3 (-> tptp.int tptp.assn)) (Ys tptp.list_int)) (=> (= (@ (@ tptp.map_Pr8991440229025900053n_assn F2) Xs) (@ (@ tptp.map_int_assn G3) Ys)) (= (@ tptp.size_s6829681357464350627n_assn Xs) (@ tptp.size_size_list_int Ys)))))
% 3.15/3.51 (assert (forall ((F2 (-> tptp.produc6575502325842934193n_assn tptp.assn)) (Xs tptp.list_P8527749157015355191n_assn) (G3 (-> tptp.nat tptp.assn)) (Ys tptp.list_nat)) (=> (= (@ (@ tptp.map_Pr8991440229025900053n_assn F2) Xs) (@ (@ tptp.map_nat_assn G3) Ys)) (= (@ tptp.size_s6829681357464350627n_assn Xs) (@ tptp.size_size_list_nat Ys)))))
% 3.15/3.51 (assert (forall ((F2 (-> tptp.int tptp.assn)) (Xs tptp.list_int) (G3 (-> tptp.produc6575502325842934193n_assn tptp.assn)) (Ys tptp.list_P8527749157015355191n_assn)) (=> (= (@ (@ tptp.map_int_assn F2) Xs) (@ (@ tptp.map_Pr8991440229025900053n_assn G3) Ys)) (= (@ tptp.size_size_list_int Xs) (@ tptp.size_s6829681357464350627n_assn Ys)))))
% 3.15/3.51 (assert (forall ((F2 (-> tptp.int tptp.nat)) (Xs tptp.list_int) (G3 (-> tptp.nat tptp.nat)) (Ys tptp.list_nat)) (=> (= (@ (@ tptp.map_int_nat F2) Xs) (@ (@ tptp.map_nat_nat G3) Ys)) (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_nat Ys)))))
% 3.15/3.51 (assert (forall ((F2 (-> tptp.nat tptp.assn)) (Xs tptp.list_nat) (G3 (-> tptp.produc6575502325842934193n_assn tptp.assn)) (Ys tptp.list_P8527749157015355191n_assn)) (=> (= (@ (@ tptp.map_nat_assn F2) Xs) (@ (@ tptp.map_Pr8991440229025900053n_assn G3) Ys)) (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_s6829681357464350627n_assn Ys)))))
% 3.15/3.51 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (Xs tptp.list_nat) (G3 (-> tptp.int tptp.nat)) (Ys tptp.list_int)) (=> (= (@ (@ tptp.map_nat_nat F2) Xs) (@ (@ tptp.map_int_nat G3) Ys)) (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_int Ys)))))
% 3.15/3.51 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (Xs tptp.list_nat) (G3 (-> tptp.nat tptp.nat)) (Ys tptp.list_nat)) (=> (= (@ (@ tptp.map_nat_nat F2) Xs) (@ (@ tptp.map_nat_nat G3) Ys)) (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys)))))
% 3.15/3.51 (assert (@ tptp.abel_semigroup_int tptp.ord_max_int))
% 3.15/3.51 (assert (forall ((A tptp.list_int) (B tptp.list_int) (A5 tptp.list_int) (B6 tptp.list_int)) (=> (= (@ tptp.size_size_list_int A) (@ tptp.size_size_list_int B)) (=> (= (@ tptp.size_size_list_int A5) (@ tptp.size_size_list_int B6)) (=> (= (@ (@ tptp.zip_int_int A) B) (@ (@ tptp.zip_int_int A5) B6)) (and (= A A5) (= B B6)))))))
% 3.15/3.51 (assert (forall ((A tptp.list_int) (B tptp.list_nat) (A5 tptp.list_int) (B6 tptp.list_nat)) (=> (= (@ tptp.size_size_list_int A) (@ tptp.size_size_list_nat B)) (=> (= (@ tptp.size_size_list_int A5) (@ tptp.size_size_list_nat B6)) (=> (= (@ (@ tptp.zip_int_nat A) B) (@ (@ tptp.zip_int_nat A5) B6)) (and (= A A5) (= B B6)))))))
% 3.15/3.51 (assert (forall ((A tptp.list_nat) (B tptp.list_int) (A5 tptp.list_nat) (B6 tptp.list_int)) (=> (= (@ tptp.size_size_list_nat A) (@ tptp.size_size_list_int B)) (=> (= (@ tptp.size_size_list_nat A5) (@ tptp.size_size_list_int B6)) (=> (= (@ (@ tptp.zip_nat_int A) B) (@ (@ tptp.zip_nat_int A5) B6)) (and (= A A5) (= B B6)))))))
% 3.15/3.51 (assert (forall ((A tptp.list_nat) (B tptp.list_nat) (A5 tptp.list_nat) (B6 tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat A) (@ tptp.size_size_list_nat B)) (=> (= (@ tptp.size_size_list_nat A5) (@ tptp.size_size_list_nat B6)) (=> (= (@ (@ tptp.zip_nat_nat A) B) (@ (@ tptp.zip_nat_nat A5) B6)) (and (= A A5) (= B B6)))))))
% 3.15/3.51 (assert (@ tptp.semilattice_int tptp.ord_max_int))
% 3.15/3.51 (assert (@ tptp.semigroup_int tptp.ord_max_int))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se9216721137139052372nteger tptp.one_one_Code_integer) N) (= N tptp.zero_zero_nat))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) N) (= N tptp.zero_zero_nat))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int tptp.one_one_int) N) (= N tptp.zero_zero_nat))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.bit_se9216721137139052372nteger tptp.one_one_Code_integer) (@ tptp.suc N)))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) (@ tptp.suc N)))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.bit_se1146084159140164899it_int tptp.one_one_int) (@ tptp.suc N)))))
% 3.15/3.51 (assert (forall ((N tptp.num)) (not (@ (@ tptp.bit_se9216721137139052372nteger tptp.one_one_Code_integer) (@ tptp.numeral_numeral_nat N)))))
% 3.15/3.51 (assert (forall ((N tptp.num)) (not (@ (@ tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N)))))
% 3.15/3.51 (assert (forall ((N tptp.num)) (not (@ (@ tptp.bit_se1146084159140164899it_int tptp.one_one_int) (@ tptp.numeral_numeral_nat N)))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int) (Zs tptp.list_int) (Ws tptp.list_int) (P2 (-> tptp.list_int tptp.list_int tptp.list_int tptp.list_int Bool))) (let ((_let_1 (@ tptp.size_size_list_int Zs))) (let ((_let_2 (@ tptp.size_size_list_int Ys))) (=> (= (@ tptp.size_size_list_int Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_int Ws)) (=> (@ (@ (@ (@ P2 tptp.nil_int) tptp.nil_int) tptp.nil_int) tptp.nil_int) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int) (Y3 tptp.int) (Ys3 tptp.list_int) (Z2 tptp.int) (Zs3 tptp.list_int) (W3 tptp.int) (Ws2 tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Zs3))) (let ((_let_2 (@ tptp.size_size_list_int Ys3))) (=> (= (@ tptp.size_size_list_int Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_int Ws2)) (=> (@ (@ (@ (@ P2 Xs2) Ys3) Zs3) Ws2) (@ (@ (@ (@ P2 (@ (@ tptp.cons_int X3) Xs2)) (@ (@ tptp.cons_int Y3) Ys3)) (@ (@ tptp.cons_int Z2) Zs3)) (@ (@ tptp.cons_int W3) Ws2))))))))) (@ (@ (@ (@ P2 Xs) Ys) Zs) Ws))))))))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int) (Zs tptp.list_int) (Ws tptp.list_nat) (P2 (-> tptp.list_int tptp.list_int tptp.list_int tptp.list_nat Bool))) (let ((_let_1 (@ tptp.size_size_list_int Zs))) (let ((_let_2 (@ tptp.size_size_list_int Ys))) (=> (= (@ tptp.size_size_list_int Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Ws)) (=> (@ (@ (@ (@ P2 tptp.nil_int) tptp.nil_int) tptp.nil_int) tptp.nil_nat) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int) (Y3 tptp.int) (Ys3 tptp.list_int) (Z2 tptp.int) (Zs3 tptp.list_int) (W3 tptp.nat) (Ws2 tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_int Zs3))) (let ((_let_2 (@ tptp.size_size_list_int Ys3))) (=> (= (@ tptp.size_size_list_int Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Ws2)) (=> (@ (@ (@ (@ P2 Xs2) Ys3) Zs3) Ws2) (@ (@ (@ (@ P2 (@ (@ tptp.cons_int X3) Xs2)) (@ (@ tptp.cons_int Y3) Ys3)) (@ (@ tptp.cons_int Z2) Zs3)) (@ (@ tptp.cons_nat W3) Ws2))))))))) (@ (@ (@ (@ P2 Xs) Ys) Zs) Ws))))))))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int) (Zs tptp.list_nat) (Ws tptp.list_int) (P2 (-> tptp.list_int tptp.list_int tptp.list_nat tptp.list_int Bool))) (let ((_let_1 (@ tptp.size_size_list_nat Zs))) (let ((_let_2 (@ tptp.size_size_list_int Ys))) (=> (= (@ tptp.size_size_list_int Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_int Ws)) (=> (@ (@ (@ (@ P2 tptp.nil_int) tptp.nil_int) tptp.nil_nat) tptp.nil_int) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int) (Y3 tptp.int) (Ys3 tptp.list_int) (Z2 tptp.nat) (Zs3 tptp.list_nat) (W3 tptp.int) (Ws2 tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_nat Zs3))) (let ((_let_2 (@ tptp.size_size_list_int Ys3))) (=> (= (@ tptp.size_size_list_int Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_int Ws2)) (=> (@ (@ (@ (@ P2 Xs2) Ys3) Zs3) Ws2) (@ (@ (@ (@ P2 (@ (@ tptp.cons_int X3) Xs2)) (@ (@ tptp.cons_int Y3) Ys3)) (@ (@ tptp.cons_nat Z2) Zs3)) (@ (@ tptp.cons_int W3) Ws2))))))))) (@ (@ (@ (@ P2 Xs) Ys) Zs) Ws))))))))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int) (Zs tptp.list_nat) (Ws tptp.list_nat) (P2 (-> tptp.list_int tptp.list_int tptp.list_nat tptp.list_nat Bool))) (let ((_let_1 (@ tptp.size_size_list_nat Zs))) (let ((_let_2 (@ tptp.size_size_list_int Ys))) (=> (= (@ tptp.size_size_list_int Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Ws)) (=> (@ (@ (@ (@ P2 tptp.nil_int) tptp.nil_int) tptp.nil_nat) tptp.nil_nat) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int) (Y3 tptp.int) (Ys3 tptp.list_int) (Z2 tptp.nat) (Zs3 tptp.list_nat) (W3 tptp.nat) (Ws2 tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Zs3))) (let ((_let_2 (@ tptp.size_size_list_int Ys3))) (=> (= (@ tptp.size_size_list_int Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Ws2)) (=> (@ (@ (@ (@ P2 Xs2) Ys3) Zs3) Ws2) (@ (@ (@ (@ P2 (@ (@ tptp.cons_int X3) Xs2)) (@ (@ tptp.cons_int Y3) Ys3)) (@ (@ tptp.cons_nat Z2) Zs3)) (@ (@ tptp.cons_nat W3) Ws2))))))))) (@ (@ (@ (@ P2 Xs) Ys) Zs) Ws))))))))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_nat) (Zs tptp.list_int) (Ws tptp.list_int) (P2 (-> tptp.list_int tptp.list_nat tptp.list_int tptp.list_int Bool))) (let ((_let_1 (@ tptp.size_size_list_int Zs))) (let ((_let_2 (@ tptp.size_size_list_nat Ys))) (=> (= (@ tptp.size_size_list_int Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_int Ws)) (=> (@ (@ (@ (@ P2 tptp.nil_int) tptp.nil_nat) tptp.nil_int) tptp.nil_int) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int) (Y3 tptp.nat) (Ys3 tptp.list_nat) (Z2 tptp.int) (Zs3 tptp.list_int) (W3 tptp.int) (Ws2 tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Zs3))) (let ((_let_2 (@ tptp.size_size_list_nat Ys3))) (=> (= (@ tptp.size_size_list_int Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_int Ws2)) (=> (@ (@ (@ (@ P2 Xs2) Ys3) Zs3) Ws2) (@ (@ (@ (@ P2 (@ (@ tptp.cons_int X3) Xs2)) (@ (@ tptp.cons_nat Y3) Ys3)) (@ (@ tptp.cons_int Z2) Zs3)) (@ (@ tptp.cons_int W3) Ws2))))))))) (@ (@ (@ (@ P2 Xs) Ys) Zs) Ws))))))))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_nat) (Zs tptp.list_int) (Ws tptp.list_nat) (P2 (-> tptp.list_int tptp.list_nat tptp.list_int tptp.list_nat Bool))) (let ((_let_1 (@ tptp.size_size_list_int Zs))) (let ((_let_2 (@ tptp.size_size_list_nat Ys))) (=> (= (@ tptp.size_size_list_int Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Ws)) (=> (@ (@ (@ (@ P2 tptp.nil_int) tptp.nil_nat) tptp.nil_int) tptp.nil_nat) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int) (Y3 tptp.nat) (Ys3 tptp.list_nat) (Z2 tptp.int) (Zs3 tptp.list_int) (W3 tptp.nat) (Ws2 tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_int Zs3))) (let ((_let_2 (@ tptp.size_size_list_nat Ys3))) (=> (= (@ tptp.size_size_list_int Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Ws2)) (=> (@ (@ (@ (@ P2 Xs2) Ys3) Zs3) Ws2) (@ (@ (@ (@ P2 (@ (@ tptp.cons_int X3) Xs2)) (@ (@ tptp.cons_nat Y3) Ys3)) (@ (@ tptp.cons_int Z2) Zs3)) (@ (@ tptp.cons_nat W3) Ws2))))))))) (@ (@ (@ (@ P2 Xs) Ys) Zs) Ws))))))))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_nat) (Zs tptp.list_nat) (Ws tptp.list_int) (P2 (-> tptp.list_int tptp.list_nat tptp.list_nat tptp.list_int Bool))) (let ((_let_1 (@ tptp.size_size_list_nat Zs))) (let ((_let_2 (@ tptp.size_size_list_nat Ys))) (=> (= (@ tptp.size_size_list_int Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_int Ws)) (=> (@ (@ (@ (@ P2 tptp.nil_int) tptp.nil_nat) tptp.nil_nat) tptp.nil_int) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int) (Y3 tptp.nat) (Ys3 tptp.list_nat) (Z2 tptp.nat) (Zs3 tptp.list_nat) (W3 tptp.int) (Ws2 tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_nat Zs3))) (let ((_let_2 (@ tptp.size_size_list_nat Ys3))) (=> (= (@ tptp.size_size_list_int Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_int Ws2)) (=> (@ (@ (@ (@ P2 Xs2) Ys3) Zs3) Ws2) (@ (@ (@ (@ P2 (@ (@ tptp.cons_int X3) Xs2)) (@ (@ tptp.cons_nat Y3) Ys3)) (@ (@ tptp.cons_nat Z2) Zs3)) (@ (@ tptp.cons_int W3) Ws2))))))))) (@ (@ (@ (@ P2 Xs) Ys) Zs) Ws))))))))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_nat) (Zs tptp.list_nat) (Ws tptp.list_nat) (P2 (-> tptp.list_int tptp.list_nat tptp.list_nat tptp.list_nat Bool))) (let ((_let_1 (@ tptp.size_size_list_nat Zs))) (let ((_let_2 (@ tptp.size_size_list_nat Ys))) (=> (= (@ tptp.size_size_list_int Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Ws)) (=> (@ (@ (@ (@ P2 tptp.nil_int) tptp.nil_nat) tptp.nil_nat) tptp.nil_nat) (=> (forall ((X3 tptp.int) (Xs2 tptp.list_int) (Y3 tptp.nat) (Ys3 tptp.list_nat) (Z2 tptp.nat) (Zs3 tptp.list_nat) (W3 tptp.nat) (Ws2 tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Zs3))) (let ((_let_2 (@ tptp.size_size_list_nat Ys3))) (=> (= (@ tptp.size_size_list_int Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Ws2)) (=> (@ (@ (@ (@ P2 Xs2) Ys3) Zs3) Ws2) (@ (@ (@ (@ P2 (@ (@ tptp.cons_int X3) Xs2)) (@ (@ tptp.cons_nat Y3) Ys3)) (@ (@ tptp.cons_nat Z2) Zs3)) (@ (@ tptp.cons_nat W3) Ws2))))))))) (@ (@ (@ (@ P2 Xs) Ys) Zs) Ws))))))))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_int) (Zs tptp.list_int) (Ws tptp.list_int) (P2 (-> tptp.list_nat tptp.list_int tptp.list_int tptp.list_int Bool))) (let ((_let_1 (@ tptp.size_size_list_int Zs))) (let ((_let_2 (@ tptp.size_size_list_int Ys))) (=> (= (@ tptp.size_size_list_nat Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_int Ws)) (=> (@ (@ (@ (@ P2 tptp.nil_nat) tptp.nil_int) tptp.nil_int) tptp.nil_int) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y3 tptp.int) (Ys3 tptp.list_int) (Z2 tptp.int) (Zs3 tptp.list_int) (W3 tptp.int) (Ws2 tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Zs3))) (let ((_let_2 (@ tptp.size_size_list_int Ys3))) (=> (= (@ tptp.size_size_list_nat Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_int Ws2)) (=> (@ (@ (@ (@ P2 Xs2) Ys3) Zs3) Ws2) (@ (@ (@ (@ P2 (@ (@ tptp.cons_nat X3) Xs2)) (@ (@ tptp.cons_int Y3) Ys3)) (@ (@ tptp.cons_int Z2) Zs3)) (@ (@ tptp.cons_int W3) Ws2))))))))) (@ (@ (@ (@ P2 Xs) Ys) Zs) Ws))))))))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_int) (Zs tptp.list_int) (Ws tptp.list_nat) (P2 (-> tptp.list_nat tptp.list_int tptp.list_int tptp.list_nat Bool))) (let ((_let_1 (@ tptp.size_size_list_int Zs))) (let ((_let_2 (@ tptp.size_size_list_int Ys))) (=> (= (@ tptp.size_size_list_nat Xs) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Ws)) (=> (@ (@ (@ (@ P2 tptp.nil_nat) tptp.nil_int) tptp.nil_int) tptp.nil_nat) (=> (forall ((X3 tptp.nat) (Xs2 tptp.list_nat) (Y3 tptp.int) (Ys3 tptp.list_int) (Z2 tptp.int) (Zs3 tptp.list_int) (W3 tptp.nat) (Ws2 tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_int Zs3))) (let ((_let_2 (@ tptp.size_size_list_int Ys3))) (=> (= (@ tptp.size_size_list_nat Xs2) _let_2) (=> (= _let_2 _let_1) (=> (= _let_1 (@ tptp.size_size_list_nat Ws2)) (=> (@ (@ (@ (@ P2 Xs2) Ys3) Zs3) Ws2) (@ (@ (@ (@ P2 (@ (@ tptp.cons_nat X3) Xs2)) (@ (@ tptp.cons_int Y3) Ys3)) (@ (@ tptp.cons_int Z2) Zs3)) (@ (@ tptp.cons_nat W3) Ws2))))))))) (@ (@ (@ (@ P2 Xs) Ys) Zs) Ws))))))))))
% 3.15/3.51 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int K)) tptp.one_one_int)) N) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N)))))
% 3.15/3.51 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int K)) N) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.minus_minus_int K) tptp.one_one_int))) N))))
% 3.15/3.51 (assert (forall ((K tptp.int)) (not (forall ((N4 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (forall ((M4 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (@ (@ tptp.ord_less_eq_nat N4) M4) (= (@ _let_1 M4) (@ _let_1 N4))))) (not (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N4) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) (not (@ _let_1 N4)))))))))))
% 3.15/3.51 (assert (forall ((V2 tptp.num)) (= (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat V2)) tptp.one_one_nat) (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int V2)) tptp.one_one_int)))))
% 3.15/3.51 (assert (= (@ tptp.nat2 tptp.one_one_int) (@ tptp.suc tptp.zero_zero_nat)))
% 3.15/3.51 (assert (forall ((I2 tptp.int) (J tptp.int)) (= (@ tptp.size_size_list_int (@ (@ tptp.upto I2) J)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int J) I2)) tptp.one_one_int)))))
% 3.15/3.51 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z))))
% 3.15/3.51 (assert (forall ((Ns tptp.list_nat) (I2 tptp.nat)) (=> (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) Ns) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Ns)) (@ (@ tptp.ord_less_eq_nat I2) (@ (@ tptp.nth_nat Ns) I2))))))
% 3.15/3.51 (assert (forall ((M2 tptp.int) (N tptp.int)) (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) (@ (@ tptp.upto M2) N))))
% 3.15/3.51 (assert (forall ((I2 tptp.int) (J tptp.int)) (@ (@ tptp.sorted_wrt_int tptp.ord_less_int) (@ (@ tptp.upto I2) J))))
% 3.15/3.51 (assert (= tptp.one_one_nat (@ tptp.nat2 tptp.one_one_int)))
% 3.15/3.51 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.suc (@ tptp.nat2 Z)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int tptp.one_one_int) Z))))))
% 3.15/3.51 (assert (forall ((I2 tptp.int) (J tptp.int)) (let ((_let_1 (@ tptp.upto I2))) (=> (@ (@ tptp.ord_less_eq_int I2) J) (= (@ _let_1 J) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.cons_int J) tptp.nil_int)))))))
% 3.15/3.51 (assert (forall ((P5 tptp.int)) (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P5) tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))))
% 3.15/3.51 (assert (forall ((J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I2) (= (@ (@ tptp.upt I2) J) tptp.nil_nat))))
% 3.15/3.51 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (= (= (@ (@ tptp.upt I2) J) tptp.nil_nat) (or (= J tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat J) I2)))))
% 3.15/3.51 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.upt I2) J)) (@ (@ tptp.minus_minus_nat J) I2))))
% 3.15/3.51 (assert (forall ((M2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (let ((_let_2 (@ tptp.numeral_numeral_nat M2))) (let ((_let_3 (@ (@ tptp.upt _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_nat _let_2) (@ (@ tptp.upt (@ tptp.suc _let_2)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_nat)))))))))
% 3.15/3.51 (assert (forall ((I2 tptp.nat) (K tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I2) K))) (=> (@ (@ tptp.ord_less_nat _let_1) J) (= (@ (@ tptp.nth_nat (@ (@ tptp.upt I2) J)) K) _let_1)))))
% 3.15/3.51 (assert (forall ((I2 tptp.nat)) (= (@ (@ tptp.upt I2) tptp.zero_zero_nat) tptp.nil_nat)))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.map_nat_nat tptp.suc) (@ (@ tptp.upt M2) N)) (@ (@ tptp.upt (@ tptp.suc M2)) (@ tptp.suc N)))))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N tptp.nat) (Ns tptp.list_nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.cons_nat N) Ns))) (= (= (@ (@ tptp.cons_nat M2) _let_1) (@ (@ tptp.upt M2) Q4)) (= _let_1 (@ (@ tptp.upt (@ tptp.suc M2)) Q4))))))
% 3.15/3.51 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (= (@ (@ tptp.upt I2) J) (@ (@ tptp.cons_nat I2) (@ (@ tptp.upt (@ tptp.suc I2)) J))))))
% 3.15/3.51 (assert (= tptp.upt (lambda ((I4 tptp.nat) (J2 tptp.nat)) (@ (@ (@ tptp.if_list_nat (@ (@ tptp.ord_less_nat I4) J2)) (@ (@ tptp.cons_nat I4) (@ (@ tptp.upt (@ tptp.suc I4)) J2))) tptp.nil_nat))))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) (@ (@ tptp.upt M2) N))))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) (@ (@ tptp.upt M2) N))))
% 3.15/3.51 (assert (forall ((I2 tptp.nat) (J tptp.nat) (X tptp.nat) (Xs tptp.list_nat)) (= (= (@ (@ tptp.upt I2) J) (@ (@ tptp.cons_nat X) Xs)) (and (@ (@ tptp.ord_less_nat I2) J) (= I2 X) (= (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat I2) tptp.one_one_nat)) J) Xs)))))
% 3.15/3.51 (assert (= tptp.upto_aux (lambda ((I4 tptp.int) (J2 tptp.int) (__flatten_var_0 tptp.list_int)) (@ (@ tptp.append_int (@ (@ tptp.upto I4) J2)) __flatten_var_0))))
% 3.15/3.51 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I2))) (=> (@ (@ tptp.ord_less_eq_int I2) J) (=> (@ (@ tptp.ord_less_eq_int J) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 J)) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int J) tptp.one_one_int)) K))))))))
% 3.15/3.51 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I2))) (=> (@ (@ tptp.ord_less_eq_int I2) J) (=> (@ (@ tptp.ord_less_eq_int J) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.upto J) K))))))))
% 3.15/3.51 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I2))) (=> (@ (@ tptp.ord_less_eq_int I2) J) (=> (@ (@ tptp.ord_less_eq_int J) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.cons_int J) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int J) tptp.one_one_int)) K)))))))))
% 3.15/3.51 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.bezw X) tptp.zero_zero_nat) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))))
% 3.15/3.51 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.upt I2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ _let_1 (@ tptp.suc J)) (@ (@ tptp.append_nat (@ _let_1 J)) (@ (@ tptp.cons_nat J) tptp.nil_nat)))))))
% 3.15/3.51 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.upt I2))) (let ((_let_2 (@ _let_1 (@ tptp.suc J)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat I2) J))) (and (=> _let_3 (= _let_2 (@ (@ tptp.append_nat (@ _let_1 J)) (@ (@ tptp.cons_nat J) tptp.nil_nat)))) (=> (not _let_3) (= _let_2 tptp.nil_nat))))))))
% 3.15/3.51 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat J) K))) (let ((_let_2 (@ tptp.upt I2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ _let_2 _let_1) (@ (@ tptp.append_nat (@ _let_2 J)) (@ (@ tptp.upt J) _let_1))))))))
% 3.15/3.51 (assert (forall ((X tptp.nat) (Xa tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.bezw Xa) (@ (@ tptp.modulo_modulo_nat X) Xa)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (let ((_let_3 (= Xa tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X) Xa) Y) (and (=> _let_3 (= Y (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_3) (= Y (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Xa))))))))))))))
% 3.15/3.51 (assert (= tptp.bezw (lambda ((X2 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y2) (@ (@ tptp.modulo_modulo_nat X2) Y2)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= Y2 tptp.zero_zero_nat)) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X2) Y2)))))))))))
% 3.15/3.51 (assert (forall ((I2 tptp.int) (K tptp.nat) (J tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int I2) (@ tptp.semiri1314217659103216013at_int K)))) (=> (@ (@ tptp.ord_less_eq_int _let_1) J) (= (@ (@ tptp.nth_int (@ (@ tptp.upto I2) J)) K) _let_1)))))
% 3.15/3.51 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 3.15/3.51 (assert (forall ((A tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc A)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) tptp.one_one_int))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int))))
% 3.15/3.51 (assert (= tptp.suc (lambda ((A2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A2)) tptp.one_one_int)))))
% 3.15/3.51 (assert (forall ((X tptp.nat) (Xa tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.bezw_rel) (@ (@ tptp.product_Pair_nat_nat X) Xa)))) (let ((_let_2 (@ (@ tptp.bezw Xa) (@ (@ tptp.modulo_modulo_nat X) Xa)))) (let ((_let_3 (@ tptp.product_snd_int_int _let_2))) (let ((_let_4 (= Xa tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X) Xa) Y) (=> _let_1 (not (=> (and (=> _let_4 (= Y (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_4) (= Y (@ (@ tptp.product_Pair_int_int _let_3) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_2)) (@ (@ tptp.times_times_int _let_3) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Xa)))))))) (not _let_1)))))))))))
% 3.15/3.51 (assert (forall ((I2 tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I2) M2))) (let ((_let_2 (@ tptp.upt I2))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) N) (= (@ (@ tptp.take_nat M2) (@ _let_2 N)) (@ _let_2 _let_1)))))))
% 3.15/3.51 (assert (= tptp.inf_inf_nat tptp.ord_min_nat))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M2) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.dvd_dvd_nat M2) (@ tptp.semiri1408675320244567234ct_nat N))))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.binomial N) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) _let_1)))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) N) tptp.one_one_nat)))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) tptp.zero_zero_nat) tptp.one_one_nat)))
% 3.15/3.51 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (= (@ tptp.last_nat (@ (@ tptp.upt I2) J)) (@ (@ tptp.minus_minus_nat J) tptp.one_one_nat)))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) tptp.one_one_nat) N)))
% 3.15/3.51 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (= (@ (@ tptp.times_times_nat (@ _let_1 K)) (@ (@ tptp.binomial N) K)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.binomial (@ _let_1 tptp.one_one_nat)) K))))))
% 3.15/3.51 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.binomial N) _let_1)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) K))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_2 N) (=> (@ _let_2 K) (= (@ (@ tptp.binomial N) K) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat))) (@ _let_1 K)))))))))
% 3.15/3.51 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.times_times_nat K) (@ (@ tptp.binomial N) K)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat)))))))
% 3.15/3.51 (assert (= tptp.binomial (lambda ((N3 tptp.nat) (K4 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N3) K4))) (let ((_let_2 (@ tptp.ord_less_nat N3))) (@ (@ (@ tptp.if_nat (@ _let_2 K4)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_2 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K4))) (@ (@ tptp.binomial N3) _let_1)) (@ (@ tptp.divide_divide_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) N3) tptp.one_one_nat)) (@ tptp.semiri1408675320244567234ct_nat K4)))))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))) (let ((_let_2 (@ tptp.suc K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.binomial N) _let_2) (@ (@ tptp.plus_plus_nat (@ _let_1 _let_2)) (@ _let_1 K))))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.minus_minus_nat J) (@ tptp.suc I2))) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I2) J))) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat I2) N))))))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (I2 tptp.nat) (J tptp.nat)) (= (@ (@ tptp.drop_nat M2) (@ (@ tptp.upt I2) J)) (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat I2) M2)) J))))
% 3.15/3.51 (assert (= tptp.set_or5834768355832116004an_nat (lambda ((N3 tptp.nat) (M3 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N3)) M3)))))
% 3.15/3.51 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.suc I2))) (=> (@ (@ tptp.ord_less_nat _let_1) J) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I2) J)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat _let_1) J))))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.minus_minus_nat J) I2)) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I2) J))) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat I2) N))))))
% 3.15/3.51 (assert (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.append_nat (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_atMost_nat K))) (@ (@ tptp.cons_nat _let_1) tptp.nil_nat))))))
% 3.15/3.51 (assert (forall ((K tptp.nat)) (= (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_lessThan_nat (@ tptp.suc K))) (@ (@ tptp.append_nat (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_lessThan_nat K))) (@ (@ tptp.cons_nat K) tptp.nil_nat)))))
% 3.15/3.51 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (= (@ tptp.hd_nat (@ (@ tptp.upt I2) J)) I2))))
% 3.15/3.51 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (@ tptp.distinct_nat (@ (@ tptp.upt I2) J))))
% 3.15/3.51 (assert (forall ((I2 tptp.int) (J tptp.int)) (@ tptp.distinct_int (@ (@ tptp.upto I2) J))))
% 3.15/3.51 (assert (= tptp.set_ord_lessThan_nat (lambda ((N3 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) N3)))))
% 3.15/3.51 (assert (= tptp.set_or6659071591806873216st_nat (lambda ((N3 tptp.nat) (M3 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N3)) (@ tptp.suc M3))))))
% 3.15/3.51 (assert (= tptp.set_ord_atMost_nat (lambda ((N3 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) (@ tptp.suc N3))))))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.upt M2))) (= (@ tptp.butlast_nat (@ _let_1 N)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 3.15/3.51 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.suc I2))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) J) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I2) J)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat _let_1) J))))))))
% 3.15/3.51 (assert (= tptp.set_or5832277885323065728an_int (lambda ((I4 tptp.int) (J2 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) (@ (@ tptp.minus_minus_int J2) tptp.one_one_int))))))
% 3.15/3.51 (assert (forall ((K tptp.num)) (= (@ tptp.quotient_of (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat K))) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.one_one_int))))
% 3.15/3.51 (assert (forall ((D tptp.int) (P2 (-> tptp.int Bool)) (P3 (-> tptp.int Bool)) (A3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (= (@ P2 X3) (@ P3 X3))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int2 Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int2 Xb2) A3) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ P2 X3) (@ P2 (@ (@ tptp.plus_plus_int X3) D))))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P3 X3) (@ P3 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D))))) (= (exists ((X5 tptp.int)) (@ P2 X5)) (or (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int2 X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (@ P3 X2))) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int2 X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (exists ((Y2 tptp.int)) (and (@ (@ tptp.member_int2 Y2) A3) (@ P2 (@ (@ tptp.minus_minus_int Y2) X2))))))))))))))
% 3.15/3.51 (assert (= (@ tptp.finite410649719033368117t_unit tptp.top_to1996260823553986621t_unit) tptp.one_one_nat))
% 3.15/3.51 (assert (= (@ tptp.quotient_of tptp.one_one_rat) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int)))
% 3.15/3.51 (assert (= (@ tptp.quotient_of tptp.zero_zero_rat) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)))
% 3.15/3.51 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or1266510415728281911st_int L) U)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int U) L)) tptp.one_one_int)))))
% 3.15/3.51 (assert (= (@ tptp.quotient_of (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int)))
% 3.15/3.51 (assert (forall ((K tptp.num)) (= (@ tptp.quotient_of (@ tptp.numeral_numeral_rat K)) (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int K)) tptp.one_one_int))))
% 3.15/3.51 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or5832277885323065728an_int L) U)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int U) (@ (@ tptp.plus_plus_int L) tptp.one_one_int))))))
% 3.15/3.51 (assert (= tptp.sgn_sgn_rat (lambda ((A2 tptp.rat)) (@ (@ (@ tptp.if_rat (= A2 tptp.zero_zero_rat)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2)) tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 3.15/3.51 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.plus_plus_int L) tptp.one_one_int)) U) (@ (@ tptp.set_or6656581121297822940st_int L) U))))
% 3.15/3.51 (assert (= tptp.set_or1266510415728281911st_int (lambda ((I4 tptp.int) (J2 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I4) J2)))))
% 3.15/3.51 (assert (forall ((D tptp.int) (B3 tptp.set_int) (P2 (-> tptp.int Bool)) (Q2 (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int2 Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int2 Xb2) B3) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ P2 X3) (@ P2 (@ (@ tptp.minus_minus_int X3) D))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int2 Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int2 Xb2) B3) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ Q2 X3) (@ Q2 (@ (@ tptp.minus_minus_int X3) D))))) (forall ((X4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X4) D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int2 Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int2 Xb3) B3) (not (= X4 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (and (@ P2 X4) (@ Q2 X4)) (and (@ P2 _let_1) (@ Q2 _let_1))))))))))
% 3.15/3.51 (assert (forall ((D tptp.int) (B3 tptp.set_int) (P2 (-> tptp.int Bool)) (Q2 (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int2 Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int2 Xb2) B3) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ P2 X3) (@ P2 (@ (@ tptp.minus_minus_int X3) D))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int2 Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int2 Xb2) B3) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ Q2 X3) (@ Q2 (@ (@ tptp.minus_minus_int X3) D))))) (forall ((X4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X4) D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int2 Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int2 Xb3) B3) (not (= X4 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (or (@ P2 X4) (@ Q2 X4)) (or (@ P2 _let_1) (@ Q2 _let_1))))))))))
% 3.15/3.51 (assert (forall ((D tptp.int) (A3 tptp.set_int) (P2 (-> tptp.int Bool)) (Q2 (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int2 Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int2 Xb2) A3) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ P2 X3) (@ P2 (@ (@ tptp.plus_plus_int X3) D))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int2 Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int2 Xb2) A3) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ Q2 X3) (@ Q2 (@ (@ tptp.plus_plus_int X3) D))))) (forall ((X4 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int X4) D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int2 Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int2 Xb3) A3) (not (= X4 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (and (@ P2 X4) (@ Q2 X4)) (and (@ P2 _let_1) (@ Q2 _let_1))))))))))
% 3.15/3.51 (assert (forall ((D tptp.int) (A3 tptp.set_int) (P2 (-> tptp.int Bool)) (Q2 (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int2 Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int2 Xb2) A3) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ P2 X3) (@ P2 (@ (@ tptp.plus_plus_int X3) D))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int2 Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int2 Xb2) A3) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ Q2 X3) (@ Q2 (@ (@ tptp.plus_plus_int X3) D))))) (forall ((X4 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int X4) D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int2 Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int2 Xb3) A3) (not (= X4 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (or (@ P2 X4) (@ Q2 X4)) (or (@ P2 _let_1) (@ Q2 _let_1))))))))))
% 3.15/3.51 (assert (= tptp.set_or6656581121297822940st_int (lambda ((I4 tptp.int) (J2 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) J2)))))
% 3.15/3.51 (assert (forall ((D2 tptp.int) (D tptp.int) (B3 tptp.set_int) (T3 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D2))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int2 Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int2 Xb3) B3) (not (= X4 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ _let_1 (@ (@ tptp.plus_plus_int X4) T3)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X4) D)) T3)))))))))
% 3.15/3.51 (assert (forall ((D2 tptp.int) (D tptp.int) (B3 tptp.set_int) (T3 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D2))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int2 Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int2 Xb3) B3) (not (= X4 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (not (@ _let_1 (@ (@ tptp.plus_plus_int X4) T3))) (not (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X4) D)) T3))))))))))
% 3.15/3.51 (assert (forall ((D2 tptp.int) (D tptp.int) (A3 tptp.set_int) (T3 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X4))) (let ((_let_2 (@ tptp.dvd_dvd_int D2))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int2 Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int2 Xb3) A3) (not (= X4 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ _let_2 (@ _let_1 T3)) (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 D)) T3))))))))))
% 3.15/3.51 (assert (forall ((D2 tptp.int) (D tptp.int) (A3 tptp.set_int) (T3 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X4))) (let ((_let_2 (@ tptp.dvd_dvd_int D2))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int2 Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int2 Xb3) A3) (not (= X4 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (not (@ _let_2 (@ _let_1 T3))) (not (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 D)) T3)))))))))))
% 3.15/3.51 (assert (forall ((M2 tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.set_or1266510415728281911st_int M2))) (let ((_let_2 (@ (@ tptp.plus_plus_int tptp.one_one_int) N))) (=> (@ (@ tptp.ord_less_eq_int M2) _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.insert_int2 _let_2) (@ _let_1 N))))))))
% 3.15/3.51 (assert (forall ((D2 tptp.int) (P2 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P2 X3) (@ P2 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D2))))) (= (exists ((X5 tptp.int)) (@ P2 X5)) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int2 X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D2)) (@ P2 X2))))))))
% 3.15/3.51 (assert (forall ((D tptp.int) (A3 tptp.set_int) (T3 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int T3))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int2 Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int2 Xb3) A3) (not (= X4 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.plus_plus_int X4) D)))))))))
% 3.15/3.51 (assert (forall ((D tptp.int) (T3 tptp.int) (A3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (@ (@ tptp.member_int2 T3) A3) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int2 Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int2 Xb3) A3) (not (= X4 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_int X4) T3) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X4) D)) T3))))))))
% 3.15/3.51 (assert (forall ((D tptp.int) (T3 tptp.int) (A3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (@ (@ tptp.member_int2 T3) A3) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int2 Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int2 Xb3) A3) (not (= X4 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (not (= X4 T3)) (not (= (@ (@ tptp.plus_plus_int X4) D) T3)))))))))
% 3.15/3.51 (assert (forall ((D tptp.int) (T3 tptp.int) (A3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (@ (@ tptp.member_int2 (@ (@ tptp.plus_plus_int T3) tptp.one_one_int)) A3) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int2 Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int2 Xb3) A3) (not (= X4 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (= X4 T3) (= (@ (@ tptp.plus_plus_int X4) D) T3))))))))
% 3.15/3.51 (assert (forall ((D tptp.int) (T3 tptp.int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (@ (@ tptp.member_int2 T3) B3) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int T3))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int2 Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int2 Xb3) B3) (not (= X4 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.minus_minus_int X4) D))))))))))
% 3.15/3.51 (assert (forall ((D tptp.int) (B3 tptp.set_int) (T3 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int2 Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int2 Xb3) B3) (not (= X4 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_int X4) T3) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int X4) D)) T3)))))))
% 3.15/3.51 (assert (forall ((D tptp.int) (T3 tptp.int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (@ (@ tptp.member_int2 T3) B3) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int2 Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int2 Xb3) B3) (not (= X4 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (not (= X4 T3)) (not (= (@ (@ tptp.minus_minus_int X4) D) T3)))))))))
% 3.15/3.51 (assert (forall ((D tptp.int) (T3 tptp.int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (@ (@ tptp.member_int2 (@ (@ tptp.minus_minus_int T3) tptp.one_one_int)) B3) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int2 Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int2 Xb3) B3) (not (= X4 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (= X4 T3) (= (@ (@ tptp.minus_minus_int X4) D) T3))))))))
% 3.15/3.51 (assert (forall ((P5 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.sgn_sgn_rat P5)) (@ (@ tptp.product_Pair_int_int (@ tptp.sgn_sgn_int (@ tptp.product_fst_int_int (@ tptp.quotient_of P5)))) tptp.one_one_int))))
% 3.15/3.51 (assert (= tptp.set_or1266510415728281911st_int (lambda ((I4 tptp.int) (J2 tptp.int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_int J2) I4)) tptp.bot_bot_set_int) (@ (@ tptp.insert_int2 I4) (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) J2))))))
% 3.15/3.51 (assert (forall ((D tptp.int) (A3 tptp.set_int) (T3 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int T3))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int2 Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int2 Xb3) A3) (not (= X4 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.plus_plus_int X4) D)))))))))
% 3.15/3.51 (assert (forall ((D tptp.int) (T3 tptp.int) (A3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (@ (@ tptp.member_int2 (@ (@ tptp.plus_plus_int T3) tptp.one_one_int)) A3) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int2 Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int2 Xb3) A3) (not (= X4 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_eq_int X4) T3) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int X4) D)) T3))))))))
% 3.15/3.51 (assert (forall ((D tptp.int) (T3 tptp.int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (@ (@ tptp.member_int2 (@ (@ tptp.minus_minus_int T3) tptp.one_one_int)) B3) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int T3))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int2 Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int2 Xb3) B3) (not (= X4 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.minus_minus_int X4) D))))))))))
% 3.15/3.51 (assert (forall ((D tptp.int) (B3 tptp.set_int) (T3 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int2 Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int2 Xb3) B3) (not (= X4 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_eq_int X4) T3) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int X4) D)) T3)))))))
% 3.15/3.51 (assert (forall ((D tptp.int) (P2 (-> tptp.int Bool)) (P3 (-> tptp.int Bool)) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z5) (= (@ P2 X3) (@ P3 X3))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int2 Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int2 Xb2) B3) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ P2 X3) (@ P2 (@ (@ tptp.minus_minus_int X3) D))))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P3 X3) (@ P3 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D))))) (= (exists ((X5 tptp.int)) (@ P2 X5)) (or (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int2 X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (@ P3 X2))) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int2 X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (exists ((Y2 tptp.int)) (and (@ (@ tptp.member_int2 Y2) B3) (@ P2 (@ (@ tptp.plus_plus_int Y2) X2))))))))))))))
% 3.15/3.51 (assert (forall ((A tptp.int)) (= (@ tptp.quotient_of (@ tptp.of_int A)) (@ (@ tptp.product_Pair_int_int A) tptp.one_one_int))))
% 3.15/3.51 (assert (forall ((K tptp.num)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int K)) tptp.one_one_int)) (@ tptp.numeral_numeral_rat K))))
% 3.15/3.51 (assert (forall ((K tptp.num)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int tptp.one_one_int) (@ tptp.numeral_numeral_int K))) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat K)))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (P2 (-> tptp.nat Bool))) (= (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N) (@ P2 M3))) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat2 X2) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P2 X2))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (P2 (-> tptp.nat Bool))) (= (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M3) N) (@ P2 M3))) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat2 X2) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P2 X2))))))
% 3.15/3.51 (assert (= tptp.set_or1269000886237332187st_nat (lambda ((N3 tptp.nat) (M3 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt N3) (@ tptp.suc M3))))))
% 3.15/3.51 (assert (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int)) tptp.one_one_rat))
% 3.15/3.51 (assert (= tptp.zero_zero_rat (@ tptp.abs_Rat (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))))
% 3.15/3.51 (assert (= tptp.one_one_rat (@ tptp.abs_Rat (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int))))
% 3.15/3.51 (assert (@ (@ tptp.pcr_rat (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) tptp.zero_zero_rat))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) (@ tptp.suc N)))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N))))
% 3.15/3.51 (assert (@ (@ tptp.pcr_rat (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int)) tptp.one_one_rat))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or4665077453230672383an_nat M2) N)) (@ (@ tptp.upt M2) N))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (P2 (-> tptp.nat Bool))) (= (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N) (@ P2 M3))) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat2 X2) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P2 X2))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (P2 (-> tptp.nat Bool))) (= (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M3) N) (@ P2 M3))) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat2 X2) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P2 X2))))))
% 3.15/3.51 (assert (= tptp.set_or4665077453230672383an_nat (lambda ((I4 tptp.nat) (J2 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt I4) J2)))))
% 3.15/3.51 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or4662586982721622107an_int L) (@ (@ tptp.plus_plus_int U) tptp.one_one_int)) (@ (@ tptp.set_or1266510415728281911st_int L) U))))
% 3.15/3.51 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or4662586982721622107an_int (@ (@ tptp.plus_plus_int L) tptp.one_one_int)) U) (@ (@ tptp.set_or5832277885323065728an_int L) U))))
% 3.15/3.51 (assert (= tptp.set_or4662586982721622107an_int (lambda ((I4 tptp.int) (J2 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I4) (@ (@ tptp.minus_minus_int J2) tptp.one_one_int))))))
% 3.15/3.51 (assert (forall ((P2 (-> tptp.produc3658429121746597890et_nat Bool)) (Q2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ tptp.proper P2) (=> (@ tptp.proper Q2) (@ tptp.proper (lambda ((H tptp.produc3658429121746597890et_nat)) (and (@ P2 H) (@ Q2 H))))))))
% 3.15/3.51 (assert (forall ((P2 (-> tptp.produc3658429121746597890et_nat Bool)) (Q2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ tptp.proper P2) (=> (@ tptp.proper Q2) (@ tptp.proper (lambda ((H tptp.produc3658429121746597890et_nat)) (or (@ P2 H) (@ Q2 H))))))))
% 3.15/3.51 (assert (@ tptp.proper (lambda ((Uu2 tptp.produc3658429121746597890et_nat)) false)))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ tptp.tl_nat (@ (@ tptp.upt M2) N)) (@ (@ tptp.upt (@ tptp.suc M2)) N))))
% 3.15/3.51 (assert (forall ((P2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ tptp.proper P2) (@ tptp.proper (lambda ((H tptp.produc3658429121746597890et_nat)) (and (@ tptp.in_range H) (not (@ P2 H))))))))
% 3.15/3.51 (assert (= tptp.bot_bot_assn (@ tptp.abs_assn (lambda ((Uu2 tptp.produc3658429121746597890et_nat)) false))))
% 3.15/3.51 (assert (= tptp.sup_sup_assn (lambda ((P tptp.assn) (Q tptp.assn)) (@ tptp.abs_assn (lambda ((H tptp.produc3658429121746597890et_nat)) (or (@ (@ tptp.rep_assn P) H) (@ (@ tptp.rep_assn Q) H)))))))
% 3.15/3.51 (assert (= tptp.inf_inf_assn (lambda ((P tptp.assn) (Q tptp.assn)) (@ tptp.abs_assn (lambda ((H tptp.produc3658429121746597890et_nat)) (and (@ (@ tptp.rep_assn P) H) (@ (@ tptp.rep_assn Q) H)))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat I4) N))) (@ (@ tptp.upt tptp.zero_zero_nat) M2)) (@ (@ tptp.upt N) (@ (@ tptp.plus_plus_nat M2) N)))))
% 3.15/3.51 (assert (= tptp.uminus_uminus_assn (lambda ((P tptp.assn)) (@ tptp.abs_assn (lambda ((H tptp.produc3658429121746597890et_nat)) (and (@ tptp.in_range H) (not (@ (@ tptp.rep_assn P) H))))))))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_nat N3) (@ tptp.suc tptp.zero_zero_nat)))) (@ (@ tptp.upt (@ tptp.suc M2)) (@ tptp.suc N))) (@ (@ tptp.upt M2) N))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat M2)) (@ tptp.semiri1408675320244567234ct_nat N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M2))))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N) J2)) N))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat N) M2)) tptp.one_one_nat)) M2))))
% 3.15/3.51 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N) J2)) N))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ _let_1 M2)) tptp.one_one_nat)) (@ _let_1 tptp.one_one_nat))))))
% 3.15/3.51 (assert (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K)) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) tptp.one_one_nat)))))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or4665077453230672383an_nat M2) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) (@ (@ tptp.times_times_nat M2) (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat M2) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))) (@ (@ tptp.times_times_nat M2) (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 3.15/3.51 (assert (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_nat _let_1) M2))) (= (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.binomial (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat))) (@ tptp.set_ord_atMost_nat M2)) (@ (@ tptp.power_power_nat _let_1) _let_2))))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_nat I4) (@ (@ tptp.binomial N) I4)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 3.15/3.51 (assert (= tptp.unique5026877609467782581ep_nat (lambda ((L3 tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q6 tptp.nat) (R4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q6))) (let ((_let_2 (@ tptp.numeral_numeral_nat L3))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat _let_2) R4)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R4) _let_2))) (@ (@ tptp.product_Pair_nat_nat _let_1) R4)))))) __flatten_var_0))))
% 3.15/3.51 (assert (= tptp.unique5024387138958732305ep_int (lambda ((L3 tptp.num) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q6 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q6))) (let ((_let_2 (@ tptp.numeral_numeral_int L3))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_eq_int _let_2) R4)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R4) _let_2))) (@ (@ tptp.product_Pair_int_int _let_1) R4)))))) __flatten_var_0))))
% 3.15/3.51 (assert (forall ((M2 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int M2) N) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X2 tptp.int)) X2)) (@ (@ tptp.set_or1266510415728281911st_int M2) N)) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int N) (@ (@ tptp.plus_plus_int N) tptp.one_one_int))) (@ (@ tptp.times_times_int M2) (@ (@ tptp.minus_minus_int M2) tptp.one_one_int)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 3.15/3.51 (assert (= tptp.normalize (lambda ((P6 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int P6))) (let ((_let_2 (@ tptp.product_fst_int_int P6))) (let ((_let_3 (@ (@ tptp.gcd_gcd_int _let_2) _let_1))) (let ((_let_4 (@ tptp.uminus_uminus_int _let_3))) (let ((_let_5 (@ tptp.divide_divide_int _let_1))) (let ((_let_6 (@ tptp.divide_divide_int _let_2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1)) (@ (@ tptp.product_Pair_int_int (@ _let_6 _let_3)) (@ _let_5 _let_3))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= _let_1 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ _let_6 _let_4)) (@ _let_5 _let_4)))))))))))))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.upt M2) N))) (= (@ tptp.remdups_nat _let_1) _let_1))))
% 3.15/3.51 (assert (forall ((M2 tptp.int)) (= (@ (@ tptp.gcd_gcd_int M2) tptp.one_one_int) tptp.one_one_int)))
% 3.15/3.51 (assert (forall ((M2 tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat M2) tptp.one_one_nat) tptp.one_one_nat)))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.upt M2) N))) (= (@ (@ tptp.linord738340561235409698at_nat (lambda ((X2 tptp.nat)) X2)) _let_1) _let_1))))
% 3.15/3.51 (assert (forall ((I2 tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.upto I2) J))) (= (@ (@ tptp.linord1735203802627413978nt_int (lambda ((X2 tptp.int)) X2)) _let_1) _let_1))))
% 3.15/3.51 (assert (forall ((P5 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.inverse_inverse_rat P5)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A2 tptp.int) (B2 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= A2 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A2)) B2)) (@ tptp.abs_abs_int A2))))) (@ tptp.quotient_of P5)))))
% 3.15/3.51 (assert (forall ((X tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_fst_int_int X))) (=> (@ (@ tptp.ratrel X) X) (= (@ tptp.inverse_inverse_rat (@ tptp.abs_Rat X)) (@ tptp.abs_Rat (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= _let_1 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ tptp.product_snd_int_int X)) _let_1))))))))
% 3.15/3.51 (assert (= tptp.unique4921790084139445826nteger (lambda ((L3 tptp.num) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q6 tptp.code_integer) (R4 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q6))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger L3))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le3102999989581377725nteger _let_2) R4)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R4) _let_2))) (@ (@ tptp.produc1086072967326762835nteger _let_1) R4)))))) __flatten_var_0))))
% 3.15/3.51 (assert (@ (@ (@ (@ tptp.bNF_re8279943556446156061nt_rat tptp.pcr_rat) tptp.pcr_rat) (lambda ((X2 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_fst_int_int X2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= _let_1 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ tptp.product_snd_int_int X2)) _let_1))))) tptp.inverse_inverse_rat))
% 3.15/3.51 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (= (@ (@ tptp.set_or8404916559141939852nteger (@ (@ tptp.plus_p5714425477246183910nteger L) tptp.one_one_Code_integer)) U) (@ (@ tptp.set_or4266950643985792945nteger L) U))))
% 3.15/3.51 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (= (@ (@ tptp.set_or8404916559141939852nteger L) (@ (@ tptp.plus_p5714425477246183910nteger U) tptp.one_one_Code_integer)) (@ (@ tptp.set_or189985376899183464nteger L) U))))
% 3.15/3.51 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (= (@ (@ tptp.set_or189985376899183464nteger (@ (@ tptp.plus_p5714425477246183910nteger L) tptp.one_one_Code_integer)) U) (@ (@ tptp.set_or2715278749043346189nteger L) U))))
% 3.15/3.51 (assert (= tptp.sgn_sgn_Code_integer (lambda ((K4 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (= K4 tptp.zero_z3403309356797280102nteger)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger K4) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer)))))
% 3.15/3.51 (assert (let ((_let_1 (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int))) (@ (@ tptp.ratrel _let_1) _let_1)))
% 3.15/3.51 (assert (let ((_let_1 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))) (@ (@ tptp.ratrel _let_1) _let_1)))
% 3.15/3.51 (assert (= tptp.one_one_int tptp.one_one_int))
% 3.15/3.51 (assert (= tptp.one_one_nat tptp.one_one_nat))
% 3.15/3.51 (assert (= tptp.code_integer_of_int (lambda ((K4 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.code_integer_of_int (@ (@ tptp.divide_divide_int K4) _let_2))))) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_int K4) tptp.zero_zero_int)) (@ tptp.uminus1351360451143612070nteger (@ tptp.code_integer_of_int (@ tptp.uminus_uminus_int K4)))) (@ (@ (@ tptp.if_Code_integer (= K4 tptp.zero_zero_int)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (= (@ (@ tptp.modulo_modulo_int K4) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_p5714425477246183910nteger _let_3) tptp.one_one_Code_integer))))))))))
% 3.15/3.51 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.code_integer_of_num N))) (= (@ tptp.code_integer_of_num (@ tptp.bit1 N)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1)) tptp.one_one_Code_integer)))))
% 3.15/3.51 (assert (@ (@ (@ (@ tptp.bNF_re157797125943740599nt_int (lambda ((Y4 tptp.int) (Z4 tptp.int)) (= Y4 Z4))) (@ (@ tptp.bNF_re6250860962936578807nt_int (lambda ((Y4 tptp.int) (Z4 tptp.int)) (= Y4 Z4))) tptp.ratrel)) (lambda ((A2 tptp.int) (B2 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= B2 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int A2) B2)))) (lambda ((A2 tptp.int) (B2 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= B2 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int A2) B2)))))
% 3.15/3.51 (assert (= tptp.one_one_Code_integer (@ tptp.code_integer_of_int tptp.one_one_int)))
% 3.15/3.51 (assert (= (@ tptp.code_integer_of_num tptp.one) tptp.one_one_Code_integer))
% 3.15/3.51 (assert (= tptp.fi (lambda ((M3 tptp.list_P8527749157015355191n_assn) (P6 tptp.assn) (Q6 tptp.assn) (Up tptp.assn) (Uq tptp.assn) (F3 tptp.assn)) (let ((_let_1 (@ tptp.foldr_assn_assn tptp.times_times_assn))) (=> (forall ((X2 tptp.produc6575502325842934193n_assn)) (=> (@ (@ tptp.member7957490590177025114n_assn X2) (@ tptp.set_Pr1139785259514867910n_assn M3)) (@ (@ tptp.produc7274209992780475162assn_o tptp.entails) X2))) (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ _let_1 (@ (@ tptp.map_Pr8991440229025900053n_assn tptp.produc9167289414957590229n_assn) M3)) tptp.one_one_assn)) P6)) Up)) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ _let_1 (@ (@ tptp.map_Pr8991440229025900053n_assn tptp.produc2051961928117032727n_assn) M3)) tptp.one_one_assn)) Q6)) Uq)) F3)))))))
% 3.15/3.51 (assert (@ (@ (@ (@ tptp.bNF_re7145576690424134365nt_int tptp.ratrel) tptp.ratrel) (lambda ((X2 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_fst_int_int X2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= _let_1 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ tptp.product_snd_int_int X2)) _let_1))))) (lambda ((X2 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_fst_int_int X2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= _let_1 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ tptp.product_snd_int_int X2)) _let_1))))))
% 3.15/3.51 (assert (= tptp.fI_RESULT (lambda ((M5 tptp.list_P8527749157015355191n_assn) (UP tptp.assn) (UQ tptp.assn) (F tptp.assn)) (let ((_let_1 (@ tptp.foldr_assn_assn tptp.times_times_assn))) (=> (forall ((X2 tptp.produc6575502325842934193n_assn)) (=> (@ (@ tptp.member7957490590177025114n_assn X2) (@ tptp.set_Pr1139785259514867910n_assn M5)) (@ (@ tptp.produc7274209992780475162assn_o tptp.entails) X2))) (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ _let_1 (@ (@ tptp.map_Pr8991440229025900053n_assn tptp.produc9167289414957590229n_assn) M5)) tptp.one_one_assn)) UP)) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ _let_1 (@ (@ tptp.map_Pr8991440229025900053n_assn tptp.produc2051961928117032727n_assn) M5)) tptp.one_one_assn)) UQ)) F)))))))
% 3.15/3.51 (assert (= tptp.code_num_of_integer (lambda ((K4 tptp.code_integer)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_le3102999989581377725nteger K4) tptp.one_one_Code_integer)) tptp.one) (@ (@ tptp.produc7336495610019696514er_num (lambda ((L3 tptp.code_integer) (J2 tptp.code_integer)) (let ((_let_1 (@ tptp.code_num_of_integer L3))) (let ((_let_2 (@ (@ tptp.plus_plus_num _let_1) _let_1))) (@ (@ (@ tptp.if_num (= J2 tptp.zero_z3403309356797280102nteger)) _let_2) (@ (@ tptp.plus_plus_num _let_2) tptp.one)))))) (@ (@ tptp.code_divmod_integer K4) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 3.15/3.51 (assert (= tptp.code_int_of_integer (lambda ((K4 tptp.code_integer)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_le6747313008572928689nteger K4) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus_uminus_int (@ tptp.code_int_of_integer (@ tptp.uminus1351360451143612070nteger K4)))) (@ (@ (@ tptp.if_int (= K4 tptp.zero_z3403309356797280102nteger)) tptp.zero_zero_int) (@ (@ tptp.produc1553301316500091796er_int (lambda ((L3 tptp.code_integer) (J2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.code_int_of_integer L3)))) (@ (@ (@ tptp.if_int (= J2 tptp.zero_z3403309356797280102nteger)) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))) (@ (@ tptp.code_divmod_integer K4) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))))))
% 3.15/3.51 (assert (= tptp.code_bit_cut_integer (lambda ((K4 tptp.code_integer)) (@ (@ (@ tptp.if_Pro5737122678794959658eger_o (= K4 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc6677183202524767010eger_o tptp.zero_z3403309356797280102nteger) false)) (@ (@ tptp.produc9125791028180074456eger_o (lambda ((R4 tptp.code_integer) (S4 tptp.code_integer)) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) K4)) R4) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger R4)) S4))) (= S4 tptp.one_one_Code_integer)))) (@ (@ tptp.code_divmod_abs K4) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 3.15/3.51 (assert (= tptp.code_nat_of_integer (lambda ((K4 tptp.code_integer)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_le3102999989581377725nteger K4) tptp.zero_z3403309356797280102nteger)) tptp.zero_zero_nat) (@ (@ tptp.produc1555791787009142072er_nat (lambda ((L3 tptp.code_integer) (J2 tptp.code_integer)) (let ((_let_1 (@ tptp.code_nat_of_integer L3))) (let ((_let_2 (@ (@ tptp.plus_plus_nat _let_1) _let_1))) (@ (@ (@ tptp.if_nat (= J2 tptp.zero_z3403309356797280102nteger)) _let_2) (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat)))))) (@ (@ tptp.code_divmod_integer K4) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 3.15/3.51 (assert (= (@ tptp.code_int_of_integer tptp.one_one_Code_integer) tptp.one_one_int))
% 3.15/3.51 (assert (= tptp.code_divmod_integer (lambda ((K4 tptp.code_integer) (L3 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.code_divmod_abs K4) L3))) (let ((_let_2 (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_3 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= K4 tptp.zero_z3403309356797280102nteger)) (@ _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ _let_3 L3)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ _let_3 K4)) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R4 tptp.code_integer) (S4 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R4))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S4 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger L3) S4)))))) _let_1))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= L3 tptp.zero_z3403309356797280102nteger)) (@ _let_2 K4)) (@ (@ tptp.produc6499014454317279255nteger tptp.uminus1351360451143612070nteger) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le6747313008572928689nteger K4) tptp.zero_z3403309356797280102nteger)) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R4 tptp.code_integer) (S4 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R4))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S4 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger L3)) S4)))))) _let_1))))))))))))
% 3.15/3.51 (assert (= tptp.code_divmod_integer (lambda ((K4 tptp.code_integer) (L3 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.code_divmod_abs K4) L3))) (let ((_let_2 (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= K4 tptp.zero_z3403309356797280102nteger)) (@ _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= L3 tptp.zero_z3403309356797280102nteger)) (@ _let_2 K4)) (@ (@ (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_C8797469213163452608nteger tptp.produc6499014454317279255nteger) tptp.times_3573771949741848930nteger)) tptp.sgn_sgn_Code_integer) L3) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= (@ tptp.sgn_sgn_Code_integer K4) (@ tptp.sgn_sgn_Code_integer L3))) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R4 tptp.code_integer) (S4 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R4))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S4 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer L3)) S4)))))) _let_1))))))))))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L3) M2) (= (@ tptp.groups4561878855575611511st_nat L3) N2))))) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N2) M2)) tptp.one_one_nat)) N2))))
% 3.15/3.51 (assert (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M2) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L3) M2) (= (@ tptp.groups4561878855575611511st_nat L3) N2))))) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L3) (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)) (= (@ tptp.groups4561878855575611511st_nat L3) N2)))))) (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L3) M2) (= (@ (@ tptp.plus_plus_nat (@ tptp.groups4561878855575611511st_nat L3)) tptp.one_one_nat) N2))))))))))
% 3.15/3.51 (assert (forall ((K tptp.num)) (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat K)) (@ (@ tptp.fract (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.one_one_int))))
% 3.15/3.51 (assert (forall ((K tptp.int)) (= (@ (@ tptp.fract K) tptp.one_one_int) (@ tptp.ring_1_of_int_rat K))))
% 3.15/3.51 (assert (forall ((A tptp.int)) (= (@ (@ tptp.fract A) tptp.zero_zero_int) (@ (@ tptp.fract tptp.zero_zero_int) tptp.one_one_int))))
% 3.15/3.51 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.fract (@ tptp.semiri1314217659103216013at_int K)) tptp.one_one_int) (@ tptp.semiri681578069525770553at_rat K))))
% 3.15/3.51 (assert (= tptp.one_one_rat (@ (@ tptp.fract tptp.one_one_int) tptp.one_one_int)))
% 3.15/3.51 (assert (= tptp.zero_zero_rat (@ (@ tptp.fract tptp.zero_zero_int) tptp.one_one_int)))
% 3.15/3.51 (assert (forall ((N tptp.int) (M2 tptp.int)) (=> (not (= N tptp.zero_zero_int)) (= (@ (@ tptp.fract (@ (@ tptp.plus_plus_int M2) N)) N) (@ (@ tptp.plus_plus_rat (@ (@ tptp.fract M2) N)) tptp.one_one_rat)))))
% 3.15/3.51 (assert (forall ((W tptp.num)) (= (@ (@ tptp.fract (@ tptp.numeral_numeral_int W)) tptp.one_one_int) (@ tptp.numeral_numeral_rat W))))
% 3.15/3.51 (assert (= tptp.numeral_numeral_rat (lambda ((K4 tptp.num)) (@ (@ tptp.fract (@ tptp.numeral_numeral_int K4)) tptp.one_one_int))))
% 3.15/3.51 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_eq_int B) A)))))
% 3.15/3.51 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.fract A) B)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_int A) B)))))
% 3.15/3.51 (assert (= tptp.fract (lambda ((Xa4 tptp.int) (X2 tptp.int)) (@ tptp.abs_Rat (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= X2 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int Xa4) X2))))))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_int A) B))) (let ((_let_2 (@ (@ tptp.fract A) B))) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat _let_1)) _let_2) (@ (@ tptp.ord_less_rat _let_2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))))
% 3.15/3.51 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_int B) A)))))
% 3.15/3.51 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.fract A) B)) tptp.one_one_rat) (@ (@ tptp.ord_less_int A) B)))))
% 3.15/3.51 (assert (= (@ (@ tptp.fract (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 3.15/3.51 (assert (@ (@ (@ (@ tptp.bNF_re3461391660133120880nt_rat (lambda ((Y4 tptp.int) (Z4 tptp.int)) (= Y4 Z4))) (@ (@ tptp.bNF_re2214769303045360666nt_rat (lambda ((Y4 tptp.int) (Z4 tptp.int)) (= Y4 Z4))) tptp.pcr_rat)) (lambda ((A2 tptp.int) (B2 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= B2 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int A2) B2)))) tptp.fract))
% 3.15/3.51 (assert (forall ((W tptp.num)) (= (@ (@ tptp.fract (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) tptp.one_one_int) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))))
% 3.15/3.51 (assert (= tptp.archim3151403230148437115or_rat (lambda ((X2 tptp.rat)) (@ tptp.the_int (lambda ((Z3 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z3)) X2) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z3) tptp.one_one_int)))))))))
% 3.15/3.51 (assert (forall ((K tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.euclid3395696857347342551nt_int K)) tptp.one_one_int)))
% 3.15/3.51 (assert (= tptp.euclid3398187327856392827nt_nat (lambda ((N3 tptp.nat)) tptp.one_one_nat)))
% 3.15/3.51 (assert (= tptp.euclid3395696857347342551nt_int (lambda ((K4 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K4)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 3.15/3.51 (assert (= tptp.inverse_inverse_rat (@ (@ (@ tptp.map_fu5673905371560938248nt_rat tptp.rep_Rat) tptp.abs_Rat) (lambda ((X2 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_fst_int_int X2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= _let_1 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ tptp.product_snd_int_int X2)) _let_1)))))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) tptp.one_one_nat) (= (@ tptp.num_of_nat N) tptp.one))))
% 3.15/3.51 (assert (@ (@ tptp.pcr_int (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat)) tptp.one_one_int))
% 3.15/3.51 (assert (= tptp.one_one_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))))
% 3.15/3.51 (assert (= (@ tptp.code_integer_of_nat tptp.one_one_nat) tptp.one_one_Code_integer))
% 3.15/3.51 (assert (forall ((P2 (-> tptp.int Bool)) (I2 tptp.int) (J tptp.int)) (= (@ (@ tptp.list_all_int P2) (@ (@ tptp.upto I2) J)) (@ (@ (@ tptp.all_interval_int P2) I2) J))))
% 3.15/3.51 (assert (forall ((P2 (-> tptp.int Bool)) (I2 tptp.int) (J tptp.int)) (= (@ (@ tptp.list_ex_int P2) (@ (@ tptp.upto I2) J)) (not (@ (@ (@ tptp.all_interval_int (@ (@ tptp.comp_o_o_int (lambda ((_lvar_0 Bool)) (not _lvar_0))) P2)) I2) J)))))
% 3.15/3.51 (assert (= tptp.all_interval_int (lambda ((P (-> tptp.int Bool)) (I4 tptp.int) (J2 tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int2 X2) (@ (@ tptp.set_or1266510415728281911st_int I4) J2)) (@ P X2))))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ tptp.unit_f2748546683901255202or_nat (@ tptp.suc N)) tptp.one_one_nat)))
% 3.15/3.51 (assert (= tptp.unit_f2748546683901255202or_nat (lambda ((N3 tptp.nat)) (@ (@ (@ tptp.if_nat (= N3 tptp.zero_zero_nat)) tptp.zero_zero_nat) tptp.one_one_nat))))
% 3.15/3.51 (assert (forall ((P2 (-> tptp.nat Bool)) (I2 tptp.nat) (J tptp.nat)) (= (@ (@ tptp.list_all_nat P2) (@ (@ tptp.upt I2) J)) (@ (@ (@ tptp.all_interval_nat P2) I2) J))))
% 3.15/3.51 (assert (forall ((P2 (-> tptp.nat Bool)) (I2 tptp.nat) (J tptp.nat)) (= (@ (@ tptp.list_ex_nat P2) (@ (@ tptp.upt I2) J)) (not (@ (@ (@ tptp.all_interval_nat (@ (@ tptp.comp_o_o_nat (lambda ((_lvar_0 Bool)) (not _lvar_0))) P2)) I2) J)))))
% 3.15/3.51 (assert (forall ((N2 tptp.set_nat)) (=> (@ (@ tptp.member_nat2 tptp.one_one_nat) N2) (= (@ tptp.gcd_Gcd_nat N2) tptp.one_one_nat))))
% 3.15/3.51 (assert (= (@ tptp.gcd_Lcm_nat tptp.bot_bot_set_nat) tptp.one_one_nat))
% 3.15/3.51 (assert (= tptp.all_interval_nat (lambda ((P (-> tptp.nat Bool)) (I4 tptp.nat) (J2 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat2 X2) (@ (@ tptp.set_or4665077453230672383an_nat I4) J2)) (@ P X2))))))
% 3.15/3.51 (assert (forall ((M2 tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (= (@ (@ tptp.gcd_lcm_int M2) N) tptp.one_one_int) (and (or (= M2 tptp.one_one_int) (= M2 _let_1)) (or (= N tptp.one_one_int) (= N _let_1)))))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_nat)) (= (@ tptp.gcd_Lcm_nat (@ tptp.set_nat2 Xs)) (@ (@ (@ tptp.fold_nat_nat tptp.gcd_lcm_nat) Xs) tptp.one_one_nat))))
% 3.15/3.51 (assert (forall ((Xs tptp.list_int)) (= (@ tptp.gcd_Lcm_int (@ tptp.set_int2 Xs)) (@ (@ (@ tptp.fold_int_int tptp.gcd_lcm_int) Xs) tptp.one_one_int))))
% 3.15/3.51 (assert (= tptp.gcd_Lcm_nat (lambda ((M5 tptp.set_nat)) (@ (@ (@ tptp.if_nat (@ tptp.finite_finite_nat M5)) (@ (@ (@ tptp.lattic7826324295020591184_F_nat tptp.gcd_lcm_nat) tptp.one_one_nat) M5)) tptp.zero_zero_nat))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.algebr934650988132801477me_nat N) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))
% 3.15/3.51 (assert (forall ((A tptp.nat) (B tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat X))) (=> (@ (@ tptp.algebr934650988132801477me_nat A) B) (=> (@ _let_1 A) (=> (@ _let_1 B) (= X tptp.one_one_nat)))))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.algebr934650988132801477me_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) N))))
% 3.15/3.51 (assert (forall ((H2 tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (= (@ tptp.in_range (@ (@ tptp.produc7507926704131184380et_nat H2) As2)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat2 X2) As2) (@ (@ tptp.ord_less_nat X2) (@ tptp.lim_Product_unit H2)))))))
% 3.15/3.51 (assert (forall ((A tptp.int) (B tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X))) (=> (@ (@ tptp.algebr932160517623751201me_int A) B) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ tptp.abs_abs_int X) tptp.one_one_int)))))))
% 3.15/3.51 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (=> (not (@ tptp.in_range X)) (not (forall ((H3 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (= X (@ (@ tptp.produc7507926704131184380et_nat H3) As)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat2 X3) As) (@ (@ tptp.ord_less_nat X3) (@ tptp.lim_Product_unit H3))))))))))
% 3.15/3.51 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (=> (@ tptp.in_range X) (not (forall ((H3 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (= X (@ (@ tptp.produc7507926704131184380et_nat H3) As)) (not (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat2 X4) As) (@ (@ tptp.ord_less_nat X4) (@ tptp.lim_Product_unit H3)))))))))))
% 3.15/3.51 (assert (forall ((X tptp.produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ tptp.in_range X) Y) (not (forall ((H3 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (= X (@ (@ tptp.produc7507926704131184380et_nat H3) As)) (= Y (not (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat2 X2) As) (@ (@ tptp.ord_less_nat X2) (@ tptp.lim_Product_unit H3))))))))))))
% 3.15/3.51 (assert (let ((_let_1 (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.intrel _let_1) _let_1)))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (@ (@ (@ tptp.hoare_8945653483474564448t_unit tptp.one_one_assn) (@ tptp.heap_Time_wait N)) (lambda ((Uu2 tptp.product_unit)) tptp.one_one_assn))))
% 3.15/3.51 (assert (= tptp.inf_inf_Product_unit (lambda ((Uu3 tptp.product_unit) (Uv tptp.product_unit)) tptp.product_Unity)))
% 3.15/3.51 (assert (forall ((P2 tptp.assn) (Phi Bool)) (=> (forall ((H3 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P2) H3) Phi)) (@ (@ (@ tptp.hoare_8945653483474564448t_unit P2) (@ tptp.refine_Imp_assert Phi)) (lambda ((Uu2 tptp.product_unit)) P2)))))
% 3.15/3.51 (assert (= (@ (@ tptp.minus_7197305767214868737atural tptp.zero_z2226904508553997617atural) tptp.one_one_Code_natural) tptp.zero_z2226904508553997617atural))
% 3.15/3.51 (assert (forall ((X tptp.code_natural) (Xa tptp.code_natural) (Y tptp.code_natural)) (let ((_let_1 (@ tptp.log X))) (let ((_let_2 (or (@ (@ tptp.ord_le1926595141338095240atural X) tptp.one_one_Code_natural) (@ (@ tptp.ord_le5570908160329646204atural Xa) X)))) (=> (= (@ _let_1 Xa) Y) (and (=> _let_2 (= Y tptp.one_one_Code_natural)) (=> (not _let_2) (= Y (@ (@ tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural) (@ _let_1 (@ (@ tptp.divide5121882707175180666atural Xa) X)))))))))))
% 3.15/3.51 (assert (= tptp.log (lambda ((B2 tptp.code_natural) (I4 tptp.code_natural)) (@ (@ (@ tptp.if_Code_natural (or (@ (@ tptp.ord_le1926595141338095240atural B2) tptp.one_one_Code_natural) (@ (@ tptp.ord_le5570908160329646204atural I4) B2))) tptp.one_one_Code_natural) (@ (@ tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural) (@ (@ tptp.log B2) (@ (@ tptp.divide5121882707175180666atural I4) B2)))))))
% 3.15/3.51 (assert (forall ((V2 tptp.code_natural) (W tptp.code_natural)) (let ((_let_1 (@ tptp.bit1 tptp.one))) (let ((_let_2 (@ tptp.bit1 _let_1))) (let ((_let_3 (@ tptp.bit0 _let_1))) (let ((_let_4 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 _let_3)))))))))))))))) (let ((_let_5 (@ tptp.bit0 tptp.one))) (let ((_let_6 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 _let_5)))))) (let ((_let_7 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 _let_2)))))))))))))))))))))) (let ((_let_8 (@ (@ (@ tptp.minus_shift (@ tptp.numera5444537566228673987atural (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 _let_7)))))))))) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.modulo8411746178871703098atural W) _let_4)) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 _let_6))))))))))))) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural W) _let_4)) (@ tptp.numera5444537566228673987atural (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 _let_2)))))))))))))) (let ((_let_9 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 _let_3)))))))))))))))) (let ((_let_10 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 _let_7))))))))) (let ((_let_11 (@ (@ (@ tptp.minus_shift (@ tptp.numera5444537566228673987atural (@ tptp.bit1 _let_10))) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.modulo8411746178871703098atural V2) _let_9)) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 _let_6))))))))))))) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural V2) _let_9)) (@ tptp.numera5444537566228673987atural (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 _let_5))))))))))))))))) (= (@ tptp.next (@ (@ tptp.produc3574140220909816553atural V2) W)) (@ (@ tptp.produc6639722614265839536atural (@ (@ tptp.plus_p4538020629002901425atural (@ (@ (@ tptp.minus_shift (@ tptp.numera5444537566228673987atural (@ tptp.bit0 _let_10))) _let_11) (@ (@ tptp.plus_p4538020629002901425atural _let_8) tptp.one_one_Code_natural))) tptp.one_one_Code_natural)) (@ (@ tptp.produc3574140220909816553atural _let_11) _let_8))))))))))))))))
% 3.15/3.51 (assert (= tptp.range (lambda ((K4 tptp.code_natural) (__flatten_var_0 tptp.produc7822875418678951345atural)) (@ (@ (@ tptp.produc5538323210962509403atural (@ (@ (@ tptp.iterat8892046348760725948atural (@ (@ tptp.log (@ tptp.numera5444537566228673987atural (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 tptp.one)))))))))))))))))))))))))))))))) K4)) (lambda ((L3 tptp.code_natural) (__flatten_var_0 tptp.produc7822875418678951345atural)) (@ (@ (@ tptp.produc5538323210962509403atural tptp.next) (lambda ((V3 tptp.code_natural) (__flatten_var_0 tptp.produc7822875418678951345atural)) (@ (@ tptp.produc6639722614265839536atural (@ (@ tptp.plus_p4538020629002901425atural V3) (@ (@ tptp.times_2397367101498566445atural L3) (@ tptp.numera5444537566228673987atural (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 tptp.one)))))))))))))))))))))))))))))))))) __flatten_var_0))) __flatten_var_0))) tptp.one_one_Code_natural)) (lambda ((V3 tptp.code_natural) (__flatten_var_0 tptp.produc7822875418678951345atural)) (@ (@ tptp.produc6639722614265839536atural (@ (@ tptp.modulo8411746178871703098atural V3) K4)) __flatten_var_0))) __flatten_var_0))))
% 3.15/3.51 (assert (= tptp.inc_shift (lambda ((V3 tptp.code_natural) (K4 tptp.code_natural)) (@ (@ (@ tptp.if_Code_natural (= V3 K4)) tptp.one_one_Code_natural) (@ (@ tptp.plus_p4538020629002901425atural K4) tptp.one_one_Code_natural)))))
% 3.15/3.51 (assert (forall ((X tptp.code_natural) (Xa tptp.code_natural) (Y tptp.code_natural)) (let ((_let_1 (@ (@ tptp.accp_P8126237942716283194atural tptp.log_rel) (@ (@ tptp.produc3574140220909816553atural X) Xa)))) (let ((_let_2 (@ tptp.log X))) (let ((_let_3 (or (@ (@ tptp.ord_le1926595141338095240atural X) tptp.one_one_Code_natural) (@ (@ tptp.ord_le5570908160329646204atural Xa) X)))) (=> (= (@ _let_2 Xa) Y) (=> _let_1 (not (=> (and (=> _let_3 (= Y tptp.one_one_Code_natural)) (=> (not _let_3) (= Y (@ (@ tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural) (@ _let_2 (@ (@ tptp.divide5121882707175180666atural Xa) X)))))) (not _let_1))))))))))
% 3.15/3.51 (assert (= tptp.one_one_Code_natural (@ tptp.code_natural_of_nat tptp.one_one_nat)))
% 3.15/3.51 (assert (forall ((N tptp.code_natural)) (= (@ (@ tptp.minus_7197305767214868737atural (@ tptp.code_Suc N)) tptp.one_one_Code_natural) N)))
% 3.15/3.51 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.code_sub (@ tptp.bit0 M2)) (@ tptp.bit1 N)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.code_dup (@ (@ tptp.code_sub M2) N))) tptp.one_one_Code_integer))))
% 3.15/3.51 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.code_sub (@ tptp.bit1 M2)) (@ tptp.bit0 N)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.code_dup (@ (@ tptp.code_sub M2) N))) tptp.one_one_Code_integer))))
% 3.15/3.51 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.sub (@ tptp.bit0 M2)) (@ tptp.bit1 N)) (@ (@ tptp.minus_minus_int (@ tptp.dup (@ (@ tptp.sub M2) N))) tptp.one_one_int))))
% 3.15/3.51 (assert (forall ((M2 tptp.num) (N tptp.num)) (= (@ (@ tptp.sub (@ tptp.bit1 M2)) (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_int (@ tptp.dup (@ (@ tptp.sub M2) N))) tptp.one_one_int))))
% 3.15/3.51 (assert (= tptp.fract (@ (@ (@ tptp.map_fu7831380289885515383nt_rat tptp.id_int) (@ (@ tptp.map_fu3424225382358772769nt_rat tptp.id_int) tptp.abs_Rat)) (lambda ((A2 tptp.int) (B2 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= B2 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int A2) B2))))))
% 3.15/3.51 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (=> (not (@ tptp.in_range X)) (=> (@ (@ tptp.accp_P5801069581201407417et_nat tptp.in_range_rel) X) (not (forall ((H3 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H3) As))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P5801069581201407417et_nat tptp.in_range_rel) _let_1) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat2 X3) As) (@ (@ tptp.ord_less_nat X3) (@ tptp.lim_Product_unit H3)))))))))))))
% 3.15/3.51 (assert (forall ((X tptp.produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ tptp.in_range X) Y) (=> (@ (@ tptp.accp_P5801069581201407417et_nat tptp.in_range_rel) X) (not (forall ((H3 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H3) As))) (=> (= X _let_1) (=> (= Y (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat2 X2) As) (@ (@ tptp.ord_less_nat X2) (@ tptp.lim_Product_unit H3))))) (not (@ (@ tptp.accp_P5801069581201407417et_nat tptp.in_range_rel) _let_1)))))))))))
% 3.15/3.51 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (=> (@ tptp.in_range X) (=> (@ (@ tptp.accp_P5801069581201407417et_nat tptp.in_range_rel) X) (not (forall ((H3 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H3) As))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P5801069581201407417et_nat tptp.in_range_rel) _let_1) (not (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat2 X4) As) (@ (@ tptp.ord_less_nat X4) (@ tptp.lim_Product_unit H3))))))))))))))
% 3.15/3.51 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (=> (not (@ tptp.one_assn_raw X)) (=> (@ (@ tptp.accp_P5801069581201407417et_nat tptp.one_assn_raw_rel) X) (not (forall ((H3 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H3) As))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P5801069581201407417et_nat tptp.one_assn_raw_rel) _let_1) (= As tptp.bot_bot_set_nat))))))))))
% 3.15/3.51 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (=> (@ tptp.one_assn_raw X) (=> (@ (@ tptp.accp_P5801069581201407417et_nat tptp.one_assn_raw_rel) X) (not (forall ((H3 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H3) As))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P5801069581201407417et_nat tptp.one_assn_raw_rel) _let_1) (not (= As tptp.bot_bot_set_nat)))))))))))
% 3.15/3.51 (assert (forall ((X tptp.produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ tptp.one_assn_raw X) Y) (=> (@ (@ tptp.accp_P5801069581201407417et_nat tptp.one_assn_raw_rel) X) (not (forall ((H3 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H3) As))) (=> (= X _let_1) (=> (= Y (= As tptp.bot_bot_set_nat)) (not (@ (@ tptp.accp_P5801069581201407417et_nat tptp.one_assn_raw_rel) _let_1)))))))))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bNF_Ca8665028551170535155natLeq) (@ (@ tptp.produc457027306803732586at_nat (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_nat X2) N)))) (lambda ((Uu2 tptp.nat)) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_nat X2) N)))))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X2 tptp.nat) (Y2 tptp.nat)) (and (@ (@ tptp.ord_less_nat X2) N) (@ (@ tptp.ord_less_nat Y2) N) (@ (@ tptp.ord_less_eq_nat X2) Y2))))))))
% 3.15/3.51 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bNF_Ca8665028551170535155natLeq) (@ (@ tptp.produc457027306803732586at_nat (@ (@ tptp.order_underS_nat tptp.bNF_Ca8665028551170535155natLeq) N)) (lambda ((Uu2 tptp.nat)) (@ (@ tptp.order_underS_nat tptp.bNF_Ca8665028551170535155natLeq) N)))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X2 tptp.nat) (Y2 tptp.nat)) (and (@ (@ tptp.ord_less_nat X2) N) (@ (@ tptp.ord_less_nat Y2) N) (@ (@ tptp.ord_less_eq_nat X2) Y2))))))))
% 3.15/3.51 (assert (= tptp.one_one_Code_integer (@ tptp.code_Pos tptp.one)))
% 3.15/3.51 (assert (= (@ tptp.code_nat_of_natural tptp.one_one_Code_natural) tptp.one_one_nat))
% 3.15/3.51 (assert (= (@ tptp.nat_of_num tptp.one) tptp.one_one_nat))
% 3.15/3.51 (assert (= tptp.one_one_int (@ tptp.pos tptp.one)))
% 3.15/3.51 (assert (@ (@ tptp.code_pcr_natural tptp.one_one_nat) tptp.one_one_Code_natural))
% 3.15/3.51 (assert (@ (@ tptp.code_pcr_integer tptp.one_one_int) tptp.one_one_Code_integer))
% 3.15/3.51 (assert (forall ((DR1 (-> tptp.int Bool)) (DR2 (-> tptp.int Bool)) (P22 (-> tptp.product_prod_int_int Bool))) (=> (= (@ tptp.domainp_int_int (lambda ((Y4 tptp.int) (Z4 tptp.int)) (= Y4 Z4))) DR1) (=> (= (@ tptp.domainp_int_int (lambda ((Y4 tptp.int) (Z4 tptp.int)) (= Y4 Z4))) DR2) (=> (@ (@ (@ (@ tptp.bNF_re8699439704749558557nt_o_o (@ (@ tptp.basic_4387203522000727145nt_int (lambda ((Y4 tptp.int) (Z4 tptp.int)) (= Y4 Z4))) (lambda ((Y4 tptp.int) (Z4 tptp.int)) (= Y4 Z4)))) (lambda ((Y4 Bool) (Z4 Bool)) (= Y4 Z4))) P22) (lambda ((X2 tptp.product_prod_int_int)) (@ (@ tptp.ratrel X2) X2))) (= (@ tptp.domain9213661015745956397nt_rat tptp.pcr_rat) (@ (@ tptp.inf_in3604695632404883862_int_o (@ (@ tptp.basic_1567116559311922317nt_int DR1) DR2)) P22)))))))
% 39.57/39.99 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int false) X) Y) Y)))
% 39.57/39.99 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int true) X) Y) X)))
% 39.57/39.99 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat false) X) Y) Y)))
% 39.57/39.99 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat true) X) Y) X)))
% 39.57/39.99 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ (@ tptp.if_num false) X) Y) Y)))
% 39.57/39.99 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ (@ tptp.if_num true) X) Y) X)))
% 39.57/39.99 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ (@ tptp.if_rat false) X) Y) Y)))
% 39.57/39.99 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ (@ tptp.if_rat true) X) Y) X)))
% 39.57/39.99 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (@ (@ (@ tptp.if_assn false) X) Y) Y)))
% 39.57/39.99 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (@ (@ (@ tptp.if_assn true) X) Y) X)))
% 39.57/39.99 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer false) X) Y) Y)))
% 39.57/39.99 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer true) X) Y) X)))
% 39.57/39.99 (assert (forall ((X tptp.code_natural) (Y tptp.code_natural)) (= (@ (@ (@ tptp.if_Code_natural false) X) Y) Y)))
% 39.57/39.99 (assert (forall ((X tptp.code_natural) (Y tptp.code_natural)) (= (@ (@ (@ tptp.if_Code_natural true) X) Y) X)))
% 39.57/39.99 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ (@ tptp.if_set_int false) X) Y) Y)))
% 39.57/39.99 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ (@ tptp.if_set_int true) X) Y) X)))
% 39.57/39.99 (assert (forall ((X tptp.list_int) (Y tptp.list_int)) (= (@ (@ (@ tptp.if_list_int false) X) Y) Y)))
% 39.57/39.99 (assert (forall ((X tptp.list_int) (Y tptp.list_int)) (= (@ (@ (@ tptp.if_list_int true) X) Y) X)))
% 39.57/39.99 (assert (forall ((X tptp.list_nat) (Y tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat false) X) Y) Y)))
% 39.57/39.99 (assert (forall ((X tptp.list_nat) (Y tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat true) X) Y) X)))
% 39.57/39.99 (assert (forall ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int false) X) Y) Y)))
% 39.57/39.99 (assert (forall ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int true) X) Y) X)))
% 39.57/39.99 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat false) X) Y) Y)))
% 39.57/39.99 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat true) X) Y) X)))
% 39.57/39.99 (assert (forall ((X tptp.produc6271795597528267376eger_o) (Y tptp.produc6271795597528267376eger_o)) (= (@ (@ (@ tptp.if_Pro5737122678794959658eger_o false) X) Y) Y)))
% 39.57/39.99 (assert (forall ((X tptp.produc6271795597528267376eger_o) (Y tptp.produc6271795597528267376eger_o)) (= (@ (@ (@ tptp.if_Pro5737122678794959658eger_o true) X) Y) X)))
% 39.57/39.99 (assert (forall ((P2 Bool)) (or (= P2 true) (= P2 false))))
% 39.57/39.99 (assert (forall ((X tptp.produc8923325533196201883nteger) (Y tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.if_Pro6119634080678213985nteger false) X) Y) Y)))
% 39.57/39.99 (assert (forall ((X tptp.produc8923325533196201883nteger) (Y tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.if_Pro6119634080678213985nteger true) X) Y) X)))
% 39.57/39.99 (assert (not (@ (@ (@ tptp.fI_QUERY tptp.p) tptp.q) tptp.f)))
% 39.57/39.99 (set-info :filename cvc5---1.0.5_4940)
% 39.57/39.99 (check-sat-assuming ( true ))
% 39.57/39.99 ------- get file name : TPTP file name is ITP215^1
% 39.57/39.99 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_4940.smt2...
% 39.57/39.99 --- Run --ho-elim --full-saturate-quant at 10...
% 39.57/39.99 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 39.57/39.99 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
% 39.57/39.99 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
% 39.57/39.99 --- Run --no-ho-matching --finite-model/export/starexec/sandbox/solver/bin/do_THM_THF: line 35: 5127 Alarm clock ( read result; case "$result" in
% 299.61/300.12 unsat)
% 299.61/300.12 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.61/300.12 ;;
% 299.61/300.12 sat)
% 299.61/300.12 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.61/300.12 ;;
% 299.61/300.12 esac; exit 1 )
% 299.61/300.13 Alarm clock
% 299.61/300.13 % cvc5---1.0.5 exiting
% 299.61/300.13 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------